Talk_id  Date  Speaker  Title 
26835

Thursday 1/7 2:30 PM

Jose Perea, Michigan State University

TBA; zoom link @ https://sites.google.com/view/mindsseminar/home
 Jose Perea, Michigan State University
 TBA; zoom link @ https://sites.google.com/view/mindsseminar/home
 01/07/2021
 2:30 PM  3:30 PM

(Virtual Meeting Link)
 Olga Turanova (turanova@msu.edu)
No abstract available.

26848

Thursday 1/14 3:30 PM

Raymond Chan, City University of Hong Kong

TBA; zoom link @ https://sites.google.com/view/mindsseminar/home
 Raymond Chan, City University of Hong Kong
 TBA; zoom link @ https://sites.google.com/view/mindsseminar/home
 01/14/2021
 3:30 PM  4:30 PM

(Virtual Meeting Link)
 Olga Turanova (turanova@msu.edu)
TBA; (Note the unusual time: 4:30pm Shanghai, 10:30am Paris.)

26940

Wednesday 1/20 3:00 PM

Sergi Elizalde, Dartmouth College

Descents on quasiStirling permutations
 Sergi Elizalde, Dartmouth College
 Descents on quasiStirling permutations
 01/20/2021
 3:00 PM  3:50 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Bruce E Sagan (bsagan@msu.edu)
Stirling permutations were introduced by Gessel and Stanley to give a combinatorial interpretation of certain polynomials related to Stirling numbers. A very natural extension of Stirling permutations are quasiStirling permutations, which are in bijection with labeled rooted plane trees. Archer et al. introduced these permutations, and conjectured that there are $(n+1)^{n1}$ quasiStirling permutations of size $n$ having $n$ descents.
In this talk we prove this conjecture. More generally, we give the generating function for quasiStirling permutations by the number of descents, which turns out to satisfy a beautiful equation involving Eulerian polynomials. We show that some of the properties of descents on usual permutations and on Stirling permutations have an analogue for quasiStirling permutations.
Finally, we extend our results to a oneparameter family of permutations, called $k$quasiStirling permutations, which are in bijection with certain decorated trees.

26961

Thursday 1/21 2:30 PM

Daniel Kane, University of California, San Diego

Point Location and Active Learning
 Daniel Kane, University of California, San Diego
 Point Location and Active Learning
 01/21/2021
 2:30 PM  3:30 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Olga Turanova (turanova@msu.edu)
In the point location problem one is given a hyperplane arrangement and an unknown point. By making linear queries about that point one wants to determine which cell of the hyperplane arrangement it lies in. This problem has an unexpected connection to the problem in machine learning of actively learning a halfspace. We discuss these problems and their relationship and provide a new and nearly optimal algorithm for solving them.

26969

Friday 1/22 5:00 PM

Zheng Xiao, MSU

Extensions of function fields
 Zheng Xiao, MSU
 Extensions of function fields
 01/22/2021
 5:00 PM  6:00 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Zheng Xiao (xiaozhen@msu.edu)
No abstract available.

26973

Tuesday 1/26 10:00 AM


Online large lectures and coordinated courses  challenges and opportunities

 Online large lectures and coordinated courses  challenges and opportunities
 01/26/2021
 10:00 AM  11:00 AM

(Virtual Meeting Link)
 Tsvetanka Sendova (tsendova@msu.edu)
No abstract available.

26968

Tuesday 1/26 2:50 PM

Matt Stoffregen, MSU

Surgery Exact Triangles in Involutive Floer homology
 Matt Stoffregen, MSU
 Surgery Exact Triangles in Involutive Floer homology
 01/26/2021
 2:50 PM  3:40 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Honghao Gao (gaohongh@msu.edu)
We'll sketch the definition of the involutive Heegaard Floer homology constructed by HendricksManolescu, and then explain how this homology theory behaves under surgery. As a consequence, we can use the surgery formula to construct threemanifolds which are not homology cobordant to any combination of Seifert fiber spaces. This is joint work Kristen Hendricks, Jen Hom and Ian Zemke.

26943

Tuesday 1/26 4:30 PM

Luis Silvestre, University of Chicago

Integrodifferential diffusion and the Boltzmann equation
 Luis Silvestre, University of Chicago
 Integrodifferential diffusion and the Boltzmann equation
 01/26/2021
 4:30 PM  5:30 PM
 Online (virtual meeting)
 Aaron D Levin (levina@msu.edu)
Integrodifferential equations have been a very active area of research in the last 20 years. In this talk we will explain what they are and in what sense they are similar to more classical parabolic partial differential equations. We will discuss results on regularity estimates for the Boltzmann equation in this context.

26941

Wednesday 1/27 3:00 PM

Joshua Swanson, UCSD

DUSTPAN distributions as limit laws for Mahonian statistics on forests
 Joshua Swanson, UCSD
 DUSTPAN distributions as limit laws for Mahonian statistics on forests
 01/27/2021
 3:00 PM  3:50 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Bruce E Sagan (bsagan@msu.edu)
Building on work of Stanley and BjörnerWachs, we study the distribution of certain Mahonian statistics on several families of posets, including the major index on linear extensions of forests. We show that the resulting standardized distributions are often asymptotically normal. However, in certain regimes, we must introduce a new, closed family of continuous probability distributions called DUSTPAN distributions which simultaneously generalize the IrwinHall and normal distributions. In the case of forests, we use graphtheoretic statistics like height and elevation to completely determine the precise limit laws. This leads to some natural open questions about the distribution of the height of such forests.
Joint work with Sara Billey (https://arxiv.org/abs/2010.12701) building on earlier joint work with Sara Billey and Matjaž Konvalinka (https://arxiv.org/abs/1905.00975).

26960

Wednesday 1/27 4:00 PM

Vaidehee Thatte, SUNY Binghamton

Arbitrary Valuation Rings and Wild Ramification
 Vaidehee Thatte, SUNY Binghamton
 Arbitrary Valuation Rings and Wild Ramification
 01/27/2021
 4:00 PM  5:00 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Preston Wake (wakepres@msu.edu)
We aim to develop ramification theory for arbitrary valuation fields, extending the classical theory of complete discrete valuation fields with perfect residue fields. By studying wild ramification, we hope to understand the mysterious phenomenon of the $\textit{defect}$ (or ramification deficiency) unique to the positive residue characteristic case and is one of the main obstacles in obtaining resolution of singularities.
Extensions of degree $p$ in residue characteristic $p>0$ are building blocks of the general case. We present a generalization of ramification invariants for such extensions. These results enable us to construct an upper ramification filtration of the absolute Galois group of Henselian valuation fields (joint with K.Kato).

26970

Wednesday 1/27 4:00 PM

Keshav Sutrave, Michigan State University

An intro to Riemann surfaces: What your complex analysis prof. doesn’t want you to know
 Keshav Sutrave, Michigan State University
 An intro to Riemann surfaces: What your complex analysis prof. doesn’t want you to know
 01/27/2021
 4:00 PM  5:00 PM

 Danika Van Niel (vannield@msu.edu)
Riemann surfaces blend together complex analysis, geometry, and topology (and then eventually connect to PDE’s, algebraic geometry & number theory, and probably everything else).
I will only scratch the surface by introducing them, as well as the notions of branched covering, monodromy, and the RiemannHurwitz formula.
Zoom link: https://msu.zoom.us/j/91485321701
Password: SGTS

26962

Thursday 1/28 3:30 AM

Zuowei Shen, National University of Singapore

Deep Approximation via Deep Learning
 Zuowei Shen, National University of Singapore
 Deep Approximation via Deep Learning
 01/28/2021
 3:30 AM  4:30 AM
 Online (virtual meeting)
(Virtual Meeting Link)
 Olga Turanova (turanova@msu.edu)
The primary task of many applications is approximating/estimating a function through samples drawn from a probability distribution on the input space. The deep approximation is to approximate a function by compositions of many layers of simple functions, that can be viewed as a series of nested feature extractors. The key idea of deep learning network is to convert layers of compositions to layers of tuneable parameters that can be adjusted through a learning process, so that it achieves a good approximation with respect to the input data. In this talk, we shall discuss mathematical theory behind this new approach and approximation rate of deep network; how this new approach differs from the classic approximation theory, and how this new theory can be used to understand and design deep learning network.

26981

Friday 1/29 1:00 PM

Nick Rekuski, MSU

Etale Cohomology I: Preliminary
 Nick Rekuski, MSU
 Etale Cohomology I: Preliminary
 01/29/2021
 1:00 PM  2:00 PM
 Online (virtual meeting)
 Chuangtian Guan (guanchua@msu.edu)
No abstract available.

26974

Friday 1/29 5:00 PM

Zheng Xiao, MSU

$ef$ Theorem, discriminant and different in function fields
 Zheng Xiao, MSU
 $ef$ Theorem, discriminant and different in function fields
 01/29/2021
 5:00 PM  6:00 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Zheng Xiao (xiaozhen@msu.edu)
No abstract available.

26976

Tuesday 2/2 10:00 AM

Jamillah GrossCaldwell, MSU

About the Michigan Louis Stokes Alliance for Minority Participation in STEM and MSU NxtGen STEM Scholars Program
 Jamillah GrossCaldwell, MSU
 About the Michigan Louis Stokes Alliance for Minority Participation in STEM and MSU NxtGen STEM Scholars Program
 02/02/2021
 10:00 AM  11:00 AM

(Virtual Meeting Link)
 Tsvetanka Sendova (tsendova@msu.edu)
No abstract available.

26986

Tuesday 2/2 2:50 PM

Dogancan Karabas, Northwestern University

Wrapped Fukaya category via gluing sheaves, and the case of pinwheels
 Dogancan Karabas, Northwestern University
 Wrapped Fukaya category via gluing sheaves, and the case of pinwheels
 02/02/2021
 2:50 PM  3:40 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Honghao Gao (gaohongh@msu.edu)
In this talk, I will discuss some gluing techniques for microlocal sheaves, and calculate wrapped Fukaya category of some rational homology balls, which are quotients of $A_n$ Milnor fibres, via gluing sheaves on their skeleta, i.e. pinwheels.

26944

Tuesday 2/2 4:00 PM

Samit Dasgupta, Duke University

Stark's Conjectures and Hilbert's 12th Problem
 Samit Dasgupta, Duke University
 Stark's Conjectures and Hilbert's 12th Problem
 02/02/2021
 4:00 PM  5:00 PM
 Online (virtual meeting)
 Aaron D Levin ()
In this talk we will discuss two central problems in algebraic number theory and their interconnections: explicit class field theory (also known as Hilbert's 12th Problem), and the special values of Lfunctions. The goal of explicit class field theory is to describe the abelian extensions of a ground number field via analytic means intrinsic to the ground field. Meanwhile, there is an abundance of conjectures on the special values of Lfunctions at certain integer points. Of these, Stark's Conjecture has special relevance toward explicit class field theory. I will describe my recent proof, joint with Mahesh Kakde, of the BrumerStark conjecture away from p=2. This conjecture states the existence of certain canonical elements in CM abelian extensions of totally real fields. Next I will describe our proof of an exact formula for these BrumerStark units that had been developed by many authors over the last 15 years. We show that the BrumerStark units along with other elementary quantities generate the maximal abelian extension of totally real number fields, thereby giving a solution to Hilbert's 12th problem for these fields.

26975

Wednesday 2/3 3:00 PM

Richard Stanley, MIT

Two Analogues of Pascal's Triangle
 Richard Stanley, MIT
 Two Analogues of Pascal's Triangle
 02/03/2021
 3:00 PM  3:50 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Bruce E Sagan (bsagan@msu.edu)
Pascal's triangle is closely associated with the expansion of
the product $(1+x)^n$. We will discuss two analogous arrays of numbers
that are associated with the products
$\prod_{i=0}^{n1} \left(1+x^{2^i}+x^{2^{i+1}}\right)$ and
$\prod_{i=1}^n \left(1+x^{F_{i+1}}\right)$, where $F_{i+1}$ is a Fibonacci
number. All three arrays are special cases of a twoparameter family that
might be interesting to investigate further.

26988

Wednesday 2/3 4:00 PM

Laure Flapan, MSU

Fano manifolds associated to hyperkähler manifolds
 Laure Flapan, MSU
 Fano manifolds associated to hyperkähler manifolds
 02/03/2021
 4:00 PM  5:00 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Laure Flapan (flapanla@msu.edu)
Many of the known examples of hyperkähler manifolds arise from geometric constructions that begin with a Fano manifold whose cohomology looks like that of a K3 surface. In this talk, I will focus on a program whose goal is to reverse this process, namely to begin with a hyperkähler manifold and from it produce geometrically a Fano manifold. This is joint work in progress with K. O’Grady, E. Macrì, and G. Saccà.
Passcode: MSUALG

26963

Thursday 2/4 2:30 PM

Tino Ullrich , TU Chemnitz

A New Subsampling Technique for Random Points and Optimal Least Squares Approximation of HighDimensional Functions
 Tino Ullrich , TU Chemnitz
 A New Subsampling Technique for Random Points and Optimal Least Squares Approximation of HighDimensional Functions
 02/04/2021
 2:30 PM  3:30 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Olga Turanova (turanova@msu.edu)
We provide a new general upper bound for the minimal L2worstcase recovery error in the framework of RKHS, where only n function samples are allowed. This quantity can be bounded in terms of the singular numbers of the compact embedding into the space of square integrable functions. It turns out that in many relevant situations this quantity is asymptotically only worse by square root of log(n) compared to the singular numbers. The algorithm which realizes this behavior is a weighted least squares algorithm based on a specific set of sampling nodes which works for the whole class of functions simultaneously. These points are constructed out of a random draw with respect to distribution tailored to the spectral properties of the reproducing kernel (importance sampling) in combination with a subsampling procedure coming from the celebrated proof of Weaver's conjecture, which was shown to be equivalent to the KadisonSinger problem. For the above multivariate setting, it is still a fundamental open problem whether sampling algorithms are as powerful as algorithms allowing general linear information like Fourier or wavelet coefficients. However, the gap is now rather small. As a consequence, we may study wellknown scenarios where it was widely believed that sparse grid sampling recovery methods perform optimally. It turns out that this is not the case for dimensions d > 2.
This is joint work with N. Nagel and M. Schaefer from TU Chemnitz.

26989

Friday 2/5 1:00 PM

Joshua Ruiter, MSU

Pinning of algebraic groups
Pinnings play an important role in the classification of reductive algebraic groups. Even though the subject can get abstract, pinnings are actually quite concrete. We'll write down matrices to describe pinnings of classical groups like $\operatorname{SL}_n$ and $\operatorname{Sp}_n$ and talk a little bit about how pinnings fit into the classification theorem.

26985

Friday 2/5 5:00 PM

Zheng Xiao, MSU

Function fields different theory continued
 Zheng Xiao, MSU
 Function fields different theory continued
 02/05/2021
 5:00 PM  6:00 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Zheng Xiao (xiaozhen@msu.edu)
No abstract available.

26993

Tuesday 2/9 10:00 AM

Dirk Colbry

Curriculum reform in MTH/CMSE 314
 Dirk Colbry
 Curriculum reform in MTH/CMSE 314
 02/09/2021
 10:00 AM  11:00 AM
 Online (virtual meeting)
(Virtual Meeting Link)
 Tsvetanka Sendova (tsendova@msu.edu)
No abstract available.

26942

Tuesday 2/9 2:50 PM

Irving Dai, MIT

Lattice homology and instantons
 Irving Dai, MIT
 Lattice homology and instantons
 02/09/2021
 2:50 PM  3:40 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Honghao Gao (gaohongh@msu.edu)
We show that if Y is the boundary of an almostrational plumbing, then the framed instanton Floer homology of Y is isomorphic to its Heegaard Floer homology. This class of 3manifolds includes all Seifert fibered rational homology spheres. Our proof utilizes lattice homology, and relies on a decomposition theorem for instanton Floer cobordism maps established by John Baldwin and Steven Sivek. This is joint work with Antonio Alfieri, John Baldwin, and Steven Sivek.

26950

Tuesday 2/9 4:00 PM

Jordan Ellenberg, University of Wisconsin–Madison

Beyond rank
 Jordan Ellenberg, University of Wisconsin–Madison
 Beyond rank
 02/09/2021
 4:00 PM  5:00 PM
 Online (virtual meeting)
 Aaron D Levin ()
The notion of the rank of a matrix is one of the most fundamental in linear algebra. The analogues of this notion in multilinear algebra — e.g., what is the “rank” of an m x n x p array of numbers? — are much less wellunderstood, and are often thought of as of niche interest. At least, that’s how I was brought up to think of them, until Terry Tao explained to me that the resolution of the cap set conjecture by Croot, Lev, Pach, Gijswijt and myself really made use of these ideas! In fact, these notions are of great current interest in a wide range of mathematical subjects at the moment! Issues about “higher rank” arise in complexity theory, data science, geometric combinatorics, additive number theory, quantum mechanics, and commutative algebra — I will manage to say something about some tobespecified proper subset of these topics, and am happy to chat afterwards about the others.

26995

Wednesday 2/10 3:00 PM

Nicholas Ovenhouse, University of Minnesota

Laurent Polynomials from the Super Ptolemy Relation
 Nicholas Ovenhouse, University of Minnesota
 Laurent Polynomials from the Super Ptolemy Relation
 02/10/2021
 3:00 PM  3:50 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Bruce E Sagan (bsagan@msu.edu)
In classical geometry, Ptolemy's theorem relates the lengths of the sides of a quadrilateral to the lengths of the diagonals. Fixing a triangulation of a polygon, the length of any diagonal can be expressed (using Ptolemy's theorem) as a Laurent polynomial in the lengths of diagonals in the triangulation. There is a combinatorial description of the terms in this Laurent polynomial due to Schiffler, in terms of "Tpaths". Recently, Penner and Zeitlin constructed a superalgebra from a triangulation, and an analogue of the Ptolemy relation in this situation. I will describe a generalization of "Tpaths" which enumerate the terms in the corresponding super Laurent polynomials. This is joint work with Gregg Musiker and Sylvester Zhang.

26954

Wednesday 2/10 4:00 PM

Tudor Padurariu, IAS

Noncommutative resolutions and intersection cohomology for quotient singularities
 Tudor Padurariu, IAS
 Noncommutative resolutions and intersection cohomology for quotient singularities
 02/10/2021
 4:00 PM  5:00 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Laure Flapan (flapanla@msu.edu)
It is an important problem to define a Ktheoretic version of intersection cohomology, with expected applications in representation theory. One step further is to look for a categorification of intersection cohomology. For good moduli spaces $X$ of Artin stack $Y$ (as defined by Alper), we construct some noncommutative resolutions $D(X)$ inside the category $D^b(Y)$. Further, we construct subcategories $I(X)$ of $D(X)$ whose periodic cyclic homology is given by the intersection cohomology of $X$. In particular, the Ktheory of $I(X)$ is a natural definition of intersection Ktheory for the variety $X$.
Passcode: MSUALG

26964

Thursday 2/11 2:30 PM

Massimo Fornasier , Technische Universität München

Consensusbased Optimization on the Sphere
 Massimo Fornasier , Technische Universität München
 Consensusbased Optimization on the Sphere
 02/11/2021
 2:30 PM  3:30 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Olga Turanova (turanova@msu.edu)
I present new stochastic multiparticle models for global optimization of nonconvex functions on the sphere. These models belong to the class of ConsensusBased Optimization methods. In fact, particles move over the manifold driven by a drift towards an instantaneous consensus point, computed as a combination of the particle locations weighted by the cost function according to Laplace's principle. The consensus point represents an approximation to a global minimizer. The dynamics is further perturbed by a random vector field to favor exploration, whose variance is a function of the distance of the particles to the consensus point. In particular, as soon as the consensus is reached, then the stochastic component vanishes. In the first part of the talk, I present the wellposedness of the model on the sphere and we derive rigorously its meanfield approximation for large particle limit.
In the second part I address the proof of convergence of numerical schemes to global minimizers provided conditions of wellpreparation of the initial datum. The proof combines the meanfield limit with a novel asymptotic analysis, and classical convergence results of numerical methods for SDE. We present several numerical experiments, which show that the proposed algorithm scales well with the dimension and is extremely versatile. To quantify the performances of the new approach, we show that the algorithm is able to perform essentially as good as ad hoc state of the art methods in challenging problems in signal processing and machine learning, namely the phase retrieval problem and the robust subspace detection.
Joint work with H. Huang, L. Pareschi, and P. Sünnen

26990

Friday 2/12 11:00 AM

Patricio Herbst, University of Michigan; Arthur Bakker, Freudenthal Institute, Utrecht University, the Netherlands

Journal for Research in Mathematics Education and Educational Studies in Mathematics: Perspectives from the Editors
 Patricio Herbst, University of Michigan; Arthur Bakker, Freudenthal Institute, Utrecht University, the Netherlands
 Journal for Research in Mathematics Education and Educational Studies in Mathematics: Perspectives from the Editors
 02/12/2021
 11:00 AM  12:00 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Lisa Keller (kellerl@msu.edu)
In this talk we will share the priorities that animate each editorial team’s approach to handling articles as well as writing editorial essays. Both journals are committed to publishing excellent research in mathematics education writ large, no matter its focus, theories, or methods. We are especially interested in publishing research that adds to our methodological and theoretical toolboxes and educates our taste as researchers. The editors will discuss the particular mission and focus of each Journal, the challenges and opportunities in their work as editors and offer advice for those involved in preparing and reviewing manuscripts. Register in advance for the colloquium via ZOOM: https://bit.ly/3alJuom

26999

Friday 2/12 1:00 PM

Chuangtian Guan, MSU

Etale cohomology
 Chuangtian Guan, MSU
 Etale cohomology
 02/12/2021
 1:00 PM  2:00 PM
 C117 Wells Hall
 Joshua Ruiter (ruiterj2@msu.edu)
We'll continue reading through Milne's notes on etale cohomology.

26998

Friday 2/12 5:00 PM

Zheng Xiao, MSU

Function fields differentials
 Zheng Xiao, MSU
 Function fields differentials
 02/12/2021
 5:00 PM  6:00 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Zheng Xiao (xiaozhen@msu.edu)
No abstract available.

26994

Tuesday 2/16 10:00 AM

Rachael Lund

New technologies that worked and that didn't (Packback, Catme, FlipGrid)
 Rachael Lund
 New technologies that worked and that didn't (Packback, Catme, FlipGrid)
 02/16/2021
 10:00 AM  11:00 AM
 Online (virtual meeting)
(Virtual Meeting Link)
 Tsvetanka Sendova (tsendova@msu.edu)
No abstract available.

26953

Tuesday 2/16 2:50 PM

Linh Truong, University of Michigan

Upsilon invariant and rightveering open book decompositions
 Linh Truong, University of Michigan
 Upsilon invariant and rightveering open book decompositions
 02/16/2021
 2:50 PM  3:40 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Honghao Gao (gaohongh@msu.edu)
In 2010, Hedden showed that the OzsvathSzabo concordance invariant tau can detect whether a fibered knot induces the tight contact structure on the threesphere. In 2017, OzsvathStipsiczSzabo constructed a oneparameter family of concordance invariants Upsilon, which recovers tau as a special case. I will discuss a sufficient condition using Upsilon for the monodromy of the open book decomposition of a fibered knot to be rightveering. As an application, I will discuss a generalization of Baker's conjecture on the concordance of tight, fibered knots. This is joint work with Dongtai He and Diana Hubbard.

26971

Tuesday 2/16 4:00 PM

Walter Strauss, Brown University

Steady Water Waves
 Walter Strauss, Brown University
 Steady Water Waves
 02/16/2021
 4:00 PM  5:00 PM
 Online (virtual meeting)
 Aaron D Levin ()
The mathematical study of water waves began with the derivation of the
basic mathematical equations of any fluid by Euler in 1752. Later, water
waves, which have a free boundary at the air interface, played a central role
in the work of Poisson, Cauchy, Stokes, LeviCivita and many others.
In the last quarter century it has become a particularly active mathematical
research area.
I will limit my discussion to classical 2D traveling water waves with vorticity.
By means of local and global bifurcation theory using topological degree,
we now know that there exist many such waves. They are exact smooth
solutions of the Euler equations with the physical boundary conditions.
Numerical computations provide insight into their properties. I will mention
a number of properties that are the subjects of current research such as:
their heights, their steepness, the possibility of selfintersection, and
their stability or instability.

27000

Wednesday 2/17 3:00 PM

Tom Roby, University of Connecticut

An actionpacked introduction to homomesy
 Tom Roby, University of Connecticut
 An actionpacked introduction to homomesy
 02/17/2021
 3:00 PM  3:50 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Bruce E Sagan (bsagan@msu.edu)
Dynamical Algebraic Combinatorics explores maps on sets of discrete combinatorial objects with particular attention to their orbit structure. Interesting counting questions immediately arise: How many orbits are there? What are their sizes? What is the period of the map if it's invertible? Are there any interesting statistics on the objects that are wellbehaved under the map?
One particular phenomenon of interest is ``homomesy'', where a statistic on the set of objects has the same average for each orbit of an action. Along with its intrinsic interest as a kind of hidden ``invariant'', homomesy can be used to help understand certain properties of the action. Proofs of homomesy often lead one to develop tools that further our understanding of the underlying dynamics, e.g., by finding an equivariant bijection. These notions can be lifted to higher (piecewiselinear and birational) realms, of which the combinatorial situation is a discrete shadow, and the resulting identities are somewhat surprising. Maps that can be decomposed as products of ``toggling'' involutions are particularly amenable to this line of analysis.
This talk will be a introduction to these ideas, giving a number of examples.

26957

Wednesday 2/17 4:00 PM

François Greer, IAS

A tale of two Severi curves
 François Greer, IAS
 A tale of two Severi curves
 02/17/2021
 4:00 PM  5:00 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Laure Flapan (flapanla@msu.edu)
Let $(S,L)$ be a general polarized K3 surface with $c_1(L)^2=2g2$. A general member of the linear system $L\simeq \mathbb P^g$ is a smooth curve of genus $g$. For $0\leq h\leq g$, define the Severi variety $V_h(S,L)\subset L$ to be the locus of curves with geometric genus $\leq h$. As expected, $V_h(S,L)$ has dimension $h$. We consider the case $h=1$, where the Severi variety is a (singular) curve. Our first result is that the geometric genus of $V_1(S,L)$ goes to infinity with $g$; we give a lower bound $\sim e^{c\sqrt{g}}$. Next we consider the analogous question for Severi curves of a rational elliptic surface, and give a polynomial upper bound instead. Modular forms play a central role in both arguments.
Passcode: MSUALG

26965

Thursday 2/18 2:30 PM

Mikhail Belkin , University of California, San Diego

A theory of optimization and transition to linearity in deep learning
 Mikhail Belkin , University of California, San Diego
 A theory of optimization and transition to linearity in deep learning
 02/18/2021
 2:30 PM  3:30 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Olga Turanova (turanova@msu.edu)
The success of deep learning is due, to a large extent, to the remarkable effectiveness of gradientbased optimization methods applied to large neural networks. In this talk I will discuss some general mathematical principles allowing for efficient optimization in overparameterized nonlinear systems, a setting that includes deep neural networks. Remarkably, it seems that optimization of such systems is "easy". In particular, optimization problems corresponding to these systems are not convex, even locally, but instead satisfy locally the PolyakLojasiewicz (PL) condition allowing for efficient optimization by gradient descent or SGD. We connect the PL condition of these systems to the condition number associated to the tangent kernel and develop a nonlinear theory parallel to classical analyses of overparameterized linear equations.
In a related but conceptually separate development, I will discuss a new perspective on the remarkable recently discovered phenomenon of transition to linearity (constancy of NTK) in certain classes of large neural networks. I will show how this transition to linearity results from the scaling of the Hessian with the size of the network.
Joint work with Chaoyue Liu and Libin Zhu

27006

Friday 2/19 1:00 PM

Shen Yu, MSU

Serre's GAGA
In this talk, I will talk about Serre’s GAGA and if time permits, I will talk about its application.

27005

Friday 2/19 5:00 PM

Keping Huang, MSU

Additive polynomials towards Carlitz module
 Keping Huang, MSU
 Additive polynomials towards Carlitz module
 02/19/2021
 5:00 PM  6:00 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Zheng Xiao (xiaozhen@msu.edu)
No abstract available.

27022

Tuesday 2/23 10:00 AM

Shelley Kandola, MSU

Strengthening the Quality of Mathematical Writing for Math Majors at the University of Minnesota
 Shelley Kandola, MSU
 Strengthening the Quality of Mathematical Writing for Math Majors at the University of Minnesota
 02/23/2021
 10:00 AM  11:00 AM
 Online (virtual meeting)
(Virtual Meeting Link)
 Tsvetanka Sendova (tsendova@msu.edu)
No abstract available.

26951

Tuesday 2/23 2:50 PM

Thang Le, Georgia Tech

Quantum trace map for $SL_n$ skein algebras of surfaces
 Thang Le, Georgia Tech
 Quantum trace map for $SL_n$ skein algebras of surfaces
 02/23/2021
 2:50 PM  3:40 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Honghao Gao (gaohongh@msu.edu)
For a punctured surface there are two quantizations of the $SL_n$ character variety. The first quantization is the $SL_n$ skein algebra, and the second one is the quantization of the higher Teichmuller space.
When $n=2$ Bonahon and Wong showed that there is an algebra homomorphism, called the quantum trace, from the first quantized algebra to the second one. We show for general n a similar quantum trace map exists.
The construction of the $SL_n$ quantum trace is based on the theory of stated $SL_n$ skein algebra, developed in a joint work with A. Sikora, and a work of Chekhov and Shapiro.

27018

Wednesday 2/24 3:00 PM

Sarah Mason, Wake Forest University

Quasisymmetric Macdonald polynomials
 Sarah Mason, Wake Forest University
 Quasisymmetric Macdonald polynomials
 02/24/2021
 3:00 PM  3:50 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Bruce E Sagan (bsagan@msu.edu)
We introduce a quasisymmetric analogue of Macdonald polynomials, originating from work by Corteel, Mandelshtam, and Williams on multiline queues. Along the way we produce a new and compactified combinatorial formula for Macdonald polynomials. This is joint work with Corteel, Haglund, Mandelshtam, and Williams.

26958

Wednesday 2/24 4:00 PM

Ignacio Barros, Université ParisSaclay

Pencils on surfaces with normal crossings and the Kodaira dimension of $M_{g,n}$
 Ignacio Barros, Université ParisSaclay
 Pencils on surfaces with normal crossings and the Kodaira dimension of $M_{g,n}$
 02/24/2021
 4:00 PM  5:00 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Laure Flapan (flapanla@msu.edu)
The first half of the talk will be a colloquium style talk, where I will recall the history of the problem of determining the Kodaira dimension of the moduli space of curves. In the second half I will report on joint work with D. Agostini, where we study smoothing of pencils of curves on surfaces with normal crossings. As a consequence we obtain new instances of $(g,n)$ where $M_{g,n}$ is of negative Kodaira dimension and provide bounds for the Kodaira dimension of $M_{16}$ and $M_{12,8}$.
Passcode: MSUALG

26983

Thursday 2/25 3:30 AM

Zaiwen Wen, Peking University, China

Stochastic SecondOrder Methods For Deep Learning
 Zaiwen Wen, Peking University, China
 Stochastic SecondOrder Methods For Deep Learning
 02/25/2021
 3:30 AM  4:30 AM
 Online (virtual meeting)
(Virtual Meeting Link)
 Olga Turanova (turanova@msu.edu)
Stochastic methods are widely used in deep learning. In this talk, we first review the stateoftheart methods such as KFAC. Then we present a structured stochastic quasiNewton method and a sketchy empirical natural gradient method. Numerical results on deep convolution networks illustrate that our methods are quite competitive to SGD and KFAC.

27021

Friday 2/26 1:00 PM

Shitan Xu, MSU

Etale fundamental group
 Shitan Xu, MSU
 Etale fundamental group
 02/26/2021
 1:00 PM  2:00 PM
 C117 Wells Hall
 Joshua Ruiter (ruiterj2@msu.edu)
We continue our series reading through Milne's notes on etale cohomology.

27020

Friday 2/26 5:00 PM

Keping Huang, Michigan State University

Carlitz exponentials and Carlitz modules
 Keping Huang, Michigan State University
 Carlitz exponentials and Carlitz modules
 02/26/2021
 5:00 PM  6:00 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Keping Huang (huangk23@msu.edu)
No abstract available.

27017

Monday 3/1 2:00 PM

Priyanga Ganesan, Texas A&M University

Quantum Graphs
 Priyanga Ganesan, Texas A&M University
 Quantum Graphs
 03/01/2021
 2:00 PM  2:50 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Brent Nelson (brent@math.msu.edu)
Quantum graphs are an operator space generalization of classical graphs. In this talk, I will motivate the idea of a quantum graph and its significance in quantum communication. We will look at the different notions of quantum graphs that arise in operator systems theory, noncommutative topology and quantum information theory. I will then introduce a nonlocal game with quantum inputs and classical outputs, that generalizes the non local graph coloring game. This is based on joint work with Michael Brannan and Samuel Harris.

26991

Tuesday 3/2 10:00 AM

Willie Wong

Experiences with promoting student collaboration in undergraduate math classes via software tools.
 Willie Wong
 Experiences with promoting student collaboration in undergraduate math classes via software tools.
 03/02/2021
 10:00 AM  11:00 AM
 Online (virtual meeting)
(Virtual Meeting Link)
 Tsvetanka Sendova (tsendova@msu.edu)
No abstract available.

26967

Tuesday 3/2 2:50 PM

Break Day, no talk

No talk
 Break Day, no talk
 No talk
 03/02/2021
 2:50 PM  3:40 PM
 Online (virtual meeting)
 Honghao Gao (gaohongh@msu.edu)
No abstract available.

26956

Wednesday 3/3 4:00 PM

Rankeya Datta, University of Illinois at Chicago

Openness of splinter loci in prime characteristic.
 Rankeya Datta, University of Illinois at Chicago
 Openness of splinter loci in prime characteristic.
 03/03/2021
 4:00 PM  5:00 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Joe Waldron (waldro51@msu.edu)
A splinter is a notion of singularity that has seen numerous applications of late, especially in connection with the direct summand theorem, the mixed characteristic minimal model program, CohenMacaulayness of absolute integral closures and vanishing theorems. However, many basic questions about splinters remain elusive. One such problem is whether the splinter condition spreads from a point to an open neighborhood of a noetherian scheme. In this talk, we will address this question in prime characteristic and show that a locally noetherian scheme whose associated
absolute Frobenius is finite map has an open splinter locus. In particular,
all varieties over perfect fields of positive characteristic have open splinter loci. If time permits, we will show how our methods also give openness of splinter loci for a large class of schemes that do not necessarily have finite Frobenius. This talk is based on joint work in progress with Kevin Tucker.

26984

Thursday 3/4 2:30 PM

Ronald DeVore, Texas A&M University

Deep Learning and Neural Networks: The Mathematical View
 Ronald DeVore, Texas A&M University
 Deep Learning and Neural Networks: The Mathematical View
 03/04/2021
 2:30 PM  3:30 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Olga Turanova (turanova@msu.edu)
Deep Learning is much publicized and has had great empirical success on challenging problems in learning. Yet there is no quantifiable proof of performance and certified guarantees for these methods. This talk will give an overview of Deep Learning from the viewpoint of mathematics and numerical computation.

27019

Friday 3/5 11:00 AM

Peter Liljedahl, Simon Fraser University

Building Thinking Classrooms
 Peter Liljedahl, Simon Fraser University
 Building Thinking Classrooms
 03/05/2021
 11:00 AM  12:00 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Lisa Keller (kellerl@msu.edu)
Much of how classrooms look and much of what happens in them today is guided by institutional norms laid down at the inception of an industrialage model of public education. These norms have enabled a culture of teaching and learning that is often devoid of student thinking. In this session I present some of the results of over 15 years of research
into how K12 and postsecondary teachers can transform their classrooms from a space where students mimic to where students think. The practiced discussed will intertwine with, and make extensive references to, the recently published book, Building Thinking Classrooms in Mathematics: 14 Teaching Practices for Enhancing Learning. Register in advance for the
colloquium:
https://bit.ly/3bafgVE
After registering, you will receive a confirmation email containing information about joining the
meeting.

27007

Friday 3/5 3:00 PM

Chloe Lewis

Taking Topology to the Supreme Court – An Introduction to the Mathematics of Gerrymandering
 Chloe Lewis
 Taking Topology to the Supreme Court – An Introduction to the Mathematics of Gerrymandering
 03/05/2021
 3:00 PM  4:00 PM

(Virtual Meeting Link)
 Keshav Sutrave (sutravek@msu.edu)
This year, elected officials in state governments across the country will use the results of the 2020 Census to choose their voters, rather than giving voters the chance to choose them, by drawing unfair Congressional district maps in a process known as gerrymandering. In this talk we’ll look at some mathematical methods of quantifying the partisan gerrymander and discuss the role of the U.S. Supreme Court in informing such methods.

27025

Friday 3/5 5:00 PM

Keping Huang, MSU

Carlitz modules and Drinfeld modules
 Keping Huang, MSU
 Carlitz modules and Drinfeld modules
 03/05/2021
 5:00 PM  6:00 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Keping Huang (huangk23@msu.edu)
No abstract available.

27024

Tuesday 3/9 10:00 AM

Ashley Ahlin, MSU

MSU Math Outreach programs (or, sharing the beauty and joy of mathematics with your future students)
 Ashley Ahlin, MSU
 MSU Math Outreach programs (or, sharing the beauty and joy of mathematics with your future students)
 03/09/2021
 10:00 AM  11:00 AM
 Online (virtual meeting)
(Virtual Meeting Link)
 Tsvetanka Sendova (tsendova@msu.edu)
No abstract available.

26966

Tuesday 3/9 2:50 PM

Roger Casals, UC Davis

Lagrangian Fillings of Legendrian links: Two Constructions in Floer Theory
 Roger Casals, UC Davis
 Lagrangian Fillings of Legendrian links: Two Constructions in Floer Theory
 03/09/2021
 2:50 PM  3:40 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Honghao Gao (gaohongh@msu.edu)
In this talk I will review our current understanding in the classification of Lagrangian fillings for Legendrian links in the standard contact 3sphere. The talk will present two illustrative constructions: one explaining how to build and detect infinitely many Lagrangian fillings using the Legendrian Contact DGA, and the other explaining how to classify fillings for the Hopf link using pseudoholomorphic foliations. First, I will present the basic objects of interest and survey the recent developments in the field (work with H. Gao, and work with E. Zaslow). Then I will delve into new and inprogress results on the Legendrian Contact DGA (work with L. Ng). Finally, I will report on how pseudoholomorphic curves might help us classify Lagrangian fillings in certain cases. During the course of the talk, I will try to highlight some of the interesting open questions and new methods that arise from our current work as well as future directions.

27015

Tuesday 3/9 3:00 PM

Shiwen Zhang, U Minnesota

The landscape law for tight binding Hamiltonians
 Shiwen Zhang, U Minnesota
 The landscape law for tight binding Hamiltonians
 03/09/2021
 3:00 PM  4:00 PM

(Virtual Meeting Link)
 Jeffrey Hudson Schenker (schenke6@msu.edu)
The localization landscape theory, introduced in 2012 by Filoche and Mayboroda, considers the socalled the landscape function u solving Hu=1 for an operator H. The landscape theory has remarkable power in studying the eigenvalue problems of H and has led to numerous ``landscape baked’’ results in mathematics, as well as in theoretical and experimental physics. In this talk, we will discuss some recent results of the landscape theory for tightbinding Hamiltonians H=\Delta+V on Z^d. We introduce a box counting function, defined through the discrete landscape function of H. For any deterministic bounded potential, we give estimates for the integrated density of states from above and below by the landscape box counting function, which we call the landscape law. For the Anderson model, we get a refined lower bound for the IDS, throughout the spectrum. We will also discuss some numerical experiments in progress on the socalled practical landscape law for the continuous Anderson model. This talk is based on joint work with D. N. Arnold, M. Filoche, S. Mayboroda, and Wei Wang.

26945

Tuesday 3/9 4:00 PM

Andrea Nahmod, University of Massachusetts Amherst

Propagation of randomness under the flow of nonlinear dispersive equations
 Andrea Nahmod, University of Massachusetts Amherst
 Propagation of randomness under the flow of nonlinear dispersive equations
 03/09/2021
 4:00 PM  5:00 PM
 Online (virtual meeting)
 Aaron D Levin ()
The study of partial differential equations (PDEs) with randomness has become an important and influential subject in the last few decades. In this talk we focus on the time dynamics of solutions of nonlinear dispersive equations with random initial data. It is well known that in many situations, randomization improves the behavior of solutions to PDEs: the key underlying difficulty is in understanding how randomness propagates under the flow of nonlinear PDEs. In this context, starting with an overview of J. Bourgain's seminal work on the invariance of Gibbs measures for nonlinear Schrödinger equations we describe new methods that offer deeper insights. We discuss in particular the theory of random tensors, a powerful new framework that we developed with Yu Deng and Haitian Yue, which allows us to unravel the propagation of randomness beyond the linear evolution of random data and probe the underlying random structure that lives on high frequencies/fine scales. This enables us to show the existence and uniqueness of solutions to the NLS in an optimal range relative to the probabilistic scaling. A beautiful feature of the solution we find is its explicit expansion in terms of multilinear Gaussians with adapted random tensor coefficients.

27027

Wednesday 3/10 3:00 PM

Bridget Tenner, DePaul University

Odd diagram classes of permutations
 Bridget Tenner, DePaul University
 Odd diagram classes of permutations
 03/10/2021
 3:00 PM  3:50 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Bruce E Sagan (bsagan@msu.edu)
Recently, Brenti and Carnevale introduced an odd analogue of the classical permutation diagram. This gives rise to odd analogues of other permutation aspects such as length and inversions. Unlike in the classical setting, multiple permutations might have the same odd diagram. This prompts the study of "odd diagram classes": sets of permutations having the same odd diagram. We will discuss the rich combinatorial structure of these classes, including connections to pattern avoiding permutations and the Bruhat order.
This is joint work with Francesco Brenti and Angela Carnevale.

26987

Wednesday 3/10 4:00 PM

Joe Waldron, MSU

Minimal model program for threefolds of mixed characteristic
 Joe Waldron, MSU
 Minimal model program for threefolds of mixed characteristic
 03/10/2021
 4:00 PM  5:00 PM
 Online (virtual meeting)
 Laure Flapan (flapanla@msu.edu)
A major obstacle to extending the minimal model program away from characteristic zero is the lack of cohomology vanishing theorems such as Kodaira vanishing. In this talk we describe the minimal model program and then discuss a new way to overcome this difficulty in the arithmetic situation, which has enabled the development of the minimal model program for arithmetic threefolds of residue characteristic greater than 5. This is joint work with Bhatt, Ma, Patakfalvi, Schwede, Tucker and Witaszek.

27001

Thursday 3/11 3:30 AM

Jianfeng Cai, Hong Kong University of Science and Technology

Landscape analysis of nonconvex optimizations in phase retrieval
 Jianfeng Cai, Hong Kong University of Science and Technology
 Landscape analysis of nonconvex optimizations in phase retrieval
 03/11/2021
 3:30 AM  4:30 AM
 Online (virtual meeting)
(Virtual Meeting Link)
 Olga Turanova (turanova@msu.edu)
Nonconvex optimization is a ubiquitous tool in scientific and engineering research. For many important problems, simple nonconvex optimization algorithms often provide good solutions efficiently and effectively, despite possible local minima. One way to explain the success of these algorithms is through the global landscape analysis. In this talk, we present some results along with this direction for phase retrieval. The main results are, for several of nonconvex optimizations in phase retrieval, a local minimum is also global and all other critical points have a negative directional curvature. The results not only explain why simple nonconvex algorithms usually find a global minimizer for phase retrieval, but also are useful for developing new efficient algorithms with a theoretical guarantee by applying algorithms that are guaranteed to find a local minimum.

28034

Friday 3/12 1:00 PM

Qi Peikai, MSU

Student algebra seminar
 Qi Peikai, MSU
 Student algebra seminar
 03/12/2021
 1:00 PM  2:00 PM
 C117 Wells Hall
(Virtual Meeting Link)
 Joshua Ruiter (ruiterj2@msu.edu)
Continue reading Milne's notes on etale cohomology

27008

Friday 3/12 3:00 PM

Jamie Schmidt; Alex Sietsema

Pattern Avoidance in Cyclic Permutations
 Jamie Schmidt; Alex Sietsema
 Pattern Avoidance in Cyclic Permutations
 03/12/2021
 3:00 PM  4:00 PM

 Keshav Sutrave (sutravek@msu.edu)
Pattern avoidance in permutations is a wellstudied field of enumerative combinatorics. We will discuss the classical version for linear permutations and then introduce a recent variant for cyclic permutations. Finally, we will present our new results counting cyclic avoidance sets for pairs of length 4 patterns and give examples of how those results arise from counting arguments, including a proof for a cyclic variant of the ErdősSzekeres Therorem.

28032

Friday 3/12 5:00 PM

Keping Huang, MSU

Drinfeld modules, continued
 Keping Huang, MSU
 Drinfeld modules, continued
 03/12/2021
 5:00 PM  6:00 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Keping Huang (huangk23@msu.edu)
No abstract available.

28038

Monday 3/15 11:00 AM

Peter Liljedahl, Simon Fraser University

Building Thinking Classrooms
 Peter Liljedahl, Simon Fraser University
 Building Thinking Classrooms
 03/15/2021
 11:00 AM  12:00 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Lisa Keller (kellerl@msu.edu)
Due to inclement weather in Canada affecting the internet connection on March 5th, the Mathematics Education Colloquium will pick up where it left off on Monday, March 15th, 11:00 am  noon. Dr. Peter Liljedahl from Simon Fraser University will be presenting Building Thinking Classrooms. Abstract: Much of how classrooms look and much of what happens in them today is guided by institutional norms laid down at the inception of an industrialage model of public education. These norms have enabled a culture of teaching and learning that is often devoid of student thinking. In this session I present some of the results of over 15 years of research into how K12 and postsecondary teachers can transform their classrooms from a space where students mimic to where students think. The practiced discussed will intertwine with, and make extensive references to, the recently published book, Building Thinking Classrooms in Mathematics: 14 Teaching Practices for Enhancing Learning.

28040

Monday 3/15 2:00 PM

Luis Scoccola, Michigan State University

Approximate and discrete vector bundles in theory and in applications
 Luis Scoccola, Michigan State University
 Approximate and discrete vector bundles in theory and in applications
 03/15/2021
 2:00 PM  3:00 PM
 Online (virtual meeting)
 Shelley Kandola (kandola2@msu.edu)
Synchronization problems, such as the problem of reconstructing a 3D shape from a set of 2D projections, can often be modeled by principal bundles. Similarly, the application of local PCA to a point cloud concentrated around a manifold approximates the tangent bundle of the manifold. In the first case, the characteristic classes of the bundle provide obstructions to global synchronization, while, in the second case, they provide obstructions to dimensionality reduction.
I will describe joint work with Jose Perea in which we propose several notions of approximate and discrete vector bundle, study the extent to which they determine true vector bundles, and give algorithms for the stable and consistent computation of lowdimensional characteristic classes directly from these combinatorial representations. No previous knowledge of the theory of vector bundles will be assumed.

27014

Monday 3/15 2:00 PM

Christopher Shirley, ParisSaclay University

Stationary random Schrödinger operators at small disorder
 Christopher Shirley, ParisSaclay University
 Stationary random Schrödinger operators at small disorder
 03/15/2021
 2:00 PM  3:00 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Jeffrey Hudson Schenker (schenke6@msu.edu)
In this presentation, we will study Schrödinger operators with stationary potential and the existence of stationary Bloch waves for several types of stationarity and in particular in the random case. We will see that the Bloch waves of the unperturbed operator seem to vanish at weak disorder in the case of shortrange correlations. This phenomenon suggests a resonance problem, difficult to study due to the lack of compactness.
We therefore investigate this problem using Mourre theory.

28036

Tuesday 3/16 10:00 AM


Coffee hour and hands on experience with Gather.town

 Coffee hour and hands on experience with Gather.town
 03/16/2021
 10:00 AM  11:00 AM
 Online (virtual meeting)
(Virtual Meeting Link)
 Tsvetanka Sendova (tsendova@msu.edu)
No abstract available.

26978

Tuesday 3/16 2:50 PM

Keegan Boyle, UBC

Equivariant genera of strongly invertible knots
 Keegan Boyle, UBC
 Equivariant genera of strongly invertible knots
 03/16/2021
 2:50 PM  3:40 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Honghao Gao (gaohongh@msu.edu)
Given a knot $K$, the minimum genus of an orientable surface embedded in $S^3$ or $B^4$ with boundary $K$ is a natural measure of knot complexity. In this talk I will generalize this idea to involutions on knots, focusing on the case where the involution preserves the orientation of $S^3$, but reverses the orientation of $K$. This talk is elementary in nature and will be very accessible. This is joint work with Ahmad Issa.

26946

Tuesday 3/16 4:00 PM

Martin Olsson, UC Berkeley

The Zariski topology, linear systems, and reconstruction of algebraic varieties
 Martin Olsson, UC Berkeley
 The Zariski topology, linear systems, and reconstruction of algebraic varieties
 03/16/2021
 4:00 PM  5:00 PM
 Online (virtual meeting)
 Aaron D Levin ()
The classical VeblenYoung theorem characterizes axiomatically projective spaces over fields. It is natural to ask for generalizations of this fundamental result to arbitrary algebraic varieties. In this colloquium I will survey work in this direction, and discuss recent progress characterizing algebraic varieties in terms of their Zariski topological spaces. The main new results are joint with János Kollár, Max Lieblich, and Will Sawin.

28037

Wednesday 3/17 3:00 PM

Stephanie van Willigenburg, University of British Columbia

The epositivity of chromatic symmetric functions
 Stephanie van Willigenburg, University of British Columbia
 The epositivity of chromatic symmetric functions
 03/17/2021
 3:00 PM  3:50 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Bruce E Sagan (bsagan@msu.edu)
The chromatic polynomial was generalized to the chromatic symmetric function by Stanley in his seminal 1995 paper. This function is currently experiencing a flourishing renaissance, in particular the study of the positivity of chromatic symmetric functions when expanded into the basis of elementary symmetric functions, that is, epositivity.
In this talk we approach the question of epositivity from various angles. Most pertinently we resolve the 1995 statement of Stanley that no known graph exists that is not contractible to the claw, and whose chromatic symmetric function is not epositive.
This is joint work with Soojin Cho, Samantha Dahlberg, Angele Foley and Adrian She, and no prior knowledge is assumed.

28033

Wednesday 3/17 4:00 PM

Tristan Wells, Michigan State University

Crash Course on Handles and 4 Manifolds
 Tristan Wells, Michigan State University
 Crash Course on Handles and 4 Manifolds
 03/17/2021
 4:00 PM  5:00 PM

 Danika Vanniel (vannield@msu.edu)
Abstract: I will quickly introduce some background of 4 manifolds and their important characteristics, like the intersection form. Then I will roughly follow chapter 4 of Gompf and Stipsicz book on 4 manifolds, chapters 4 and 5, in formulating handle decompositions of 4 manifolds. After considering handle moves, I will then mention how this tool is useful in knot theory and surgery on 3 and 4 manifolds.
https://msu.zoom.us/j/91485321701
Password: SGTS

26955

Wednesday 3/17 4:00 PM

Daniel Bragg, University of California, Berkeley

Compactifications of supersingular twistor spaces
 Daniel Bragg, University of California, Berkeley
 Compactifications of supersingular twistor spaces
 03/17/2021
 4:00 PM  5:00 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Rajesh S Kulkarni (kulkar23@msu.edu)
Supersingular twistor spaces are certain families of K3 surfaces over A^1 associated to a supersingular K3 surface. We will describe a geometric construction that produces families of K3 surfaces over P^1 which compactify supersingular twistor spaces. The key input is a construction relating Brauer classes of order p on a scheme of characteristic p to certain sheaves of twisted differential operators. We will give some results on the geometry of compactified supersingular twistor spaces, and some applications.

27002

Thursday 3/18 2:30 PM

Roberto Imbuzeiro Oliveira, IMPA, Rio de Janeiro

Sample average approximation with heavier tails
 Roberto Imbuzeiro Oliveira, IMPA, Rio de Janeiro
 Sample average approximation with heavier tails
 03/18/2021
 2:30 PM  3:30 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Olga Turanova (turanova@msu.edu)
Consider an "ideal" optimization problem where constraints and objective function are defined in terms of expectations over some distribution P. The sample average approximation (SAA)  a fundamental idea in stochastic optimization  consists of replacing the expectations by an average over a sample from P. A key question is how much the solutions of the SAA differ from those of the original problem. Results by Shapiro from many years ago consider what happens asymptotically when the sample size diverges, especially when the solution of the ideal problem lies on the boundary of the feasible set. In joint work with Philip Thompson (Purdue), we consider what happens with finite samples. As we will see, our results improve upon the nonasymptotic state of the art in various ways: we allow for heavier tails, unbounded feasible sets, and obtain bounds that (in favorable cases) only depend on the geometry of the feasible set in a small neighborhood of the optimal solution. Our results combine "localization" and "fixedpoint" type arguments inpired by the work of Mendelson with chainingtype inequalities. One of our contributions is showing what can be said when the SAA constraints are random.

28039

Thursday 3/18 5:00 PM

Brent Nelson, Michigan State University

Complex analysis applied to operator algebras
 Brent Nelson, Michigan State University
 Complex analysis applied to operator algebras
 03/18/2021
 5:00 PM  5:50 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Brent Nelson (banelson@msu.edu)
Given a positive definite matrix $D\in M_n(\mathbb{C})$ with $\text{Tr}(D)=1$, one can define a linear functional $\varphi\colon M_n(\mathbb{C})\to \mathbb{C}$ by $\varphi(x):=\text{Tr}(Dx)$ which we call a faithful state. This positive definite matrix also encodes a noncommutative dynamical system through $x\mapsto D^{it} x D^{it}$ for $t\in \mathbb{R}$. From the perspective of operator algebras, it is useful to encode this dynamical system as... well, an algebra of operators. More precisely, as a $*$algebra $\mathcal{M}$ containing $M_n(\mathbb{C})$ in a way that remembers the action of $\mathbb{R}$. In the general (infinite dimensional) setting, this is accomplished using crossed products and Tomita–Takesaki theory. In this talk, I will apply these methods to the more modest finite dimensional case, and show how a little bit of complex analysis allows one to find the analogue of $\text{Tr}$ on this larger $*$algebra $\mathcal{M}$. (This talk will assume some familiarity with linear algebra and complex analysis, but nothing further.)

28035

Friday 3/19 1:00 PM

Ivan So, MSU

Student algebra seminar
 Ivan So, MSU
 Student algebra seminar
 03/19/2021
 1:00 PM  2:00 PM
 C117 Wells Hall
(Virtual Meeting Link)
 Joshua Ruiter (ruiterj2@msu.edu)
Continue reading Milne's notes on etale cohomology

28041

Friday 3/19 3:00 PM

Laure Flapan, Michigan State University

AMS/AWM Joint Lecture: The Hodge Conjecture (or how to make a million dollars the hard way)
 Laure Flapan, Michigan State University
 AMS/AWM Joint Lecture: The Hodge Conjecture (or how to make a million dollars the hard way)
 03/19/2021
 3:00 PM  4:00 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Teena Meredith Gerhardt (gerhar18@msu.edu)
The Hodge Conjecture, one of the seven Millennium Prize problems, provides a compelling description of the interaction between the topological, analytic, and algebraic structure of a smooth projective variety. In this talk, I will give a gentle introduction to the Hodge Conjecture and describe work related to and inspired by the Conjecture.
(The talk will be followed by a 30minute meetandgreet.)

29040

Friday 3/19 5:00 PM

Keping Huang, MSU

Endomorphisms of Drinfeld modules
 Keping Huang, MSU
 Endomorphisms of Drinfeld modules
 03/19/2021
 5:00 PM  6:00 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Keping Huang (huangk23@msu.edu)
No abstract available.

29044

Monday 3/22 2:00 PM

Balija Santoshkumar, MSU

Robust Zerocrossing Detection in Noisy Signals Using Topological Signal Processing
 Balija Santoshkumar, MSU
 Robust Zerocrossing Detection in Noisy Signals Using Topological Signal Processing
 03/22/2021
 2:00 PM  3:00 PM
 Online (virtual meeting)
 Shelley Kandola (kandola2@msu.edu)
Detecting zerocrossings in noisy signals is a classical problem that has been researched for over
a century. Some of the prominent applications of zerocrossing detection are phase and frequency
determination in oscillatory systems, smooth switching operations in power systems, image processing and recognition, speech processing and reconstruction of audio signals, biometrics using human
iris, and bar code scanners. This work leverages Topological Signal Processing (TSP), more specifically persistent homology, to develop a simple but powerful zero crossing detection algorithm. The
algorithm utilizes zerodimensional persistent homology to estimate the zerocrossings in a noisy
signal, and uses the resulting persistence diagram to find out the significant splits in data to bound
the zero crossings. We compare the accuracy and speed of our approach with available methods
in the literature using different types of noisy signals, as well as showing sensitivity studies that
consider the sampling frequency (SF), and Signal to Noise Ratio (SNR). Our results show that
TSP can be directly applied to unfiltered signals with moderate to high noise levels for finding
the zerocrossings. In contrast to many existing tools, our approach does not require any complex
analog circuitry, iterative solvers, or filtering.

27028

Tuesday 3/23 10:00 AM

Sarah Klanderman , Marian University

MasteryBased Grading in Calculus
 Sarah Klanderman , Marian University
 MasteryBased Grading in Calculus
 03/23/2021
 10:00 AM  11:00 AM
 Online (virtual meeting)
(Virtual Meeting Link)
 Tsvetanka Sendova (tsendova@msu.edu)
No abstract available.

26992

Tuesday 3/23 2:50 PM

Samantha Allen, Dartmouth

Using surgery to study unknotting with a single twist
 Samantha Allen, Dartmouth
 Using surgery to study unknotting with a single twist
 03/23/2021
 2:50 PM  3:40 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Honghao Gao (gaohongh@msu.edu)
Ohyama showed that any knot can be unknotted by performing two full twists, each on a set of parallel strands. We consider the question of whether or not a given knot can be unknotted with a single full twist, and if so, what are the possible linking numbers associated to such a twist. It is observed that if a knot can be unknotted with a single twist, then some surgery on the knot bounds a rational homology ball. Using tools such as classical invariants and invariants arising from Heegaard Floer theory, we give obstructions for a knot to be unknotted with a single twist of a given linking number. In this talk, I will discuss some of these obstructions, their implications (especially for alternating knots), many examples, and some unanswered questions. This talk is based on joint work with Charles Livingston.

29045

Wednesday 3/24 3:00 PM

Jo EllisMonaghan, Kortewegde Vries Instituut voor Wiskunde, Universiteit van Amsterdam

Graph theoretical tools for DNA selfassembly
 Jo EllisMonaghan, Kortewegde Vries Instituut voor Wiskunde, Universiteit van Amsterdam
 Graph theoretical tools for DNA selfassembly
 03/24/2021
 3:00 PM  3:50 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Bruce E Sagan (bsagan@msu.edu)
Applications of immediate concern have driven some of the most interesting questions in the field of graph theory, for example graph drawing and computer chip layout problems, random graph theory and modeling the internet, graph connectivity measures and ecological systems, etc. Currently, scientists are engineering selfassembling DNA molecules to serve emergent applications in biomolecular computing, nanoelectronics, biosensors, drug delivery systems, and organic synthesis. Often, the selfassembled objects, e.g. lattices or polyhedral skeletons, may be modeled as graphs. Thus, these new technologies in selfassembly are now generating challenging new design problems for which graph theory is a natural tool. We will present some new applications in DNA selfassembly and describe some of the graphtheoretical design strategy problems arising from them. We will see how finding optimal design strategies leads to developing new algorithms for graphs, addressing new computational complexity questions, and finding new graph invariants corresponding to the minimum number of components necessary to build a target structure under various laboratory settings.

29041

Wednesday 3/24 4:00 PM

Alexander Volberg, MSU

Weighted Poincare inequality and discrete potential theory on graphs with cycles
 Alexander Volberg, MSU
 Weighted Poincare inequality and discrete potential theory on graphs with cycles
 03/24/2021
 4:00 PM  5:00 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Dapeng Zhan (zhan@msu.edu)
TBD

26977

Wednesday 3/24 4:00 PM

Stefan Patrikis, Ohio State University

Lifting Galois representations
 Stefan Patrikis, Ohio State University
 Lifting Galois representations
 03/24/2021
 4:00 PM  5:00 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Igor Rapinchuk (rapinchu@msu.edu)
I will survey joint work with Najmuddin Fakhruddin and Chandrashekhar Khare in which we prove in many cases existence of geometric padic lifts of "odd" mod p Galois representations, valued in general reductive groups. Then I will discuss applications to modularity of reducible mod p Galois representations, including most cases of a generalization of Serre's modularity conjecture to reducible (but not necessarily indecomposable) odd twodimensional representations of the Galois group of Q. Passcode: MSUALG

27003

Thursday 3/25 2:30 PM

Rachel Ward , University of Texas at Austin

Function Approximation via Sparse Random Features
 Rachel Ward , University of Texas at Austin
 Function Approximation via Sparse Random Features
 03/25/2021
 2:30 PM  2:30 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Olga Turanova (turanova@msu.edu)
Random feature methods have been successful in various machine learning tasks, are easy to compute, and come with theoretical accuracy bounds. They serve as an alternative approach to standard neural networks since they can represent similar function spaces without a costly training phase. However, for accuracy, random feature methods require more measurements than trainable parameters, limiting their use for datascarce applications or problems in scientific machine learning. This paper introduces the sparse random feature method that learns parsimonious random feature models utilizing techniques from compressive sensing. We provide uniform bounds on the approximation error for functions in a reproducing kernel Hilbert space depending on the number of samples and the distribution of features. The error bounds improve with additional structural conditions, such as coordinate sparsity, compact clusters of the spectrum, or rapid spectral decay. We show that the sparse random feature method outperforms shallow networks for wellstructured functions and applications to scientific machine learning tasks.

27009

Friday 3/26 3:00 PM

Joe Melby

The Figure Eight Knot (The Friendliest Knot)
 Joe Melby
 The Figure Eight Knot (The Friendliest Knot)
 03/26/2021
 3:00 PM  4:00 PM

(Virtual Meeting Link)
 Keshav Sutrave (sutravek@msu.edu)
Even on its laziest days, the figureeight knot keeps climbers from falling and a boat's sails in place better than the measly trefoil overhand knot (totally inferior knot). Does the figureeight save lives? Many would say so. We will discuss the topology and geometry of this lifesaving knot, which is the unique 4crossing and the simplest hyperbolic knot. Our friend the figureeight knot will guide us as we introduce some important classical concepts and techniques in the fields of knot theory and lowdimensional topology. This is a BYOR (Bring Your Own Rope) event due to COVID19.

29046

Friday 3/26 5:00 PM

Keping Huang, MSU

Cyclotomic function fields
 Keping Huang, MSU
 Cyclotomic function fields
 03/26/2021
 5:00 PM  6:00 PM
 Online (virtual meeting)
 Keping Huang (huangk23@msu.edu)
No abstract available.

29052

Monday 3/29 2:00 PM

Jiahui Chen, MSU

Evolutionary de RhamHodge method
 Jiahui Chen, MSU
 Evolutionary de RhamHodge method
 03/29/2021
 2:00 PM  3:00 PM
 Online (virtual meeting)
 Shelley Kandola (kandola2@msu.edu)
The de RhamHodge theory is a landmark of the 20 th Century’s mathematics and has had a great impact on mathematics, physics, computer science, and engineering. This work introduces an evolutionary de RhamHodge method to provide a unified paradigm for the multiscale geometric and topological analysis of evolving manifolds constructed from a filtration, which induces a family of evolutionary de Rham complexes. While the present method can be easily applied to close manifolds, the emphasis is given to more challenging compact manifolds with 2manifold boundaries, which require appropriate analysis and treatment of boundary conditions on differential forms to maintain proper topological properties. Three sets of unique evolutionary Hodge Laplacians are proposed to generate three sets of topologypreserving singular spectra, for which the multiplicities of zero eigenvalues correspond to exactly the persistent Betti numbers of dimensions 0, 1, and 2. Additionally, three sets of nonzero eigenvalues further reveal both topological persistence and geometric progression during the manifold evolution. Extensive numerical experiments are carried out via the discrete exterior calculus to demonstrate the potential of the proposed paradigm for data representation and shape analysis. To demonstrate the utility of the proposed method, the application is considered to the protein Bfactor predictions of a few challenging cases for which other existing models do not work well.

26980

Tuesday 3/30 11:00 AM

Renaud Detcherry, Bourgogne

A quantum obstruction to purely cosmetic surgeries
 Renaud Detcherry, Bourgogne
 A quantum obstruction to purely cosmetic surgeries
 03/30/2021
 11:00 AM  11:50 AM
 Online (virtual meeting)
(Virtual Meeting Link)
 Honghao Gao (gaohongh@msu.edu)
The cosmetic surgery conjecture asks whether it is possible that two Dehnsurgeries on the same nontrivial knot in S³ give the same oriented 3manifolds. We will present new obstructions for a knot to admit purely cosmetic surgeries, using ReshetikhinTuraev invariants. In particular, we will show that if a knot admits purely cosmetic surgeries, then the slopes of the surgery are +1/5k unless the Jones polynomial of K is 1 at the fifth root of unity.

29042

Tuesday 3/30 4:00 PM

CRLT Players , https://crlt.umich.edu/crltplayers

Shoulda, Woulda, Coulda: Moving Beyond Failure and Actively Cultivating a More Equitable Academy
 CRLT Players , https://crlt.umich.edu/crltplayers
 Shoulda, Woulda, Coulda: Moving Beyond Failure and Actively Cultivating a More Equitable Academy
 03/30/2021
 4:00 PM  5:30 PM
 Online (virtual meeting)
 Aaron D Levin ()
The University of Michigan Math Department is hosting a special colloquium on Tuesday, March 30, 4pm5:30pm. The CRLT players will present an interactive workshop using a video case study to stimulate reflection on our academic climate and norms. We warmly invite staff, graduate students, postdocs, and faculty from both the UM and MSU Mathematics Departments to attend this unique event. Please note that this workshop is not recommended for undergraduate students. This colloquium is organized by the UM Math Department's Climate Committee and Learning Community for Inclusive Teaching (LCIT). Preregistration is required. Registration Link: https://umich.zoom.us/meeting/register/tJckfu6opjkrH9CMTj5lZzXoHTDyldlT_X_5 Systems of higher education in the U.S. create differential advantage and disadvantage for the people who work and learn in them. When individuals move through these systemsas administrators, instructors, or learnersthey make choices to participate in the perpetuation or the disruption of these inequities. While some perpetuation of inequity can be attributed to ignorance, it is often true that individuals who do understand the harmful impacts of unjust behavior, processes, and structures often fail to address them. This session centers around an embodied case study depicting one manâ€™s meditation on a personal failure and the choices he made afterward that defined his path as an educator. Through session activities, participants will reflect on what failures of this kind indicate about the educational environments in which they occur and how such reflection might prime them to reshape the spaces in which they have responsibilities. In this session, participants will: Reflect on their personal failures to act for justice. Consider how their lived relationship to social inequities within and outside of their educational environment shape their willingness and ability to act. Explore the tension between risk and responsibility when disrupting the status quo. Practice identifying opportunities for proactive justice work in their spheres of influence in the academy. Content flag: The theatrical portion of this session contains strong language. It includes descriptions of sexist, heterosexist, and ableist behaviors and reflection on systemic inequities related to race and socioeconomic status. Note: This colloquium workshop will last 90 minutes, not the typical hour.

29047

Wednesday 3/31 3:00 PM

Ira Gessel, Brandeis University

Counting graphs with neighborhood restrictions
 Ira Gessel, Brandeis University
 Counting graphs with neighborhood restrictions
 03/31/2021
 3:00 PM  3:50 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Bruce E Sagan (bsagan@msu.edu)
A graph is called pointdetermining (or mating type) if no two vertices have the same neighborhood. An arbitrary graph can be reduced to a pointdetermining graph by contracting each set of vertices with the same neighborhood to a single vertex, and this decomposition enables us to give a simple exponential generating function for counting pointdetermining graphs, as accomplished by Ronald Read in 1989. In this talk we will discuss a closely related problem: counting graphs in which no two vertices have complementary neighborhoods. The decomposition approach does not work here. Instead we apply inclusionexclusion, similarly to its use in rook theory, to obtain a simple exponential generating function for these graphs. We also discuss how this application of inclusionexclusion is related to Möbius inversion, and how it can be applied to some related problems.

29043

Wednesday 3/31 4:00 PM

Peter Yuditskii, Johannes Kepler University Linz

The Deift conjecture
 Peter Yuditskii, Johannes Kepler University Linz
 The Deift conjecture
 03/31/2021
 4:00 PM  5:00 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Dapeng Zhan (zhan@msu.edu)
At his 60th birthday conference in 2005, Percy Deift was asked to present a list of unsolved problems. This list was updated ten years later, on his 70th birthday conference. As the number one unsolved problem in both lists we still have the following conjecture.
Problem 1.1 (KdV with almost periodic initial data). Consider the Korteweg–de Vries (KdV) equation
$$u_t +uu_x +u_{xxx} =0 $$
with initial data
$$u(x,t=0)=q(x),\quad x\in\mathbb{R}.$$
In the 1970’s, McKean and Trubowitz proved the remarkable result that if the initial data $q(x)$ is periodic, $q(x + T ) = q(x)$ for some $T > 0$, then the solution $u(x, t)$ is almost periodic in time. This result leads to the following natural conjecture: The same is true if $q(x)$ is almost periodic, i.e., if the initial data is almost periodic in space, the solution evolves almost periodically in time.
Zoom Link:
https://msu.zoom.us/j/94297154840
Passcode: the same as the last time

26997

Wednesday 3/31 4:00 PM

Oscar Rivero, University of Warwick

Motivic congruences and Sharifi's conjecture
 Oscar Rivero, University of Warwick
 Motivic congruences and Sharifi's conjecture
 03/31/2021
 4:00 PM  5:00 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Preston Wake (wakepres@msu.edu)
Let f be a cuspidal eigenform of weight two, and let p be a prime at which f is congruent to an Eisenstein series. Beilinson constructed a class arising from the cupproduct of two Siegel units and proved a striking relationship with the first derivative L'(f,0) at the near central point s=0 of the Lseries of f. In this talk, I will motivate the study of congruences between modular forms at the level of cohomology classes, and will report on a joint work with Victor Rotger where we prove two congruence formulas relating the motivic part of L'(f,0) modulo p and L''(f,0) modulo p with circular units. The proofs make use of delicate Galois properties satisfied by various integral lattices and exploits PerrinRiou's, Coleman's and Kato's work on the Euler systems of circular units and BeilinsonKato elements and, most crucially, the work of FukayaKato.

27004

Thursday 4/1 2:30 PM

Yi Ma , University of California, Berkeley

Deep Networks from First Principles
 Yi Ma , University of California, Berkeley
 Deep Networks from First Principles
 04/01/2021
 2:30 PM  2:30 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Olga Turanova (turanova@msu.edu)
In this talk, we offer an entirely “white box’’ interpretation of deep (convolution) networks from the perspective of data compression (and group invariance). In particular, we show how modern deep layered architectures, linear (convolution) operators and nonlinear activations, and even all parameters can be derived from the principle of maximizing rate reduction (with group invariance). All layers, operators, and parameters of the network are explicitly constructed via forward propagation, instead of learned via back propagation. All components of soobtained network, called ReduNet, have precise optimization, geometric, and statistical interpretation. There are also several nice surprises from this principled approach: it reveals a fundamental tradeoff between invariance and sparsity for class separability; it reveals a fundamental connection between deep networks and Fourier transform for group invariance – the computational advantage in the spectral domain (why spiking neurons?); this approach also clarifies the mathematical role of forward propagation (optimization) and backward propagation (variation). In particular, the soobtained ReduNet is amenable to finetuning via both forward and backward (stochastic) propagation, both for optimizing the same objective.
This is joint work with students Yaodong Yu, Ryan Chan, Haozhi Qi of Berkeley, Dr. Chong You now at Google Research, and Professor John Wright of Columbia University.

29048

Friday 4/2 1:00 PM

Joshua Ruiter, MSU

Student algebra seminar
 Joshua Ruiter, MSU
 Student algebra seminar
 04/02/2021
 1:00 PM  2:00 PM
 C117 Wells Hall
(Virtual Meeting Link)
 Joshua Ruiter (ruiterj2@msu.edu)
The category of sheaves on the etale site of a variety or scheme.

27023

Tuesday 4/6 10:00 AM

Gabriel Nagy, MSU

Embedding interactive graphs (GeoGebra) in Webwork
 Gabriel Nagy, MSU
 Embedding interactive graphs (GeoGebra) in Webwork
 04/06/2021
 10:00 AM  11:00 AM
 Online (virtual meeting)
(Virtual Meeting Link)
 Tsvetanka Sendova (tsendova@msu.edu)
No abstract available.

26979

Tuesday 4/6 2:50 PM

Charlie Frohman, U Iowa

A Geometric Kauffman Bracket
 Charlie Frohman, U Iowa
 A Geometric Kauffman Bracket
 04/06/2021
 2:50 PM  3:40 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Honghao Gao (gaohongh@msu.edu)
This is joint work with Joanna KaniaBartoszynska and Thang Le $\\$
I will discuss the representation theory of the Kauffman bracket skein algebra of a finite type surface at a root of unity whose order is not divisible by 4. $\\$
Specifically, the Kauffman bracket skein algebra is an algebra with trace in the sense of De Concini, Procesi, Reshetikhin and Rosso, so it has a well defined character variety of trace preserving representations, which can be identified with a branched cover of the SL(2,C)character variety of the fundamental group of the underlying surface. $\\$
In the case of a closed surface the branched cover is trivial so its just the character variety of the fundamental group of the surface. $\\$
The skein algebra is also a Poisson order, so the character variety representations of the Kauffman bracket skein algebra of a closed surface decomposes into representations corresponding to irreducible, abelian and central representations of the fundamental group of the underlying surface. The irreducible representations of the fundamental group of the surface correspond to irreducible representations of the skein algebra. $\\$
We then use this as basic data to define an invariant of framed links in a threemanifold equipped with an irreducible representation of its fundamental group. The invariant satisfies the Kauffman bracket skein relations. $\\$
Such a representation could be the lift of the holonomy of a hyperbolic structure on the threemanifold, hence the title : A Geometric Kauffman Bracket. $\\$

26947

Tuesday 4/6 4:00 PM

Emily Riehl, Johns Hopkins University

Elements of ∞Category Theory
 Emily Riehl, Johns Hopkins University
 Elements of ∞Category Theory
 04/06/2021
 4:00 PM  5:00 PM
 Online (virtual meeting)
 Aaron D Levin ()
Confusingly for the uninitiated, experts in weak infinitedimensional category theory make use of different definitions of an ∞category, and theorems in the ∞categorical literature are often proven "analytically", in reference to the combinatorial specifications of a particular model. In this talk, we present a new point of view on the foundations of ∞category theory, which allows us to develop the basic theory of ∞categories  adjunctions, limits and colimits, co/cartesian fibrations, and pointwise Kan extensions  "synthetically" starting from axioms that describe an ∞cosmos, the infinitedimensional category in which ∞categories live as objects. We demonstrate that the theorems proven in this manner are "modelindependent", i.e., invariant under change of model. Moreover, there is a formal language with the feature that any statement about ∞categories that is expressible in that language is also invariant under change of model, regardless of whether it is proven through synthetic or analytic techniques. This is joint work with Dominic Verity.

29060

Wednesday 4/7 3:00 PM

Volker Strehl, FriedrichAlexanderUniversität

A valuation problem for strict partitions — and where it comes from
 Volker Strehl, FriedrichAlexanderUniversität
 A valuation problem for strict partitions — and where it comes from
 04/07/2021
 3:00 PM  3:50 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Bruce E Sagan (bsagan@msu.edu)
I will present a rational function valuation on strict partitions as shapes
that is defined via shifted standard tableaux. The goal is to determine
explicit expressions for this valuation by solving a linear system that
reflects the lattice structure of strict partitions.
Somewhat surprisingly, this leads into the area of symmetric functions.
The problem as such may appear as an isolated curiosity, yet is motivated
by the extension of the model for an asymmetric annihilation process originally proposed by A. Ayyer and K. Mallick (2010).

29050

Wednesday 4/7 4:00 PM

Dapeng Zhan, MSU

SchrammLoewner evolution and hypergeometric functions
 Dapeng Zhan, MSU
 SchrammLoewner evolution and hypergeometric functions
 04/07/2021
 4:00 PM  5:00 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Dapeng Zhan (zhan@msu.edu)
SchrammLoewner evolution (SLE for short) is a family of random fractal curves, which describe the scaling limits of some lattice models. When one studies SLE with additional marked points, and requires that those SLE satisfy certain nice properties, some special functions come into play. They arise as the solution of some secondorder partial differential equations. In this talk, I will describe how the onevariable and multivariable hypergeometric functions are used to study the timereversal of SLE$_\kappa(\rho_1,\dots,\rho_m)$ curves.
We use the same zoom link ant passcode as before.

26952

Wednesday 4/7 4:00 PM

Sarah Frei, Rice University

Rational points on moduli spaces of sheaves on K3 surfaces
 Sarah Frei, Rice University
 Rational points on moduli spaces of sheaves on K3 surfaces
 04/07/2021
 4:00 PM  5:00 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Rajesh S Kulkarni (kulkar23@msu.edu)
In this talk, I will report on ongoing work with Ryan Takahashi in which we study BrauerManin obstructions to the existence of rational points on moduli spaces of sheaves on K3 surfaces. There are Brauer classes naturally arising out of geometric constructions, and we aim to find conditions under which these Brauer classes obstruct the existence of certain kinds of sheaves on a K3 surface over a number field.

28028

Thursday 4/8 2:30 PM

Mahdi Soltanolkotabi, University of Southern California

Precise Tradeoffs for Adversarial Training
 Mahdi Soltanolkotabi, University of Southern California
 Precise Tradeoffs for Adversarial Training
 04/08/2021
 2:30 PM  3:30 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Olga Turanova (turanova@msu.edu)
Despite breakthrough performance, modern learning models are known to be highly vulnerable to small adversarial perturbations in their inputs. While a wide variety of recent adversarial training methods have been effective at improving robustness to perturbed inputs (robust accuracy), often this benefit is accompanied by a decrease in accuracy on benign inputs (standard accuracy), leading to a tradeoff between often competing objectives. Complicating matters further, recent empirical evidence suggests that a variety of other factors (size and quality of training data, model size, etc.) affect this tradeoff in somewhat surprising ways. In this talk we will provide a precise and comprehensive understanding of the role of adversarial training in the context of linear regression with Gaussian features and binary classification in a mixture model. We precisely characterize the standard/robust accuracy and the corresponding tradeoff achieved by a contemporary minimax adversarial training approach in a highdimensional regime where the number of data points and the parameters of the model grow in proportion to each other. Our theory for adversarial training algorithms also facilitates the rigorous study of how a variety of factors (size and quality of training data, model overparametrization etc.) affect the tradeoff between these two competing accuracies.

29064

Friday 4/9 1:00 PM

Chuangtian Guan, MSU

Formal Groups
 Chuangtian Guan, MSU
 Formal Groups
 04/09/2021
 1:00 PM  2:00 PM
 Online (virtual meeting)
 Chuangtian Guan (guanchua@msu.edu)
No abstract available.

27010

Friday 4/9 3:00 PM

Nick Krupansky

Home Economics 400: Basic financial concepts for entering the working world.
 Nick Krupansky
 Home Economics 400: Basic financial concepts for entering the working world.
 04/09/2021
 3:00 PM  4:00 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Keshav Sutrave (sutravek@msu.edu)
While we have undoubtedly mastered quantitative problem solving, in the coming months many of us will deal with some very common and personal quantitative decisions that we haven't encountered before: retirement benefits. The sooner you have a basic grasp of what benefits are available to you and their impact, the sooner you can make informed decisions and potential compare employment opportunities. As potential new employees, learn the basics of common retirement offerings for US employment and associated tax implications from a student with firsthand experience.

29061

Saturday 4/10 9:30 AM

Our undergraduate research teams!

Exchange Program REU Final Presentations

29063

Monday 4/12 2:00 PM

Haibin Hang, University of Delaware

Correspondence modules and their diagrams
 Haibin Hang, University of Delaware
 Correspondence modules and their diagrams
 04/12/2021
 2:00 PM  3:00 PM
 Online (virtual meeting)
 Shelley Kandola (kandola2@msu.edu)
In this talk, I will introduce correspondence modules (cmodules), which generalize persistence and zigzag modules. I also will introduce the persistence sheaf of sections of a cmodule, which is used to analyze its structure and prove an interval decomposition theorem. Several applications in which cmodules arise naturally will be discussed.

27013

Monday 4/12 2:00 PM

Rui Han , Louisiana State University

Spectral gaps in graphene structures
 Rui Han , Louisiana State University
 Spectral gaps in graphene structures
 04/12/2021
 2:00 PM  3:00 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Jeffrey Hudson Schenker (schenke6@msu.edu)
We will present a full spectral analysis for a model of graphene in magnetic fields with constant flux through every hexagonal comb. In particular, we provide a rigorous foundation for selfsimilarity by showing that for any irrational flux, the spectrum of graphene is a zero measure Cantor set. I will also discuss the spectral decomposition, Hausdorff dimension of the spectrum and existence of Dirac cones. This talk is based on joint works with S. Becker and S. Jitomirskaya.

29051

Tuesday 4/13 10:00 AM

Susan Richter, MSU

Impact of Math Gateway Reforms on Student Success
 Susan Richter, MSU
 Impact of Math Gateway Reforms on Student Success
 04/13/2021
 10:00 AM  11:00 AM
 Online (virtual meeting)
(Virtual Meeting Link)
 Tsvetanka Sendova (tsendova@msu.edu)
No abstract available.

26972

Tuesday 4/13 2:50 PM

Mustafa Hajij, Santa Clara University

AlgebraicallyInformed Deep Networks (AIDN): A Deep Learning Approach to Represent Algebraic Structures
 Mustafa Hajij, Santa Clara University
 AlgebraicallyInformed Deep Networks (AIDN): A Deep Learning Approach to Represent Algebraic Structures
 04/13/2021
 2:50 PM  3:40 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Honghao Gao (gaohongh@msu.edu)
One of the central problems in the interface of deep learning and mathematics is that of building learning systems that can automatically uncover underlying mathematical laws from observed data. In this work, we make one step towards building a bridge between algebraic structures and deep learning, and introduce\textbf {AIDN},\textit {AlgebraicallyInformed Deep Networks}.\textbf {AIDN} is a deep learning algorithm to represent any finitelypresented algebraic object with a set of deep neural networks. The deep networks obtained via\textbf {AIDN} are\textit {algebraicallyinformed} in the sense that they satisfy the algebraic relations of the presentation of the algebraic structure that serves as the input to the algorithm. Our proposed network can robustly compute linear and nonlinear representations of most finitelypresented algebraic structures such as groups, associative algebras, and Lie algebras. We evaluate our proposed approach and demonstrate its applicability to algebraic and geometric objects that are significant in lowdimensional topology. In particular, we study solutions for the YangBaxter equations and their applications on braid groups. Further, we study the representations of the TemperleyLieb algebra. Finally, we show, using the ReshetikhinTuraev construction, how our proposed deep learning approach can be utilized to construct new link invariants. We believe the proposed approach would tread a path toward a promising future research in deep learning applied to algebraic and geometric structures.

26948

Tuesday 4/13 4:00 PM

Adrian Ioana, UC San Diego

Classification and rigidity for group von Neumann algebras
 Adrian Ioana, UC San Diego
 Classification and rigidity for group von Neumann algebras
 04/13/2021
 4:00 PM  5:00 PM
 Online (virtual meeting)
 Aaron D Levin ()
Any countable group G gives rise to a von Neumann algebra L(G). The classification of these group von Neumann algebras is a central theme in operator algebras. I will survey recent rigidity results which provide instances when various algebraic properties of groups, such as the presence or absence of a direct product decomposition, are remembered by their von Neumann algebras. I will also explain the strongest such rigidity results, where L(G) completely remembers G, and discuss some of the open problems in the area.

29062

Wednesday 4/14 3:00 PM

Sara Billey, University of Washington

Existence and hardness of conveyor belts
 Sara Billey, University of Washington
 Existence and hardness of conveyor belts
 04/14/2021
 3:00 PM  3:50 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Bruce E Sagan (bsagan@msu.edu)
We will present the notion of a conveyor belt configuration on disjoint disks in the plane, which means a tight simple closed curve that touches the boundary of each disk. An open problem of Manuel Abellanas asks whether every set of disjoint closed unit disks in the plane can be connected by a conveyor belt, possibly touched multiple times. We will present three main results. 1) For unit disks whose centers are both xmonotone and ymonotone, or whose centers have xcoordinates that differ by at least two units, a conveyor belt always exists and can be found efficiently. 2) It is NPcomplete to determine whether disks of arbitrary radii have a conveyor belt, and it remains NPcomplete when we constrain the belt to touch disks exactly once. 3) Any disjoint set of n disks of arbitrary radii can be augmented by O(n) “guide” disks so that the augmented system has a conveyor belt touching each disk exactly once, answering a conjecture of Demaine, Demaine, and Palop. Many open problems remain on this topic and we will share some of our favorites. This talk is based on joint work with Molly Baird, Erik D. Demaine, Martin L. Demaine, David Eppstein, Sándor Fekete, Graham Gordon, Sean Griffin, Joseph S. B. Mitchell, and Joshua P. Swanson.

29058

Wednesday 4/14 3:00 PM

Ilya Kachkovskiy, MSU

Spectral bands of twodimensional periodic elliptic operators
 Ilya Kachkovskiy, MSU
 Spectral bands of twodimensional periodic elliptic operators
 04/14/2021
 3:00 PM  4:00 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Dapeng Zhan (zhan@msu.edu)
I will give an overview of spectral theory of second order elliptic operators on $\mathbb R^2$ on the example of Schrodinger operators and explain the main steps of the proof that spectral band edged are attained at finitely many values of the quasimomenta. If time permits, I will discuss related result and work in progress. The talk is based on joint work with N. Filonov.
Note: The meeting time is 3:00 pm instead of 4:00 pm.
We use the same zoom link and passcode as before.

26959

Wednesday 4/14 4:00 PM

Yihang Zhu, University of Maryland

Irreducible components of affine DeligneLusztig varieties
 Yihang Zhu, University of Maryland
 Irreducible components of affine DeligneLusztig varieties
 04/14/2021
 4:00 PM  5:00 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Igor Rapinchuk (rapinchu@msu.edu)
Affine DeligneLusztig varieties (ADLV) naturally arise from the study of Shimura varieties. We prove a formula for the number of their irreducible components, which was a conjecture of Miaofen Chen and Xinwen Zhu. Our method is to count the number of F_q points, and to relate it to certain twisted orbital integrals. We then study the growth rate of these integrals using the Base Change Fundamental Lemma of Clozel and Labesse. In an ongoing work we also give the number of irreducible components in the basic Newton stratum of a Shimura variety. This is joint work with Rong Zhou and Xuhua He. Password: MSUALG

28029

Thursday 4/15 2:30 PM

Michael Wakin, Colorado School of Mines

Spectral Properties of Timelimited Toeplitz Operators and Applications in Signal Processing
 Michael Wakin, Colorado School of Mines
 Spectral Properties of Timelimited Toeplitz Operators and Applications in Signal Processing
 04/15/2021
 2:30 PM  3:30 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Olga Turanova (turanova@msu.edu)
Toeplitz operators are fundamental and ubiquitous in signal processing and information theory as models for convolutional (filtering) systems. Due to the fact that any practical system can access only signals of finite duration, however, timelimited restrictions of Toeplitz operators are also of interest. In the discretetime case, timelimited Toeplitz operators are simply Toeplitz matrices. In this talk we survey existing and present new bounds on the eigenvalues (spectra) of timelimited Toeplitz operators, and we discuss applications of these results in various signal processing contexts. As a special case, we discuss timefrequency limiting operators, which alternatingly limit a signal in the time and frequency domains. Slepian functions arise as eigenfunctions of these operators, and we describe applications of Slepian functions in spectral analysis of multiband signals, superresolution SAR imaging, and blind beamforming in antenna arrays. This talk draws from joint work with numerous collaborators including Zhihui Zhu from the University of Denver.

29049

Thursday 4/15 5:00 PM

Rolando de Santiago, Purdue University

Groups, Group Actions, and von Neumann Algebras
 Rolando de Santiago, Purdue University
 Groups, Group Actions, and von Neumann Algebras
 04/15/2021
 5:00 PM  5:50 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Brent Nelson (banelson@msu.edu)
Given a group $G$ acting on measure space $(X,\mu)$ Murray and von Neumann’s groupmeasure space construction describes a von Neumann algebra $L^\infty(X,\mu)\rtimes G $ which encodes both the group, the space and the action. The special case where the space is a singleton and the action is trivial produces the group von Neumann algebra $L(G) $.
In this talk, we will aim to describe properties of $L^\infty(X,\mu)\rtimes G $ in terms of the group, the space and the action; compute $L^\infty(X,\mu)\rtimes G $ in special cases; and describe how the groupmeasure space varies or the group von Neumann algebra varies with $G$. All this serves to illustrate the fundamental problem in this area: von Neumann algebras tend to have poor memory of their generating data.
This talk assumes a working knowledge of group theory and linear algebra, and while knowledge of measure theory may be helpful, it is not required.

27011

Friday 4/16 3:00 PM

Paula Mercurio

An Introduction to Network Embedding for Data Clustering
 Paula Mercurio
 An Introduction to Network Embedding for Data Clustering
 04/16/2021
 3:00 PM  4:00 PM

(Virtual Meeting Link)
 Keshav Sutrave (sutravek@msu.edu)
I will introduce some of the basic ideas behind network embedding, and show how a complicated or highdimensional graph can be represented as a collection of points in a lowerdimensional vector space. This will be an expository talk focusing on random walkbased methods, and how these methods are related to certain matrixbased methods and diffusion maps. Throughout the talk, I'll show how these techniques are useful for machine learning tasks like social network analysis and image recognition.

29066

Monday 4/19 12:00 PM

Higinio Dominguez, MSU

The desire to do research: Where does it come from?
 Higinio Dominguez, MSU
 The desire to do research: Where does it come from?
 04/19/2021
 12:00 PM  1:00 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Lisa Keller (kellerl@msu.edu)
In this presentation, I will invite participants to follow me as I narrate in words and images my transition from colonial, imperialist research practices to creating knowledge with knowers. As part of this transition—which I see as continuous and liberating—I will discuss multiple powerful forces that have contributed to reinvigorate my eyes, ears, and all my senses, leading me to find my desire to do research in mathematics education desde adentro; that is, from inside the practices and wisdoms that I am trying to make sense. Two research projects, one recently completed and one that starts this Fall, will serve as important referents for gauging the intensities of my desire to do research. Participants are strongly encouraged to bring to this informal conversation insights, experiences, questions, wonderings, and contributions related to their desire to conduct research in education. There is no need to register! Just join the Zoom room at:
https://msu.zoom.us/j/91681702869
Passcode: 731530

29068

Monday 4/19 2:00 PM

Sarah Tymochko, MSU

Bifurcation Detection using Zigzag Persistence
 Sarah Tymochko, MSU
 Bifurcation Detection using Zigzag Persistence
 04/19/2021
 2:00 PM  3:00 PM
 Online (virtual meeting)
 Shelley Kandola (kandola2@msu.edu)
No abstract available.

27012

Monday 4/19 2:00 PM

Alexis Drouot, University of Washington

Mathematical aspects of topological insulators.
 Alexis Drouot, University of Washington
 Mathematical aspects of topological insulators.
 04/19/2021
 2:00 PM  3:00 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Jeffrey Hudson Schenker (schenke6@msu.edu)
Topological insulators are phases of matter that act like extraordinarily stable waveguides along their boundary. They have a rich mathematical structure that involves PDEs, spectral theory, and topology. I will survey some results and discuss some (semiclassical) directions of research.

29054

Tuesday 4/20 10:00 AM

Reshma Menon, Harvard

A yearlong introduction to calculus (integrated with functions)
 Reshma Menon, Harvard
 A yearlong introduction to calculus (integrated with functions)
 04/20/2021
 10:00 AM  11:00 AM
 Online (virtual meeting)
(Virtual Meeting Link)
 Tsvetanka Sendova (tsendova@msu.edu)
No abstract available.

26982

Tuesday 4/20 2:50 PM

Hannah Schwartz, Princeton

The failure of the 4D light bulb theorem with dual spheres of nonzero square
 Hannah Schwartz, Princeton
 The failure of the 4D light bulb theorem with dual spheres of nonzero square
 04/20/2021
 2:50 PM  3:40 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Honghao Gao (gaohongh@msu.edu)
Examples of surfaces embedded in a 4manifold that are homotopic but not isotopic are neither rare nor surprising. It is then quite amazing that, in settings such as the recent 4D light bulb theorems of both Gabai and SchneidermanTeichner, the existence of an embedded sphere of square zero intersecting a surface transversally in a single point has the power to "upgrade" a homotopy of that surface into a smooth isotopy. We will discuss the limitations of this phenonemon, using contractible 4manifolds called corks to produce homotopic spheres in a 4manifold with a common dual of nonzero square that are not smoothly isotopic.

26949

Tuesday 4/20 4:00 PM

Nicolas Addington, University of Oregon

Cubic fourfolds
 Nicolas Addington, University of Oregon
 Cubic fourfolds
 04/20/2021
 4:00 PM  5:00 PM
 Online (virtual meeting)
 Aaron D Levin ()
When I tell people that cubic fourfolds are a hot topic in algebraic geometry, they're often incredulous at what sounds like a random choice of numbers  why those and not, say, quartic threefolds? But cubic fourfolds are more interesting than hypersurfaces of other degrees and dimensions for two reasons: first, the classical question of which ones are "rational" is unexpectedly hard, lying just out of reach of both old and new techniques; second, they have unexpected connections to K3 surfaces and hyperkähler manifolds, through Hodge theory, derived categories of coherent sheaves, and beautiful geometric constructions. I'll try to give a taste of what has attracted so many people to this topic in the last 15 to 25 years.
The talk will be aimed at a general mathematical audience, including graduate students.

29067

Wednesday 4/21 3:00 PM

Victor Reiner, University of Minnesota

Conjectures on cohomology of Grassmannians
 Victor Reiner, University of Minnesota
 Conjectures on cohomology of Grassmannians
 04/21/2021
 3:00 PM  3:50 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Bruce E Sagan (bsagan@msu.edu)
The cohomology ring of the Grassmannian is wellstudied, with Hilbert series given by a qbinomial coefficient. A 2003 conjecture with G. Tudose asserts that for each m = 0,1,2,..., the subring of the cohomology generated by the elements of degree at most m also has a predictable Hilbert series.
After reviewing this conjecture, we will report on two pieces of progress from our Summer 2020 "Polymath Jr." REU group. The first reinterprets the conjecture in terms of the kconjugation operation on kbounded partitions. The second gives the Lagrangian Grassmannian analogue of the conjecture. (see arXiv:math/0309281, arXiv:2011.03179)

29059

Wednesday 4/21 4:00 PM

Seonghyeon Jeong, MSU

The Kantorovich duality and cconvexity
 Seonghyeon Jeong, MSU
 The Kantorovich duality and cconvexity
 04/21/2021
 4:00 PM  5:00 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Dapeng Zhan (zhan@msu.edu)
The Kantorovich duality was a big breakthrough in the optimal transportation problem. The Kantorovich duality provides information of the transportation plan. In this talk, I present two proofs of the Kantorovich duality. The first proof uses the cconvex functions and ArzelaAscoli to construct a solution of the dual problem. The second proof uses a geometric property of the support of the transportation plan which is called ccyclical monotonicity.
We are going to use the same zoom link and passcode as before.

26996

Wednesday 4/21 4:00 PM

Jonathan Wang, MIT

Intersection complexes and unramified Lfactors
 Jonathan Wang, MIT
 Intersection complexes and unramified Lfactors
 04/21/2021
 4:00 PM  5:00 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Preston Wake (wakepres@msu.edu)
A series of conjectures of BravermanKazhdan, Sakellaridis and SakellaridisVenkatesh propose that affine spherical varieties should provide a source for new integral representations of automorphic Lfunctions. This global problem is conjecturally (and sometimes provably) related to a certain local problem in harmonic analysis. In particular, it is conjectured that unramified local Lfactors are related to intersection complexes of formal arc spaces of spherical varietes. I will explain how we establish this connection for a large class of spherical varieties over a local function field, using techniques from geometric representation theory. This is joint work with Yiannis Sakellaridis.

28030

Thursday 4/22 4:30 AM

Shahar Mendelson, Australian National University

Approximating L_p balls via sampling
 Shahar Mendelson, Australian National University
 Approximating L_p balls via sampling
 04/22/2021
 4:30 AM  5:30 AM
 Online (virtual meeting)
(Virtual Meeting Link)
 Olga Turanova (turanova@msu.edu)
Let X be a centred random vector in R^n. The L_p norms that X endows on R^n are defined by \v\_{L_p}= (E<X,v>^p)^{1/p}. The goal is to approximate those L_p norms, and the given data consists of N independent sample points X_1,...,X_N distributed as X. More accurately, one would like to construct datadependent functionals \phi_{p,\epsilon} which satisfy with (very) high probability, that for every v in R^n, (1\epsilon) \phi_{p,\epsilon} \leq E<X,v>^p \leq (1+\epsilon) \phi_{p,\epsilon}.
I will show that the functionals \frac{1}{N}\sum_{j \in J} <X_j,v>^p are a good choice, where the set of indices J is obtained from \{1,...,N\} by removing the c\eps^2 N largest values of <X_j,v>. Under mild assumptions on X, only N=(c^p)\epsilon^{2} n measurements are required, and the probability that the functional performs well is at least 12\exp(c\epsilon^2 N).

27016

Monday 4/26 2:00 PM

Jacob Shapiro, Princeton University

Tightbinding limits in strong magnetic fields and the integer quantum Hall effect
 Jacob Shapiro, Princeton University
 Tightbinding limits in strong magnetic fields and the integer quantum Hall effect
 04/26/2021
 2:00 PM  3:00 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Jeffrey Hudson Schenker (schenke6@msu.edu)
Tightbinding models of noninteracting electrons in solids are commonly used when studying the integer quantum Hall effect or more generally topological insulators. However, up until recently there was no proof that the topological properties of these discrete Schrodinger operators agree with those of the continuum models of which they are the tightbinding limit. Before tending to this question, we first tackle the basic issue of the doublewell eigenvalue splitting in strong perpendicular constant magnetic fields in 2D. Once this is understood, we set up normresolvent convergence of a scaled continuum Schrodinger operator on L^2(R^2) (a magnetic Laplacian plus a lattice potential) to its tightbinding limit and finally show why the Chern numbers of these two models, discrete and continuum respectively, must agree. This talk is based on joint collaborations with C. L. Fefferman and M. I. Weinstein.

27026

Tuesday 4/27 2:50 PM

David Gay, University of Georgia

Diffeomorphisms of the 4sphere, Cerf theory and Montesinos twins
 David Gay, University of Georgia
 Diffeomorphisms of the 4sphere, Cerf theory and Montesinos twins
 04/27/2021
 2:50 PM  3:40 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Honghao Gao (gaohongh@msu.edu)
I'm interested in the smooth mapping class group of $S^4$, i.e. $\pi_0(\mathrm{Diff}^+(S^4))$. We know that every orientation preserving diffeomorphism of $S^4$ is pseudoisotopic to the identity (Proving this is a fun exercise, starting with the fact that there are no exotic 5spheres). Cerf theory studies the problem of turning pseudoisotopies into isotopies using parametrized Morse theory. Most of what works in Cerf theory works in dimension 5 and higher, but with a little digging one discovers statements that work in dimension 4 as well. Putting all this stuff together we can show that there is a surjective homomorphism from (a certain limit of) fundamental groups of spaces of embeddings of 2spheres in connected sums of $S^2\times S^2$ onto this smooth mapping class group of $S^4$. Furthermore, we can identify two natural, and in some sense complementary, subgroups of this fundamental group, one in the kernel of this homomorphism and one whose image we can understand explicitly in terms of Dehn twistlike diffeomorphisms supported near pairs of embedded $S^2$'s in $S^4$ (Montesinos twins).

29069

Wednesday 4/28 4:00 PM

Rami Fakhry, MSU

(Postponed to May 5) Multipoint Boundary Green's function for Chordal SLE curves
 Rami Fakhry, MSU
 (Postponed to May 5) Multipoint Boundary Green's function for Chordal SLE curves
 04/28/2021
 4:00 PM  5:00 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Dapeng Zhan (zhan@msu.edu)
For a Chordal SLE$_\kappa$ ($\kappa \in (0,8)$) curve in a simply connected domain $D$ with smooth boundary, the $n$point boundary Green's function valued at distinct points $z_1, ..., z_n\in \partial{D}$ is defined by}
\[ G(z_1,...,z_n)= \lim_{r_1,...,r_n \to 0+} \prod_{j=1}^{n} {r_j}^ { \alpha} \mathbb{P} \left[ dist(\gamma, z_k) \leqq r_k, 1 \leqq k \leqq n \right] ,\]where $ \alpha = \frac{8}{\kappa}  1 $ is the boundary exponent of SLE$_\kappa$, provided that the limit converges. In this talk, we will show that such Green's function exists for any finite number of points. Along the way we provide the rate of convergence and modulus of continuity for Green's functions as well. Finally, we give uptoconstant bounds for them.
We use the same zoom link and passcode as before.

28031

Thursday 4/29 1:00 PM

Anne Gelb, Dartmouth College

Empirical Bayesian Inference using Joint Sparsity
 Anne Gelb, Dartmouth College
 Empirical Bayesian Inference using Joint Sparsity
 04/29/2021
 1:00 PM  2:00 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Olga Turanova (turanova@msu.edu)
We develop a new empirical Bayesian inference algorithm for solving a linear inverse problem given multiple measurement vectors (MMV) of undersampled and noisy observable data. Specifically, by exploiting the joint sparsity across the multiple measurements in the sparse domain of the underlying signal or image, we construct a new support informed sparsity promoting prior. Several applications can be modeled using this framework. Our numerical experiments demonstrate that using this new prior not only improves accuracy of the recovery, but also reduces the uncertainty in the posterior when compared to standard sparsity producing priors.
This is joint work with Theresa Scarnati formerly of the Air Force Research Lab Wright Patterson and now working at Qualis Corporation in Huntsville, AL, and Jack Zhang, recent bachelor degree recipient at Dartmouth College and now enrolled at University of Minnesota’s PhD program in mathematics.
