Talk_id  Date  Speaker  Title 
29376

Tuesday 9/6 11:00 AM

Lucas Hall, MSU

Skew Products: Coactions You Can See
 Lucas Hall, MSU
 Skew Products: Coactions You Can See
 09/06/2022
 11:00 AM  11:50 AM
 C304 Wells Hall
 Brent Nelson (banelson@msu.edu)
The speaker introduces topological quivers and constructs their associated C*algebra. We present two independent constructions which arise in the presence of a cocycle (the topological ”skew product" and the algebraic coaction) and show that the constructions agree in a suitable sense. Along the way, we characterize the skew product based on some associated topological dynamics. Time permitting, we will explore future directions.

29397

Tuesday 9/6 3:00 PM

G&T Seminar, MSU

Organizational Meeting
 G&T Seminar, MSU
 Organizational Meeting
 09/06/2022
 3:00 PM  4:00 PM
 C304 Wells Hall
(Virtual Meeting Link)
 Vijay B Higgins (higgi231@msu.edu)
Organizational meeting for the GT seminar this Fall.

29378

Wednesday 9/7 4:10 PM

Sasha Volberg, MSU

Heat smoothing conjecture and BernsteinMarkov inequalities on Hamming cube
 Sasha Volberg, MSU
 Heat smoothing conjecture and BernsteinMarkov inequalities on Hamming cube
 09/07/2022
 4:10 PM  5:00 PM
 C304 Wells Hall
 Willie WaiYeung Wong (wongwil2@msu.edu)
Hamming cube and its various Poincaré type inequalities represent a crucial model for many questions ranging from Banach space theory to graph theory to theoretical computer science. We present some estimates for tail spaces on Hamming cube. We use the analytic paraproduct operator for that. We also show some BernsteinMarkov inequalities, here the novelty is in getting rid of some irritating logarithms.

29391

Thursday 9/8 3:00 PM

Lara Pudwell, Valparaiso University

Patternavoiding parking functions
 Lara Pudwell, Valparaiso University
 Patternavoiding parking functions
 09/08/2022
 3:00 PM  3:50 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Bruce E Sagan (bsagan@msu.edu)
We extend the classical definition of patterns in permutations to parking functions. In particular we study parking functions that avoid permutations of length 3. A number of wellknown combinatorial sequences arise in our analysis, and this talk will highlight several bijective results. This project is joint work with Ayomikun Adeniran.

29383

Thursday 9/8 4:10 PM

Leonid Parnovski, University College London

Floating mats and sloping beaches: spectral asymptotics of the Steklov problem on polygons
 Leonid Parnovski, University College London
 Floating mats and sloping beaches: spectral asymptotics of the Steklov problem on polygons
 09/08/2022
 4:10 PM  5:00 PM
 C304 Wells Hall
 Joseph Waldron (waldro51@msu.edu)
I will discuss asymptotic behaviour of the eigenvalues of the Steklov problem (aka DirichlettoNeumann operator) on curvilinear polygons. The answer is completely unexpected and depends on the arithmetic properties of the angles of the polygon.

29409

Monday 9/12 12:30 PM

Leonid Chekhov, Michigan State University

Symplectic groupoid and cluster algebra description of closed Riemann surfaces
 Leonid Chekhov, Michigan State University
 Symplectic groupoid and cluster algebra description of closed Riemann surfaces
 09/12/2022
 12:30 PM  1:30 PM
 C304 Wells Hall
 Linhui Shen (shenlin1@msu.edu)
We use the FockGoncharov higher Teichmuller space directed networks to solve the symplectic groupoid condition: parameterize pairs of $SL_n$ matrices (B,A) with A unipotent such that $BAB^T$ is also unipotent. A natural LiePoisson bracket on B generates the Goldman bracket on elements of A and $BAB^T$, which are simultaneously elements of the corresponding upper cluster algebras. Using this input we identify the space of Xcluster algebra elements with Teichmuller spaces of closed Riemann surfaces of genus 2 (for $n$=3) and 3 (for $n$=4) endowed with Goldman bracket structure: for $g$=2 all geodesic functions are positive Laurent polynomials and Dehn twists correspond to mutations in the corresponding quivers. This is the work in progress with Misha Shapiro.

29401

Monday 9/12 4:00 PM

Brent Nelson, MSU

Making Weight
 Brent Nelson, MSU
 Making Weight
 09/12/2022
 4:00 PM  5:30 PM
 C517 Wells Hall
 Brent Nelson (banelson@msu.edu)
A weight on a von Neumann algebra is a positive linear map that is permitted to be infinitely valued. It is a generalization of a positive linear functional that arises naturally in the context of crossed products by nondiscrete groups, and they are vital to the study of purely infinite von Neumann algebras. In this talk I will provide an introduction to the theory of weights that assumes only the definition of a von Neumann algebra.

29377

Tuesday 9/13 11:00 AM

Lara Ismert, Embry–Riddle Aeronautical University

A Liouvilleesque theorem for a weaklydefined derivation on B(H)
 Lara Ismert, Embry–Riddle Aeronautical University
 A Liouvilleesque theorem for a weaklydefined derivation on B(H)
 09/13/2022
 11:00 AM  11:50 AM
 C304 Wells Hall
 Brent Nelson (banelson@msu.edu)
Liouville’s Theorem states that any bounded entire function on the complex plane is necessarily constant. In this talk, we discuss an analogous theorem for a weaklydefined derivation on B(H) studied in recent years by Erik Christensen. As a consequence, we provide new sufficient conditions for when two operators which satisfy the Heisenberg Commutation Relation must both be unbounded.

29410

Wednesday 9/14 3:00 PM

Brendon Rhoades, UCSD

Superspace, Vandermondes, and representations
 Brendon Rhoades, UCSD
 Superspace, Vandermondes, and representations
 09/14/2022
 3:00 PM  3:50 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Bruce E Sagan (bsagan@msu.edu)
We present an extension of the Vandermonde determinant from the polynomial ring to superspace. These superspace Vandermondes are used to construct modules over the symmetric group with (occasionally conjectural) connections to geometry and coinvariant theory. Joint with Andy Wilson.

29412

Thursday 9/15 3:00 PM

Jie Yang, MSU

Organizing meeting for Student Number Theory Seminar
 Jie Yang, MSU
 Organizing meeting for Student Number Theory Seminar
 09/15/2022
 3:00 PM  4:00 PM
 C204A Wells Hall
 Jie Yang (yangji79@msu.edu)
In this first meeting, I'll give some motivations towards the study of padic modular forms, and explain some central concepts in "eigenvarieties machine" introduced by K. Buzzard. In the end, we will discuss the plan for this seminar.

29402

Thursday 9/15 4:10 PM

Jenny Wilson, University of Michigan

Stability patterns in configuration spaces
 Jenny Wilson, University of Michigan
 Stability patterns in configuration spaces
 09/15/2022
 4:10 PM  5:00 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Olga Turanova (turanova@msu.edu)
This talk will give an introduction of the recent field of 'representation stability'. I will discuss how we can use representation theory to illuminate the structure of certain families of groups or topological spaces with actions of the symmetric groups, focusing on configuration spaces as an illustrative example.

29415

Friday 9/16 4:00 PM

Anna Veselovska, Department of Mathematics, Technical University of Munich, Germany

SuperResolution on the TwoDimensional Unit Sphere
 Anna Veselovska, Department of Mathematics, Technical University of Munich, Germany
 SuperResolution on the TwoDimensional Unit Sphere
 09/16/2022
 4:00 PM  5:00 PM
 C304 Wells Hall
 Mark A Iwen (iwenmark@msu.edu)
In this talk, we discuss the problem of recovering an atomic measure on the unit 2sphere S^2 given finitely many moments with respect to spherical harmonics. The analysis relies on the formulation of this problem as an optimization problem on the space of bounded Borel measures on S^2 as suggested by Y. de
Castro & F. Gamboa and E. Candes & C. FernandezGranda. We construct a dual certificate using a kernel given in an explicit form and make a concrete analysis of the interpolation problem. We support our theoretical results by various numerical examples related to direct solution of the optimization
problem and its discretization.
This is a joint work with Frank Filbir and Kristof Schroder.

29414

Monday 9/19 12:30 PM

Alexander Vainshtein, Haifa University

Cluster structures on SL_n and the BelavinDrinfeld classification
 Alexander Vainshtein, Haifa University
 Cluster structures on SL_n and the BelavinDrinfeld classification
 09/19/2022
 12:30 PM  1:30 PM
 C304 Wells Hall
 Michael Shapiro (mshapiro@msu.edu)
Cluster structures were discovered by S. Fomin and A. Zelevinsky about twenty years
ago and quickly found applications in various fields of mathematics and mathematical physics.
In the latter, several advances were made in a study of classical and quantum integrable
systems arising in the context of cluster structures. These systems "live" on PoissonLie
groups and their Poisson homogeneous spaces, hence it is important to understand an
interplay between cluster and Poisson structures on such objects.
In this talk I will explain a construction of a family of (generalized) cluster structures in the
algebra of regular functions on SL_n related to the BelavinDrinfeld classification
of PoissonLie structures on SL_n.
Based on a joint work with M.~Gekhtman (Notre Dame) and M.~Shapiro (MSU).

29413

Monday 9/19 1:00 PM

Craig Gross, MSU

All aboard! A mathematical study of transit equity in Baltimore
 Craig Gross, MSU
 All aboard! A mathematical study of transit equity in Baltimore
 09/19/2022
 1:00 PM  2:00 PM
 C117 Wells Hall
(Virtual Meeting Link)
 Craig Gross (grosscra@msu.edu)
In 2015, the governor of Maryland canceled a light rail project through the city of Baltimore that had been planned and funded for over a decade. Instead, the money was diverted to funding highways near the richer, whiter suburbs of the city. As Baltimore is home to some of the most extreme classdisparity and segregation in the country, this decision significantly hurt the potential for a more equitable transit system. But by how much?
$\\$
This talk will be a tour through a mathematical investigation of how the canceled light rail might have increased access to jobs across the city. In particular, we use some dimensionreduction and clustering algorithms on CDC Social Vulnerability Indices to explore which parts of the city may be socioeconomically disadvantaged. We then compute job accessibility metrics to determine how the light rail would have affected these regions. We also give some considerations for converting a collection of many relevant indicators into more interpretable, manageable metrics for future transit studies.
$\\$
This is joint work with Adam Lee, Kethaki Varadan, and Yangxinyu Xie.
$\\$
This will be a hybrid seminar and take place in C117 Wells Hall and via Zoom at https://msu.zoom.us/j/99426648081?pwd=ZEljM3BPUXg2MjVUMVM5TnlzK2NQZz09 .

29424

Monday 9/19 4:00 PM

Brent Nelson, MSU

Worth Their Weight
 Brent Nelson, MSU
 Worth Their Weight
 09/19/2022
 4:00 PM  5:30 PM
 C517 Wells Hall
 Brent Nelson (banelson@msu.edu)
I will continue my introduction to weights. I will briefly mention equivalent conditions of normality for weights before moving onto a discussion of semicyclic representations and TomitaTakesaki theory. I will conclude with a detailed examination of Plancherel weights on locally compact groups.

29419

Tuesday 9/20 11:00 AM

Alberto Takase, MSU and UC Irvine

Spectral estimates of dynamicallydefined and amenable operator families (In collaboration with Siegfried Beckus)
 Alberto Takase, MSU and UC Irvine
 Spectral estimates of dynamicallydefined and amenable operator families (In collaboration with Siegfried Beckus)
 09/20/2022
 11:00 AM  11:50 AM
 C304 Wells Hall
 Ilya Kachkovskiy (ikachkov@msu.edu)
For dynamicallydefined operator families, the Hausdorff distance of the spectra is estimated by the distance of the underlying dynamical systems while the group is amenable.
We prove that if the group has strict polynomial growth and both the group action and the coefficients are Lipschitz continuous, then the spectral estimate has a square root behavior or, equivalently, the spectrum map is $\frac{1}{2}$Holder continuous.
We prove the behavior can be improved resulting in the spectrum map being Lipschitz continuous if the coefficients are locallyconstant.
In 1990, the square root behavior was established for the Almost Mathieu Operator or, more generally, the quasiperiodic operators with Lipschitz continuous potentials.
Our results extend the square root behavior to a bigger class of operators such as (magnetic) discrete Schrodinger operators with finite range and with Lipschitz continuous coefficients.

29403

Tuesday 9/20 3:00 PM

Bin Sun, Oxford

$L^2$Betti numbers of fiber bundles
 Bin Sun, Oxford
 $L^2$Betti numbers of fiber bundles
 09/20/2022
 3:00 PM  4:00 PM
 C304 Wells Hall
(Virtual Meeting Link)
 Vijay B Higgins (higgi231@msu.edu)
We study the $L^2$Betti numbers of fiber bundles $F \rightarrow E \rightarrow B$ of manifolds. Under certain conditions (e.g., when $F$ is simply connected), $b_*^{(2)}(E)$ can be computed using the twisted $L^2$Betti numbers of $B.$ We relate the twisted and untwisted $L^2$Betti numbers of $B$ when $\pi_1(B)$ is locally indicable. As an application, we compute $b_*^{(2)}(E)$ when $B$ is either a surface or a nonpositively curved $3$manifold. This is a joint work with Dawid Kielak.

29425

Tuesday 9/20 4:00 PM


Organizational Meeting

 Organizational Meeting
 09/20/2022
 4:00 PM  5:00 PM
 C517 Wells Hall
 Ivan So (soivan@msu.edu)
No abstract available.

29416

Wednesday 9/21 3:00 PM

Alex Wilson, Dartmouth

A DiagramLike Basis for the Multiset Partition Algebra
 Alex Wilson, Dartmouth
 A DiagramLike Basis for the Multiset Partition Algebra
 09/21/2022
 3:00 PM  3:50 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Bruce E Sagan (bsagan@msu.edu)
There's a classical connection between the representation theory of the symmetric group and the general linear group called SchurWeyl Duality. Variations on this principle yield analogous connections between the symmetric group and other objects such as the partition algebra and more recently the multiset partition algebra. The partition algebra has a wellknown basis indexed by graphtheoretic diagrams which allows the multiplication in the algebra to be understood visually as combinations of these diagrams. I will present an analogous basis for the multiset partition algebra and show how this basis can be used to describe generators and construct representations for the algebra.

29380

Wednesday 9/21 4:10 PM

Michael McNulty, MSU

Conditionally Stable SelfSimilar Blowup for the Supercritical Quadratic Wave Equation Beyond the Light Cone
 Michael McNulty, MSU
 Conditionally Stable SelfSimilar Blowup for the Supercritical Quadratic Wave Equation Beyond the Light Cone
 09/21/2022
 4:10 PM  5:00 PM
 C304 Wells Hall
 Willie WaiYeung Wong (wongwil2@msu.edu)
Nonlinear wave equations of powertype serve as excellent toy models for geometric PDEs such as the YangMills and wave maps equations. Of great interest in the energy supercritical setting is that of threshold phenomena. In this setting, unstable selfsimilar blowup solutions are believed to play an essential role in describing the threshold of singularity formation. We will discuss the stability of an explicitly known, unstable selfsimilar blowup solution of the energy supercritical quadratic wave equation in a region of spacetime which extends beyond the time of blowup. To overcome this instability, we introduce a new canonical method to investigate unstable selfsimilar solutions. This work represents the first steps toward an understanding of threshold phenomena in the energy supercritical setting.

29438

Thursday 9/22 2:30 PM

Rayan Saab, University of California, San Diego (UCSD)

Quantizing neural networks
 Rayan Saab, University of California, San Diego (UCSD)
 Quantizing neural networks
 09/22/2022
 2:30 PM  3:30 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Mark A Iwen (iwenmark@msu.edu)
Neural networks are highly nonlinear functions often parametrized by a staggering number of weights. Miniaturizing these networks and implementing them in hardware is a direction of research that is fueled by a practical need, and at the same time connects to interesting mathematical problems. For example, by quantizing, or replacing the weights of a neural network with quantized (e.g., binary) counterparts, massive savings in cost, computation time, memory, and power consumption can be attained. Of course, one wishes to attain these savings while preserving the action of the function on domains of interest.
We present datadriven and computationally efficient methods for quantizing the weights of already trained neural networks and we prove that our methods have favorable error guarantees under a variety of assumptions. We also discuss extensions and provide the results of numerical experiments, on large multilayer networks, to illustrate the performance of our methods. Time permitting, we will also discuss open problems and related areas of research.

29423

Thursday 9/22 3:00 PM

Peikai Qi, MSU

Modular form and Hecke operator1
 Peikai Qi, MSU
 Modular form and Hecke operator1
 09/22/2022
 3:00 PM  4:00 PM
 C204A Wells Hall
 Peikai Qi (qipeikai@msu.edu)
In the talk, we will review the definition of modular form and hecke algebra.

29387

Thursday 9/22 4:10 PM

Chenyang Xu, Princeton University

Kstability and birational geometry
 Chenyang Xu, Princeton University
 Kstability and birational geometry
 09/22/2022
 4:10 PM  5:00 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Joseph Waldron (waldro51@msu.edu)
The notion of Kstability for a Fano varieties was introduced by differential geometers in late 90s, to capture the existence of a KählerEinstein metric. In the last decade, it has gradually become clear to algebraic geometers that Kstability provides a rich algebraic theory in higher dimensional geometry. In particular, it can be used to solve the longstanding question of constructing moduli spaces for Fano varieties.
I will survey the background of Kstability and how algebraic geometers’ understanding of it has evolved. In particular, I will explain algebraic geometry plays a key role of establishing the equivalence between Kstability and the existence of a KählerEinstein metric, i.e. the YauTianDonaldson Conjecture, for all Fano varieties. If time permits, I want to also discuss the construction of Kmoduli spaces parametrizing Fano varieties, and how the recipe given by Kstability can be used to resolve the issues that mystify people for a long time.

29421

Monday 9/26 12:30 PM

Jiuzu Hong, University of North Carolina at Chapel Hill

BD Schubert varieties of parahoric group schemes and global Demazure modules of twisted current algebras
 Jiuzu Hong, University of North Carolina at Chapel Hill
 BD Schubert varieties of parahoric group schemes and global Demazure modules of twisted current algebras
 09/26/2022
 12:30 PM  1:30 PM
 C304 Wells Hall
 Linhui Shen (shenlin1@msu.edu)
It is wellknown that there is a duality between affine Demazure modules and the spaces of sections of line bundles on Schubert varieties in affine Grassmannians. This should be regarded as a local theory. In this talk, I will explain an algebraic theory of global Demazure modules of twisted current algebras. Moreover, these modules are dual to the spaces of sections of line bundles on BeilinsonDrinfeld Schubert varieties of certain parahoric groups schemes, where the factorizations of global Demazure modules are compatible with the factorizations of line bundles. This generalizes the work of DumanskiFeiginFinkelberg in the untwisted setting. In order to establish this duality in the twisted case, following the works of Zhu, we prove the flatness of BD Schubert varieties, and establish factorizable and equivariant structures on the rigidified line bundles over BD Grassmannians of these parahoric group schemes. This work is joint with Huanhuan Yu.

29427

Monday 9/26 1:00 PM

Remy Liu, MSU

Understanding dataset characteristics via diffusion on graph
 Remy Liu, MSU
 Understanding dataset characteristics via diffusion on graph
 09/26/2022
 1:00 PM  2:00 PM
 C117 Wells Hall
(Virtual Meeting Link)
 Craig Gross (grosscra@msu.edu)
Classical graph signal processing provides powerful techniques for understanding and modifying graph signals from the spectral domain, but they come with high computational costs. More recently, diffusion on graphs has been sought as an alternative approach to modifying graph signals; it is much more computationally efficient and is easy to interpret from the spatial perspective. Here, we present two different studies utilizing diffusion wavelets on a graph to filter graph signals for downstream analysis. In the first study, we aim to understand how and what is being utilized by Graph Neural Networks to achieve graphrelated tasks. We do so by observing the performance difference between using the filtered graph and the original graph. We demonstrate that some image datasets, such as CIFAR and MNIST, rely on lowfrequency signals; on the contrary, heterophilic datasets, such as WebKB, rely more heavily on highfrequency signals. In the second study on computational biology using gene interaction networks and gene expression data, we observe similar results where different frequency bands perform differently in a taskspecific manner. In summary, our studies demonstrate the practical usage of graph diffusion to modify graph signals, leading to improved downstream prediction performance and a better understanding of the graph datasets' characteristics.
$\\$
This will be a hybrid seminar and take place in C117 Wells Hall and via Zoom at https://msu.zoom.us/j/99426648081?pwd=ZEljM3BPUXg2MjVUMVM5TnlzK2NQZz09 .

29417

Monday 9/26 3:00 PM

Patrick Daniels, University of Michigan

Canonical integral models for Shimura varieties defined by tori
 Patrick Daniels, University of Michigan
 Canonical integral models for Shimura varieties defined by tori
 09/26/2022
 3:00 PM  4:00 PM
 C304 Wells Hall
 Georgios Pappas (pappasg@msu.edu)
Pappas and Rapoport have recently conjectured the existence of canonical integral models for Shimura varieties with parahoric level structure, which are characterized using Scholze's theory of padic shtukas. We will illustrate the conjecture using the example of Shimura varieties defined by tori, where (surprisingly) the theory is already nontrivial. Along the way we will explain a connection with the BhattScholze theory of prismatic Fcrystals.

29408

Monday 9/26 4:00 PM

Aldo Garcia Guinto, MSU

Conjugate Variables and Dual Systems
 Aldo Garcia Guinto, MSU
 Conjugate Variables and Dual Systems
 09/26/2022
 4:00 PM  5:30 PM
 C517 Wells Hall
 Brent Nelson (banelson@msu.edu)
In free probability, the semicircular operators are the analogue of the Gaussian distribution in classical probability. We will be using the semicircular operators to motivate two notions of free probability: conjugate variables and dual systems. The conjugate variables are used to define free Fisher information, which is analogue of Fisher information in classical probability. While the dual systems are related to a cohomology theory for von Neumann algebras. It turns out that these two notions are not as different as they may seem.

29429

Wednesday 9/28 3:00 PM

Ayomikun Adeniran, Colby College

Parking completions
 Ayomikun Adeniran, Colby College
 Parking completions
 09/28/2022
 3:00 PM  3:50 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Bruce E Sagan (bsagan@msu.edu)
Parking functions are wellknown objects in combinatorics. One interesting generalization of parking functions are parking completions. A parking completion corresponds to a set of preferences where all cars park assuming some of the spots on the street are already occupied. In this talk, we will explore how parking completions are related to restricted lattice paths. We will also present results for both the ordered and unordered variations of the problem by use of a pair of operations (termed Join and Split). A nice consequence of our results is a new volume formula for most PitmanStanley polytopes. This is joint work with H. Nam, P.E. Harris, G. DorpalenBarry, S. Butler, J.L. Martin, C. Hettle, and Q. Liang.

29389

Wednesday 9/28 4:10 PM

ShiZhuo Looi, UC Berkeley

Asymptotics for odd and evendimensional waves
 ShiZhuo Looi, UC Berkeley
 Asymptotics for odd and evendimensional waves
 09/28/2022
 4:10 PM  5:00 PM
 C304 Wells Hall
 Willie WaiYeung Wong (wongwil2@msu.edu)
In this talk, I will give a survey of recent and upcoming results on various linear, semilinear and quasilinear wave equations on a wide class of dynamical spacetimes in various even and odd spatial dimensions. These results include asymptotics for a wide range of nonlinearities. We also highlight a dichotomy in odd dimensions between stationary and nonstationary backgrounds and explain how the stationary backgrounds lead to a faster decay rate for waves.
For many of these results, the spacetimes under consideration have only weak asymptotic flatness conditions and are allowed to be large perturbations of the Minkowski spacetime. We explain the dichotomy between even and odddimensional wave behaviour and how we view this dichotomy as a generalisation of the contrast between the classical weak Huygens' principle and the classical strong Huygens' principle. Part of this work is joint with Mihai Tohaneanu and Jared Wunsch.

29442

Thursday 9/29 3:00 PM

Peikai Qi, MSU

Hecke algebra and AtkinLehnerLi’s theory
 Peikai Qi, MSU
 Hecke algebra and AtkinLehnerLi’s theory
 09/29/2022
 3:00 PM  4:00 PM
 C204A Wells Hall
 Peikai Qi (qipeikai@msu.edu)
We will use double closet to define Hecke algebra. And then we will have an review of AtkinLehnerLi’s theory without proof. If you miss the last seminar, it doesn’t matter. you can also understand most of this section.

29393

Thursday 9/29 4:10 PM

Nam Le, Indiana University Bloomington

Hessian eigenvalues and hyperbolic polynomials
 Nam Le, Indiana University Bloomington
 Hessian eigenvalues and hyperbolic polynomials
 09/29/2022
 4:10 PM  5:00 PM
 C304 Wells Hall
 Olga Turanova (turanova@msu.edu)
Hessian eigenvalues are natural nonlinear analogues of the classical Dirichlet eigenvalues. The Hessian eigenvalues and their corresponding eigenfunctions are expected to share many analytic and geometric properties (such as uniqueness, stability, maxmin principle, global smoothness, BrunnMinkowski inequality, etc) as their Dirichlet counterparts. In this talk, I will discuss these issues and some recent progresses in various geometric settings. The focus will be mostly on the case of the MongeAmpere eigenfunctions and related degenerate equations. I will also explain the unexpected role of hyperbolic polynomials in our analysis. I will not assume any familiarity with these concepts.

29439

Monday 10/3 4:00 PM

Lucas Hall, MSU

Introduction to Graph Algebras
 Lucas Hall, MSU
 Introduction to Graph Algebras
 10/03/2022
 4:00 PM  5:30 PM
 C517 Wells Hall
 Brent Nelson (banelson@msu.edu)
We introduce directed graphs and demonstrate how to generate a C*algebra which reflects certain features of the graph. Time permitting, we will introduce two uniqueness theorems for their representations and explore a few of their consequences.

29407

Tuesday 10/4 11:00 AM

Bin Sun, University of Oxford

Generalized wreath products and rigidity of their von Neumann algebras
 Bin Sun, University of Oxford
 Generalized wreath products and rigidity of their von Neumann algebras
 10/04/2022
 11:00 AM  11:50 AM
 C304 Wells Hall
 Brent Nelson (banelson@msu.edu)
We construct the first positive examples to the Connes' Rigidity Conjecture, i.e., we construct groups $G$ with Kazhdan's property (T) such that if $H$ is a group with the same von Neumann algebra as $G$, then $H\cong G$. In this talk, I will focus on the grouptheoretic side of this result and talk about how we applied geometric group theory to solve problems from von Neumann algebra. This is joint work with Ionut Chifan, Adrian Ioana, and Denis Osin.

30445

Tuesday 10/4 1:00 PM

Round Table Discussion, MSU

Assessment Modalities in gateway courses
 Round Table Discussion, MSU
 Assessment Modalities in gateway courses
 10/04/2022
 1:00 PM  2:00 PM
 C517 Wells Hall
 Tsvetanka Sendova (tsendova@msu.edu)
No abstract available.

30447

Tuesday 10/4 3:00 PM

Peter Johnson, Michigan State University

Knot lattice homology and the GukovManolescu 2variable series
 Peter Johnson, Michigan State University
 Knot lattice homology and the GukovManolescu 2variable series
 10/04/2022
 3:00 PM  4:00 PM
 C304 Wells Hall
(Virtual Meeting Link)
 Peter Kilgore Johnson (john8251@msu.edu)
In previous work of Akhmechet, Krushkal, and the speaker, a unification of lattice cohomology and the $\widehat{Z}$invariant was established. Both theories are combinatorially defined invariants of plumbed 3manifolds, but with quite different origins. Lattice cohomology, due to Némethi, is motivated by the study of normal surface singularities and is isomorphic to Heegaard Floer homology for plumbing trees. On the other hand, $\widehat{Z}$, due to GukovPeiPutrovVafa, is a power series coming from a physical theory and is conjectured to recover quantum invariants of 3manifolds at roots of unity. In this talk, I will discuss work in progress relating knot lattice homology and the GukovManolescu 2variable series, the knot theoretic counterparts to lattice homology and $\widehat{Z}$. This is joint work with Ross Akhmechet and Sunghyuk Park.

30454

Tuesday 10/4 4:30 PM

Ivan So

Basics on Intersection Theory
 Ivan So
 Basics on Intersection Theory
 10/04/2022
 4:30 PM  5:30 PM
 C517 Wells Hall
 Ivan So ()
No abstract available.

29446

Wednesday 10/5 3:00 PM

Caroline Klivans, Brown University

Flowfiring processes
 Caroline Klivans, Brown University
 Flowfiring processes
 10/05/2022
 3:00 PM  3:50 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Bruce E Sagan (bsagan@msu.edu)
I will discuss a discrete nondeterministic flowfiring process for topological cell complexes. The process is a form of discrete diffusion; a flow is repeatedly diverted according to a discrete Laplacian. The process is also an instance of higherdimensional chipfiring. I will motivate and introduce the system and then focus on two important features – whether or not the system is terminating and whether or not the system is confluent.

29392

Wednesday 10/5 4:10 PM

Konstantin Matetski, MSU

Polynuclear growth and the Toda lattice
 Konstantin Matetski, MSU
 Polynuclear growth and the Toda lattice
 10/05/2022
 4:10 PM  5:00 PM
 C304 Wells Hall
 Willie WaiYeung Wong (wongwil2@msu.edu)
Polynuclear growth is one of the basic models in the KardarParisiZhang universality class, which describes a onedimensional crystal growth. For a particular initial state, it describes the length of the longest increasing subsequence for uniformly random permutations (the problem first studied by S. Ulam). In my joint work with J. Quastel and D. Remenik we expressed the distribution functions of the polynuclear growth in terms of the solutions of the Toda lattice, one of the classical integrable systems. A suitable rescaling of the model yields a nontrivial continuous limit of the polynuclear growth (the KPZ fixed point) and the respective equations (KadomtsevPetviashvili).

29435

Thursday 10/6 2:30 PM

Weijie Su, University of Pennsylvania

1WMINDS talk (passcode is the first prime number > 100).
 Weijie Su, University of Pennsylvania
 1WMINDS talk (passcode is the first prime number > 100).
 10/06/2022
 2:30 PM  3:30 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Mark A Iwen (iwenmark@msu.edu)
What Should a Good Deep Neural Network Look Like? Insights from a LayerPeeled Model and the Law of EquiSeparation
See https://sites.google.com/view/mindsseminar/home

30451

Thursday 10/6 3:00 PM

Jie Yang, MSU

Integral modular forms
 Jie Yang, MSU
 Integral modular forms
 10/06/2022
 3:00 PM  4:00 PM
 C204A Wells Hall
 Jie Yang (yangji79@msu.edu)
We'll describe integral aspects of modular form theory, and discuss some applications.

29263

Thursday 10/6 4:10 PM

Lisa Piccirillo, Massachusetts Institute of Technology

Exotic phenomena in 4dimensional topology
 Lisa Piccirillo, Massachusetts Institute of Technology
 Exotic phenomena in 4dimensional topology
 10/06/2022
 4:10 PM  5:00 PM
 C304 Wells Hall
 Brent Nelson (banelson@msu.edu)
In favorable circumstances, topological 4manifolds and surfaces in them can be classified. In contrast, little is known about smooth 4manifolds and smooth surfaces. Several of the hardest problems in 4dimensional topology (eg. the Poincare conjecture) simply ask whether the topological classification fails in the smooth setting; such failures are called exotica. In this talk, I will discuss some historic and recent progress towards detecting exotic phenomena, and outline some promising approaches.

30464

Monday 10/10 1:00 PM

Cullen Haselby, MSU

Efficient Modewise Measurements for Compressive Sensing or Recovery of Tensor Data
 Cullen Haselby, MSU
 Efficient Modewise Measurements for Compressive Sensing or Recovery of Tensor Data
 10/10/2022
 1:00 PM  2:00 PM
 C117 Wells Hall
(Virtual Meeting Link)
 Craig Gross (grosscra@msu.edu)
Recovery of sparse vectors and lowrank matrices from a small number of linear measurements is wellknown to be possible under various model assumptions on the measurements. The key requirement on the measurement matrices is typically the restricted isometry property, that is, approximate orthonormality when acting on the subspace to be recovered. Among the most widely used random matrix measurement models are (a) independent subgaussian models and (b) randomized Fourierbased models, allowing for the efficient computation of the measurements.
$\\$
For the now ubiquitous tensor data, direct application of the known recovery algorithms to the vectorized or matricized tensor is memoryheavy because of the huge measurement matrices to be constructed and stored. In this talk, we will discuss two different modewise measurement schemes and related recovery algorithms. These modewise operators act on the pairs or other small subsets of the tensor modes separately. They require significantly less memory than the measurements working on the vectorized tensor, and experimentally can recover the tensor data from fewer measurements and do not require impractical storage.
$\\$
This will be a hybrid seminar and take place in C117 Wells Hall and via Zoom at https://msu.zoom.us/j/99426648081?pwd=ZEljM3BPUXg2MjVUMVM5TnlzK2NQZz09 .

29445

Monday 10/10 3:00 PM

Pavel Čoupek, MSU

Ramification bounds for mod p étale cohomology via prismatic cohomology
 Pavel Čoupek, MSU
 Ramification bounds for mod p étale cohomology via prismatic cohomology
 10/10/2022
 3:00 PM  4:00 PM
 C304 Wells Hall
 Preston Wake (wakepres@msu.edu)
Let $K/\bf{Q}_p$ be a local number field of absolute ramification index $e$, and let $X$ be a proper smooth $O_K$scheme. I will discuss how one can obtain bounds on ramification of the mod $p$ Galois representations arising as the étale cohomology of (the geometric generic fiber of) $X$ in terms of $e$, the given prime $p>2$ and the cohomological degree $i$. The key tools for achieving this are the BreuilKisin and $A_{\rm inf}$cohomology theories of Bhatt, Morrow and Scholze, and a series of conditions based on a criterion of Gee and Liu regarding crystallinity of the representation attached to a free BreuilKisinFargues $G_K$module.

29422

Monday 10/10 3:00 PM

Vijay Higgins, Michigan State University

Sp(4) stated skein algebras
 Vijay Higgins, Michigan State University
 Sp(4) stated skein algebras
 10/10/2022
 3:00 PM  4:00 PM
 C204A Wells Hall
 Linhui Shen (shenlin1@msu.edu)
Skein algebras are spanned by webs or links in a thickened surface subject to skein relations. When the skein relations are the Kauffman bracket relations associated to SL(2), they provide a diagrammatic way to encode cluster algebras, as shown by Muller, and also quantum groups, as shown by Costantino and Le.
In this talk, we will explore a construction of a basis for the stated skein algebra for Sp(4) which is built from Kuperberg's web relations along with extra skein relations along the boundary of the surface. We will use the basis to obtain results about the structure of the skein algebra, relating it to the quantum group associated to Sp(4). We will also recover Kuperberg's result about the Sp(4) web category.

29440

Monday 10/10 4:00 PM

Lucas Hall, MSU

Graph algebras: universality, uniqueness, and ideal structure
 Lucas Hall, MSU
 Graph algebras: universality, uniqueness, and ideal structure
 10/10/2022
 4:00 PM  5:30 PM
 C517 Wells Hall
 Brent Nelson (banelson@msu.edu)
We illustrate various aspects of graph algebras introduced last week, including usage of the universal property, aspects of their representation theory, and ideals, pointing to relationships with the structure of the underlying graph.

30448

Tuesday 10/11 11:00 AM

Jacob Gloe, MSU

Diffusion for a Quantum Particle in a Lindbladian Environment with a Periodic Hamiltonian
 Jacob Gloe, MSU
 Diffusion for a Quantum Particle in a Lindbladian Environment with a Periodic Hamiltonian
 10/11/2022
 11:00 AM  12:00 PM
 C304 Wells Hall
 Jeffrey Hudson Schenker (schenke6@msu.edu)
A quantum particle restricted to a lattice of points has been well studied in many different contexts. In the absence of disorder or environmental interaction, the particle simply undergoes ballistic transport for many suitable Hamiltonian operators. Recently, progress has been made on introducing a Lindbladian interaction term to the model, which drastically changes the dynamics in the large time limit. We prove that indeed diffusion is present in this context for an arbitrary periodic Hamiltonian. Additionally, we show that the diffusion constant is inversely proportional to the particles' coupling strength with its environment.

29432

Tuesday 10/11 3:00 PM

Daniel Douglas, Yale

Dimers, webs, and local systems
 Daniel Douglas, Yale
 Dimers, webs, and local systems
 10/11/2022
 3:00 PM  4:00 PM
 C304 Wells Hall
(Virtual Meeting Link)
 Vijay B Higgins (higgi231@msu.edu)
For a planar bipartite graph G equipped with a SLnlocal system, we show that the determinant of the associated Kasteleyn matrix counts “nmultiwebs” (generalizations of nwebs) in G, weighted by their webtraces. We use this fact to study random nmultiwebs in graphs on some simple surfaces. Time permitting, we will discuss some relations to FockGoncharov theory. This is joint work with Rick Kenyon and Haolin Shi.

30466

Tuesday 10/11 4:30 PM

Stan Halstead

Cycles and the Chow Ring
 Stan Halstead
 Cycles and the Chow Ring
 10/11/2022
 4:30 PM  5:30 PM
 C517 Wells Hall
 Ivan So ()
Intersections between varieties and subschemes can result in structures with many varying dimensions, which naturally leads us to consider something like a homology structure. The nonHausdorff nature of the Zariski topology limits our ability to utilize algebraic topology, so we must first define cycles, the formal sum of subvarieties, to get something we can work with.

29437

Thursday 10/13 2:30 PM

Dustin Mixon, Ohio State University

1WMINDS talk (passcode is the first prime number > 100).
 Dustin Mixon, Ohio State University
 1WMINDS talk (passcode is the first prime number > 100).
 10/13/2022
 2:30 PM  3:30 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Mark A Iwen (iwenmark@msu.edu)
See https://sites.google.com/view/mindsseminar/home

29447

Thursday 10/13 3:00 PM

Patricia Hersh, University of Oregon

Generalized recursive atom ordering and equivalence to CLshellability
 Patricia Hersh, University of Oregon
 Generalized recursive atom ordering and equivalence to CLshellability
 10/13/2022
 3:00 PM  3:50 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Bruce E Sagan (bsagan@msu.edu)
When Björner and Wachs introduced one of the main forms of lexicographic shellability, namely CLshellability, they also introduced the notion of recursive atom ordering, and they proved that a finite bounded poset is CLshellable if and only if it admits a recursive atom ordering. We generalize the notion of recursive atom ordering, and we prove that any such generalized recursive atom ordering may be transformed via a reordering process into a recursive atom ordering. We also prove that a finite bounded poset admits a generalized recursive atom ordering if and only if it is ``CCshellable'' by way of a CClabeling which is selfconsistent in a certain sense. This allows us to conclude that CLshellability is equivalent to selfconsistent CCshellability. As an application, we prove that the uncrossing orders, namely the face posets for stratified spaces of planar electrical networks, are dual CLshellable.
During this talk, we will review plenty of background on poset topology and specifically regarding the technique of lexicographic shellability. This is joint work with Grace Stadnyk

30462

Thursday 10/13 3:00 PM

Sgallova Ester , MSU

Eigenalgebra
 Sgallova Ester , MSU
 Eigenalgebra
 10/13/2022
 3:00 PM  4:00 PM
 C204A Wells Hall
 Peikai Qi (qipeikai@msu.edu)
Eigenalgebra is a construction attaching to a family of commuting operators acting on some space or module that parameterizes the system of eigenvalue for some operators.

29428

Monday 10/17 1:00 PM

Evzenie Coupkova, Purdue

Unique generalization properties of a dense set of classifiers based on onedimensional random projections
 Evzenie Coupkova, Purdue
 Unique generalization properties of a dense set of classifiers based on onedimensional random projections
 10/17/2022
 1:00 PM  2:00 PM
 C117 Wells Hall
(Virtual Meeting Link)
 Craig Gross (grosscra@msu.edu)
The generalization error of a classifier is related to the complexity of the set of functions among which the classifier is chosen. We study a family of lowcomplexity classifiers consisting of thresholding a random onedimensional feature. The feature is obtained by projecting the data on a random line after embedding it into a higherdimensional space parametrized by monomials of order up to k. More specifically, the extended data is projected ntimes and the best classifier among those n, based on its performance on training data, is chosen. We show that this type of classifier is extremely flexible, as it is likely to approximate, to an arbitrary precision, any continuous function on a compact set as well as any Boolean function on a compact set that splits the support into measurable subsets. In particular, given full knowledge of the class conditional densities, the error of these lowcomplexity classifiers would converge to the optimal (Bayes) error as k and n go to infinity. On the other hand, if only a training dataset is given, we show that the classifiers will perfectly classify all the training points as k and n go to infinity. We also bound the generalization error of our random classifiers. In general, our bounds are better than those for any classifier with VC dimension greater than O (ln n) . In particular, our bounds imply that, unless the number of projections n is extremely large, there is a significant advantageous gap between the generalization error of the random projection approach and that of a linear classifier in the extended space. Asymptotically, as the number of samples approaches infinity, the gap persists for any such n. Thus, there is a potentially large gain in generalization properties by selecting parameters at random, rather than optimization.
$\\$
A preprint of this work can be found here: https://arxiv.org/abs/2108.06339
$\\$
This will be a hybrid seminar and take place in C117 Wells Hall and via Zoom at https://msu.zoom.us/j/99426648081?pwd=ZEljM3BPUXg2MjVUMVM5TnlzK2NQZz09 .

30469

Monday 10/17 3:00 PM

Preston Wake, MSU

Rational torsion in modular Jacobians
 Preston Wake, MSU
 Rational torsion in modular Jacobians
 10/17/2022
 3:00 PM  4:00 PM
 C304 Wells Hall
 Preston Wake (wakepres@msu.edu)
I will talk about Ogg's conjecture and its generalization. This is joint work with Ken Ribet (and should serve as an introduction to Ken's talk on Friday).

30450

Tuesday 10/18 11:00 AM

Lubashan Pathirana, MSU

Limiting Theorems for Discrete and Continuous Parameter Stationary and Ergodic Quantum Processes.
 Lubashan Pathirana, MSU
 Limiting Theorems for Discrete and Continuous Parameter Stationary and Ergodic Quantum Processes.
 10/18/2022
 11:00 AM  12:00 PM
 C304 Wells Hall
 Jeffrey Hudson Schenker (schenke6@msu.edu)
A discrete parameter quantum process is represented by a sequence of quantum operations, which are completely positive maps that are trace nonincreasing. Given a stationary and ergodic sequences of such maps, an ergodic theorem describing convergence to equilibrium for a general class of such processes was recently obtained by Movassagh and Schenker. Under irreducibility conditions we obtain a law of large numbers that describes the asymptotic behavior of the processes involving the Lyapunov exponent. Furthermore, a central limit type theorem is obtained under mixing conditions. In the continuous time parameter, a quantum process is represented by a doubleindexed family of positive map valued random variables. For a stationary and ergodic family of such maps, we extend the results by Movassagh and Schenker to the continuous case.

30467

Tuesday 10/18 12:30 PM

Li Li, Oakland University

Cluster algebras and Nakajima's graded quiver varieties
 Li Li, Oakland University
 Cluster algebras and Nakajima's graded quiver varieties
 10/18/2022
 12:30 PM  1:30 PM
 C204A Wells Hall
 Linhui Shen (shenlin1@msu.edu)
Nakajima's graded quiver varieties are complex algebraic varieties associated with quivers. They are introduced by Nakajima in the study of representations of universal enveloping algebras of KacMoody Lie algebras, and can be used to study cluster algebras. In the talk, I will explain how to precisely locate the supports of the triangular basis of skewsymmetric rank 2 quantum cluster algebras by applying the decomposition theorem to various morphisms related to quiver varieties, thus prove a conjecture proposed by LeeLiRupelZelevinsky in 2014.

29418

Tuesday 10/18 3:00 PM

Juan MuñozEchániz, Columbia University

Families of contact structures and monopole Floer homology
 Juan MuñozEchániz, Columbia University
 Families of contact structures and monopole Floer homology
 10/18/2022
 3:00 PM  4:00 PM
 C304 Wells Hall
(Virtual Meeting Link)
 Peter Kilgore Johnson (john8251@msu.edu)
The contact invariant, defined by Kronheimer and Mrowka, is
an element in the monopole Floer homology of a 3manifold canonically
attached to a contact structure. I will discuss how the contact
invariant places constraints on the topology of families of contact
structures, and how it can be used to detect nontrivial
contactomorphisms given by "Dehn twists" on spheres. The main new tool
is a generalisation of the contact invariant to an invariant of
families of contact structures.

30465

Wednesday 10/19 3:00 PM

Konstatin Matetski, MSU

The KPZ fixed point.
 Konstatin Matetski, MSU
 The KPZ fixed point.
 10/19/2022
 3:00 PM  3:50 PM
 C405 Wells Hall
 Dapeng Zhan (zhan@msu.edu)
The KPZ universality class contains onedimensional random growth models, which under quite general assumptions exhibit similar (nonGaussian) scaling behavior. For special initial states, the limiting distributions surprisingly coincide with those from the random matrix theory. The physical explanation is that in the space of Markov processes, these models are all being rescaled to a universal fixed point. This scaling invariant fixed point was first characterized in joint work with Jeremy Quastel and Daniel Remenik. In our work, we found a surprising relation between random growing interfaces and the solutions of the classical integrable systems.

29390

Wednesday 10/19 4:10 PM

Katherine Zhiyuan Zhang, Courant Institute, NYU

Equilibria and stability in VlasovMaxwell equation
 Katherine Zhiyuan Zhang, Courant Institute, NYU
 Equilibria and stability in VlasovMaxwell equation
 10/19/2022
 4:10 PM  5:00 PM
 C304 Wells Hall
(Virtual Meeting Link)
 Willie WaiYeung Wong (wongwil2@msu.edu)
We present results on the stability of equilibria (timeindependent solutions) of the VlasovMaxwell equation. In particular, linear stability criteria for certain classes of equilibria are discussed. We also give a result on the nonlinear stability of an initialboundary value problem for the VlasovPoisson equation.
**Note: speaker will present Virtually. Participants can join in person to view the presentation in C304, or through the Zoom link.**

30470

Thursday 10/20 3:00 PM

Pavel coupek , MSU

Eigenalgebra over field
 Pavel coupek , MSU
 Eigenalgebra over field
 10/20/2022
 3:00 PM  4:00 PM
 C204A Wells Hall
 Peikai Qi (qipeikai@msu.edu)
We move from the talks about general eigenalgebra to a special base field.

29420

Thursday 10/20 4:10 PM

Ken Ribet, UC Berkeley

The Unreasonable Effectiveness of Elliptic Curves
 Ken Ribet, UC Berkeley
 The Unreasonable Effectiveness of Elliptic Curves
 10/20/2022
 4:10 PM  5:00 PM
 C304 Wells Hall
 Joseph Waldron (waldro51@msu.edu)
If a and b are integers that satisfy a simple nonvanishing
condition, the cubic equation y^2 = x^3 + ax + b defines an elliptic
curve over the field of rational numbers. Elliptic curves have been
studied for millennia and seem to occur all over the place in
mathematics, physics and other sciences. In my talk, I'll explain how a
specific elliptic curve provides the solution to a surprisingly hard "brain
teaser" that had a big run on social media a few years ago.

29434

Friday 10/21 3:00 PM

Ken Ribet, UC Berkeley

Cyclotomic torsion points on abelian varieties over number fields
 Ken Ribet, UC Berkeley
 Cyclotomic torsion points on abelian varieties over number fields
 10/21/2022
 3:00 PM  4:00 PM
 C304 Wells Hall
 Preston Wake (wakepres@msu.edu)
Over 40 years ago, I proved the finiteness of the group of cyclotomic torsion points on an abelian variety over a number field. (A torsion point is cyclotomic if its coordinates lie in the field obtained by
adjoining all roots of unity to the base field.) If the abelian variety is one that we know well, and if the number field is the field of rational numbers, we can hope to determine explicitly the group of
its cyclotomic torsion points. I will illustrate this theme in the situation studied by Barry Mazur in his landmark "Eisenstein ideal" article, i.e., that where the abelian variety is the Jacobian of the
modular curve $X_0(p)$.

29396

Monday 10/24 3:00 PM

Nathan Chen, Columbia University

On the irrationality of some algebraic varieties and their subvarieties
 Nathan Chen, Columbia University
 On the irrationality of some algebraic varieties and their subvarieties
 10/24/2022
 3:00 PM  4:00 PM
 C304 Wells Hall
 Laure Flapan (flapanla@msu.edu)
The classical question of determining which varieties are rational has led to a huge amount of interest and activity. On the other hand, one can take on a complementary perspective  given a smooth projective variety whose nonrationality is known, how far is it from being rational? I will survey what is currently known, with an emphasis on hypersurfaces and complete intersections.

30472

Wednesday 10/26 3:00 PM

Dapeng Zhan, MSU

Boundary Green's function and Minkowski content for SLE$_\kappa(\rho)$
 Dapeng Zhan, MSU
 Boundary Green's function and Minkowski content for SLE$_\kappa(\rho)$
 10/26/2022
 3:00 PM  3:50 PM
 C405 Wells Hall
 Dapeng Zhan (zhan@msu.edu)
We prove the existence of the Minkowski content of the intersection of an SLE$_\kappa(\rho)$ curve with a real interval using the standard approach, which is to estimate the convergence rate of onepoint and twopoint boundary Green's functions of SLE$_\kappa(\rho)$. Then we show the existence of a conformally covariant measure called Minkowski content measure on the intersection of an SLE$_\kappa(\rho)$ curve with a half real line, which is closely related to the Minkowski content. Using the Minkowski content measure, we construct rooted and unrooted SLE$_\kappa(\rho)$ bubble measures, which are supported on loops and satisfy SLE$_\kappa(\rho)$type domain Markov property.

30468

Wednesday 10/26 3:00 PM

Nadia Lafrenière, Dartmouth

A Study Of Homomesy On Permutations Using The FindStat Database
 Nadia Lafrenière, Dartmouth
 A Study Of Homomesy On Permutations Using The FindStat Database
 10/26/2022
 3:00 PM  3:50 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Bruce E Sagan (bsagan@msu.edu)
We performed a systematic study of permutation statistics and
bijective maps on permutations, looking for the homomesy phenomenon.
Homomesy occurs when the average value of a statistic is the same on
each orbit of a given map. The maps that exhibit homomesy include the
Lehmer code rotation, the reverse, the complement, and the
Kreweras complement, all of which have some geometric interpretations.
The statistics studied relate to familiar notions such as inversions,
descents, and permutation patterns, among others. Beside the many new
homomesy results, I’ll discuss our research method, in which we used
SageMath to search the FindStat combinatorial statistics database to
identify potential instances of homomesy, and what this experiment
taught us about the maps themselves and the homomesy phenomenon at large.
This is joint work with Jennifer Elder, Erin McNicholas, Jessica Striker
and Amanda Welch.

30456

Thursday 10/27 2:30 PM

Guanghui Lan, Georgia Institute of Technology

1WMINDS talk (passcode is the first prime number > 100).
 Guanghui Lan, Georgia Institute of Technology
 1WMINDS talk (passcode is the first prime number > 100).
 10/27/2022
 2:30 PM  3:30 PM
 Online (virtual meeting)
 Mark A Iwen ()
See https://sites.google.com/view/mindsseminar/home

30474

Thursday 10/27 3:00 PM

Pavel coupek, MSU

Eigenalgebra over field and over DVR
 Pavel coupek, MSU
 Eigenalgebra over field and over DVR
 10/27/2022
 3:00 PM  4:00 PM
 C204A Wells Hall
 Peikai Qi (qipeikai@msu.edu)
Continuation of previous talk. Following the eigenalgebra book, after considering eigenalgebra over field, if time allow, we will talks about eigenalgebra over dvr

29384

Thursday 10/27 4:10 PM

Victor Reiner, University of Minnesota

Hop on the leftregular bandwagon!
 Victor Reiner, University of Minnesota
 Hop on the leftregular bandwagon!
 10/27/2022
 4:10 PM  5:00 PM
 C304 Wells Hall
 Joseph Waldron (waldro51@msu.edu)
We will give a gentle introduction to a class of finite semigroups
bearing the cryptic name "leftregular bands" (LRBs). These LRBs show up, for example, in the combinatorics of reflection groups and hyperplane arrangements, in the analysis of mixing times for certain cardshuffling Markov chains, as well as in the space of phylogenetic trees.
We focus on examples with large groups of symmetries that act on the semigroup algebra of the LRB. Here the wellunderstood LRB representation theory, together with some combinatorics, allow one to answer two invarianttheory questions: What is the structure of the invariant subalgebra, and how does it act on the whole semigroup algebra?
This is based on joint work with Sarah Brauner and Patty Commins (arXiv:2206.11406).

30481

Monday 10/31 12:30 PM

Linhui Shen, Michigan State University

Cluster structures on braid varieties
 Linhui Shen, Michigan State University
 Cluster structures on braid varieties
 10/31/2022
 12:30 PM  1:30 PM
 C304 Wells Hall
 Linhui Shen (shenlin1@msu.edu)
Let G be a complex simple group. Let $\beta$ be a positive braid whose Demazure product is the longest Weyl group element. The braid variety X($\beta$) generalizes many well known varieties, including positroid cells, open Richardson varieties, and double BottSamelson cells. We provide a concrete construction of the cluster structure on X($\beta$), using the weaves of Casals and Zaslow. We show that the coordinate ring of X($\beta$) is a cluster algebra, which confirms a conjecture of Leclerc as special cases. As an application, we show that X($\beta$) admits a natural Poisson structure and can be further quantized. If
time permits, I will explain several of its applications on representation theory and knot theory,
including its connections with the KazhdanLusztig Rpolynomials and a geometric interpretation of the
KhovanovRozansky homology (following the work of LamSpeyer and GalashinLam). This talk is based on joint work with Roger Casals, Eugene Gorsky, Mikhail Gorsky, Ian Le, and Jose Simental (arXiv:2207.11607).

30483

Monday 10/31 1:00 PM

Liping Yin, MSU

ExemplarBased Texture Synthesis: Past and Current Approaches
 Liping Yin, MSU
 ExemplarBased Texture Synthesis: Past and Current Approaches
 10/31/2022
 1:00 PM  2:00 PM
 C117 Wells Hall
(Virtual Meeting Link)
 Craig Gross (grosscra@msu.edu)
In this talk, we will give an overview of exemplarbased texture synthesis. For the first part of the talk, we will discuss a classical approach via matching statistics of wavelet coefficients and its shortcomings. In the second part of the talk, we will discuss more recent work using statistics of deep convolutional neural networks for more realistic texture synthesis.
$\\$
This will be a hybrid seminar and take place in C117 Wells Hall and via Zoom at https://msu.zoom.us/j/99426648081?pwd=ZEljM3BPUXg2MjVUMVM5TnlzK2NQZz09 .

29443

Monday 10/31 3:00 PM

Stephanie Chan, UMich

Integral points in families of elliptic curves
 Stephanie Chan, UMich
 Integral points in families of elliptic curves
 10/31/2022
 3:00 PM  4:00 PM
 C304 Wells Hall
 Preston Wake (wakepres@msu.edu)
Given an elliptic curve over a number field with its Weierstrass model, we can study the integral points on the curve. Taking an infinite family of elliptic curves and imposing some ordering, we may ask how often a curve has an integral point and how many integral points there are on average. We expect that elliptic curves with any nontrivial integral points are generally very sparse. In certain quadratic and cubic twist families, we prove that almost all curves contain no nontrivial integral points.

30455

Tuesday 11/1 11:00 AM

Giorgio Young, University of Michigan

Ballistic Transport for Limitperiodic Schrödinger Operators in One Dimension
 Giorgio Young, University of Michigan
 Ballistic Transport for Limitperiodic Schrödinger Operators in One Dimension
 11/01/2022
 11:00 AM  12:00 PM
 C304 Wells Hall
 Jeffrey Hudson Schenker (schenke6@msu.edu)
Abstract: In this talk, I will discuss some results on the transport properties of the class of limitperiodic continuum
Schr\"odinger operators whose potentials are approximated exponentially quickly by a sequence of periodic functions.
For such an operator $H$, and $X_H(t)$ the Heisenberg evolution of the position operator, we show the limit of $\frac{1}{t}X_H(t)\psi$ as $t\to\infty$ exists and is
nonzero for $\psi\ne 0$ belonging to a dense subspace of initial states which are sufficiently regular and of suitably rapid decay.
This is viewed as a particularly strong form of ballistic transport, and this is the first time it has been proven in a continuum almost periodic
nonperiodic setting. In particular, this statement implies that for the initial states considered, the second moment grows quadratically in time.

29433

Tuesday 11/1 3:00 PM

Ka Ho Wong, Texas A&M

On the 1loop conjecture of fundamental shadow link complements
 Ka Ho Wong, Texas A&M
 On the 1loop conjecture of fundamental shadow link complements
 11/01/2022
 3:00 PM  4:00 PM
 C304 Wells Hall
(Virtual Meeting Link)
 Vijay B Higgins (higgi231@msu.edu)
The 1loop conjecture proposed by Dimofte and Garoufalidis suggests a simple and explicit formula to compute the adjoint twisted Reidemeister torsion of hyperbolic 3manifolds with toroidal boundary in terms of the shape parameters of any ideal triangulation of the manifolds. In this talk, I will give a brief overview of the conjecture and present our recent result on the 1loop conjecture for fundamental shadow link complements. This is a joint work with Tushar Pandey.

30488

Tuesday 11/1 3:00 PM

Zhenqi Wang, Michigan State University

Local rigidity of higher rank partially hyperbolic algebraic actions
 Zhenqi Wang, Michigan State University
 Local rigidity of higher rank partially hyperbolic algebraic actions
 11/01/2022
 3:00 PM  4:00 PM
 A136 Wells Hall
 Huyi Hu (hhu@msu.edu)
We give a complete solution to the local classification program of higher rank partially hyperbolic algebraic actions. We show $C^\infty$ local rigidity of abelian ergodic algebraic actions for symmetric space examples, twisted symmetric space examples and automorphisms on nilmanifolds. The method is a combination of representation theory, harmonic analysis and a KAM iteration. A striking feature of the method is no specific information from representation theory is needed. It is the first time local rigidity for nonaccessible partially hyperbolic actions has ever been obtained other than torus examples. Even for Anosov actions, our results are new: it is the first time twisted spaces with nonabelian nilradical have been treated in the literature.

30482

Wednesday 11/2 3:00 PM

Shlomo Levental, MSU

FORMULAS FOR THE DIVERGENCE OPERATOR IN ISONORMAL GAUSSIAN SPACE
 Shlomo Levental, MSU
 FORMULAS FOR THE DIVERGENCE OPERATOR IN ISONORMAL GAUSSIAN SPACE
 11/02/2022
 3:00 PM  3:50 PM
 C405 Wells Hall
 Dapeng Zhan (zhan@msu.edu)
In this joint paper with P. Vellaisamy, we first derive some explicit formulas for the computation
of the nth order divergence operator in Malliavin calculus in the onedimensional case. We then extend these results to the case of isonormal Gaussian space. Our results generalize some of the known results for the divergence operator. Our approach in deriving the formulas is new and simple.

30478

Wednesday 11/2 3:00 PM

James Propp, University of Massachusetts, Lowell

A Pentagonal Number Theorem for Tribone Tilings
 James Propp, University of Massachusetts, Lowell
 A Pentagonal Number Theorem for Tribone Tilings
 11/02/2022
 3:00 PM  3:50 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Bruce E Sagan (bsagan@msu.edu)
Conway and Lagarias used combinatorial group theory to show that certain
roughly triangular regions in the hexagonal grid cannot be tiled by the
shapes Thurston later dubbed tribones. The ideas of Conway, Lagarias, and
Thurston have found many applications in the study of tilings in the plane.
Today I'll discuss a twoparameter family of roughly hexagonal regions in
the hexagonal grid I call benzels. A variant of Gauss’ shoelace formula
allows one to compute the signed area (aka algebraic area) enclosed by a
closed polygonal path, and by “twisting” the formula one can compute the
values of the ConwayLagarias invariant for all benzels. It emerges that the
(a,b)benzel can be tiled by tribones if and only if a and b are the paired
pentagonal numbers k(3k+1)/2, k(3k1)/2. This is joint work with Jesse Kim.

30484

Wednesday 11/2 5:00 PM

Christopher Potvin, MSU

Escapism in Math: The Mathematics of Escapes
 Christopher Potvin, MSU
 Escapism in Math: The Mathematics of Escapes
 11/02/2022
 5:00 PM  6:00 PM
 C517 Wells Hall
 Chris David Stclair (stclai22@msu.edu)
Abstract: There comes a time in every mathematician's life when they are detained by an evil dictator or warden with a soft spot for riddles. Fortunately for us, these riddles are often rooted in simple mathematics. This talk will prepare you for that inevitable occurrence by going over the mathematics involved in several prominent riddles. Along the way, we'll pick up some tricks of the trade that you can use when facing a logic puzzle to make an escape of your own.

30475

Thursday 11/3 2:30 PM

Dr. Harvey Stein, Senior VP, Labs Group, Two Sigma

Model Invariants and Functional Regularization
 Dr. Harvey Stein, Senior VP, Labs Group, Two Sigma
 Model Invariants and Functional Regularization
 11/03/2022
 2:30 PM  3:30 PM
 C304 Wells Hall
Linked Abstract
When modeling data, we would like to know that our models are extracting facts about the data itself, and not about something arbitrary, like the order of the factors used in the modeling. Formally speaking, this means we want the model to be invariant with respect to certain transformations. Here we look at different models and the nature of their invariants. We find that regression, MLE and Bayesian estimation all are invariant with respect to linear transformations, whereas regularized regressions have a far more limited set of invariants. As a result, regularized regressions produce results that are less about the data itself and more about how it is parameterized. To correct this, we propose an alternative expression of regularization which we call functional regularization. Ridge regression and lasso can be recast in terms of functional regularization, as can Bayesian estimation. But functional regularization preserves model invariance, whereas ridge and lasso do not. It is also more flexible, easier to understand, and can even be applied to nonparametric models.

30457

Thursday 11/3 2:30 PM

Alex Townsend , Cornell University

1WMINDS talk (passcode is the first prime number > 100).
 Alex Townsend , Cornell University
 1WMINDS talk (passcode is the first prime number > 100).
 11/03/2022
 2:30 PM  3:30 PM
 Online (virtual meeting)
 Mark A Iwen ()
See https://sites.google.com/view/mindsseminar/home

30486

Thursday 11/3 3:00 PM

Keping Huang, MSU

Eigenalgebras over DVR, continued
 Keping Huang, MSU
 Eigenalgebras over DVR, continued
 11/03/2022
 3:00 PM  4:00 PM
 C204A Wells Hall
 Keping Huang (huangk23@msu.edu)
No abstract available.

29386

Thursday 11/3 4:10 PM

Tasho Kaletha, University of Michigan

Representations of reductive groups over local fields
 Tasho Kaletha, University of Michigan
 Representations of reductive groups over local fields
 11/03/2022
 4:10 PM  5:00 PM
 C304 Wells Hall
 Joseph Waldron (waldro51@msu.edu)
The pioneering work of Langlands has established the theory of reductive algebraic groups and their representations as a key part of modern number theory. I will survey classical and modern results in the representation theory of reductive groups over local fields (the fields of real, complex, or padic numbers, or of Laurent series over finite fields) and discuss how they relate to Langlands' ideas, as well as to the various reflections of the basic mathematical idea of symmetry in arithmetic and geometry.

30476

Thursday 11/3 6:00 PM

Dr. Harvey Stein, Senior VP, Labs Group, Two Sigma

Current Issues in Financial Risk Management
 Dr. Harvey Stein, Senior VP, Labs Group, Two Sigma
 Current Issues in Financial Risk Management
 11/03/2022
 6:00 PM  8:00 PM
 3202 STEM
Linked Abstract
Innovations and changes in financial markets do not come without
risks. We will discuss some recent innovations and changes and
discuss their implications for risk management, such as the risks
associated with cryptocurrency, and the impact on finance of
machine learning.

30473

Monday 11/7 12:30 PM

Daniel Soskin, University of Notre Dame

Determinantal inequalities for totally positive matrices
 Daniel Soskin, University of Notre Dame
 Determinantal inequalities for totally positive matrices
 11/07/2022
 12:30 PM  1:30 PM
 C304 Wells Hall
 Linhui Shen (shenlin1@msu.edu)
Totally positive matrices are matrices in which each minor is positive. Lusztig extended the notion to reductive Lie groups. He also proved that specialization of elements of the dual canonical basis in representation theory of quantum groups at q=1 are totally nonnegative polynomials. Thus, it is important to investigate classes of functions on matrices that are positive on totally positive matrices. I will discuss two sourses of such functions. One has to do with multiplicative determinantal inequalities (joint work with M.Gekhtman). Another deals with majorizing monotonicity of symmetrized Fischer's products which are known for hermitian positive semidefinite case which brings additional motivation to verify if they hold for totally positive matrices as well (joint work with M.Skandera). The main tools we employed are network parametrization, TemperleyLieb and monomial trace immanants.

30492

Monday 11/7 1:00 PM

Yuta Hozumi, MSU

Ensemble Clustering Methods in Transcriptomics Data
 Yuta Hozumi, MSU
 Ensemble Clustering Methods in Transcriptomics Data
 11/07/2022
 1:00 PM  2:00 PM
 C117 Wells Hall
(Virtual Meeting Link)
 Craig Gross (grosscra@msu.edu)
Transcriptomic data, more specifically single cell RNA sequencing (scRNAseq), is an emerging field in biology that is used to obtain molecular understanding of cells. Analyzing scRNAseq gives insight to protein and gene regulatory networks, protein expression and diseases. In this talk, I will present ensemble clustering methods used to find clusters in scRNAseq data, which can then be used for further analysis into differential gene expression, cell trajectory and cellcell communication.
$\\$
This will be a hybrid seminar and take place in C117 Wells Hall and via Zoom at https://msu.zoom.us/j/99426648081?pwd=ZEljM3BPUXg2MjVUMVM5TnlzK2NQZz09 .

30477

Monday 11/7 2:00 PM

Calvin McPhailSnyder , Duke University

RTG Seminar: Quantum and hyperbolic invariants of knots (Introductory talk)
 Calvin McPhailSnyder , Duke University
 RTG Seminar: Quantum and hyperbolic invariants of knots (Introductory talk)
 11/07/2022
 2:00 PM  3:00 PM
 C304 Wells Hall
(Virtual Meeting Link)
 Efstratia Kalfagianni (kalfagia@msu.edu)
This talk consists of two related but distinct parts, and should be accessible if you know some algebraic topology and/or differential geometry. The first part is about quantum invariants: I will sketch how to compute the colored Jones polynomials of a knot and discuss their origin in representation theory. The second part is about hyperbolic geometry: I will discuss the basics of hyperbolic knot theory and explain how to compute hyperbolic structures and their volumes using ideal triangulations. The goal is to motivate the volume conjecture discussed in my main talk, which relates the colored Jones polynomials to the hyperbolic volume.

29399

Monday 11/7 3:00 PM

Qingjing Chen, University of California Santa Barbara

Kuznetsov components of some Fano fourfolds
 Qingjing Chen, University of California Santa Barbara
 Kuznetsov components of some Fano fourfolds
 11/07/2022
 3:00 PM  4:00 PM
 C304 Wells Hall
 Laure Flapan (flapanla@msu.edu)
Kuznetsov component A_X of an algebraic variety X is defined to be the right orthogonal of some exceptional collection in the bounded derived category of X. When X is a cubic fourfold or Gushel Mukai fourfold, A_X is a noncommutative K3 surface in the sense that its Serre functor is given by "shifting by 2". Whether or not A_X is equivalent to the bounded derived category of an actual K3 surface is believed to be related to the rationality of the variety X , therefore it has received extensive studies. Yet not many studies seem to answer the question of when the Kuznetsov component of a cubic fourfold is equivalent to that of a Gushel Mukai fourfold, we believe that the answer of this question should be interesting for it will give a part of "Torelli theorem for noncommutative K3 surfaces". In this talk, I will present some partial results which address the previous question.

30489

Monday 11/7 4:00 PM

Brent Nelson, MSU

Free transport, I
 Brent Nelson, MSU
 Free transport, I
 11/07/2022
 4:00 PM  5:30 PM
 C517 Wells Hall
 Brent Nelson (banelson@msu.edu)
In operator algebras, specifically free probability, free transport is a technique for producing statepreserving isomorphisms between C* and von Neumann algebras that was developed by Guionnet and Shlyakhtenko in their 2014 Inventiones paper. The inspiration for their work comes from the field of optimal transport, specifically work of Brenier from 1991 who showed that under very mild assumptions one can push forward a probability measure on $\mathbb{R}^n$ to the Gaussian measure. In the noncommutative case, Guionnet and Shlyakhtenko showed that if $x_1,\ldots, x_n$ are selfadjoint operators in a tracial von Neumann algebra $(M,\tau)$ whose distribution satisfies an "integrationbyparts" formula up to a small perturbation, then these operators generate a copy of the free group factor $L(\mathbb{F}_n)$. In this series of talks, I will give an overview of their proof, discuss some applications of their result, and survey the current state of free transport theory.

29411

Tuesday 11/8 3:00 PM

Calvin McPhailSnyder , Duke University

Hyperbolic tensor networks and the volume conjecture
 Calvin McPhailSnyder , Duke University
 Hyperbolic tensor networks and the volume conjecture
 11/08/2022
 3:00 PM  4:00 PM
 C304 Wells Hall
(Virtual Meeting Link)
 Efstratia Kalfagianni (kalfagia@msu.edu)
Quantum invariants of links like the colored Jones polynomial (which arise from the quantum ChernSimons theory of WittenReshetikhinTuraev) have a purely algebraic construction in terms of the representation theory of quantum groups. Despite this algebraic nature they appear to be connected to geometry: a class of related volume conjectures assert that their semiclassical asymptotics determine geometric invariants like the hyperbolic volume. To better understand these conjectures a number of authors have studied ways to twist quantum invariants by geometric data. In particular, Blanchet, Geer, PatureauMirand, and Reshetikhin recently defined quantum holonomy invariants depending on a link in S^3 and a flat 𝔰𝔩₂ connection on its complement. Their construction uses certain unusual cyclic modules of quantum 𝔰𝔩₂. For technical reasons the invariants are quite difficult to compute. In this talk (based on joint work with Nicolai Reshetikhin) I will explain how to effectively compute them using hyperbolic tensor networks constructed from quantum dilogarithms. Our construction reveals deep connections with hyperbolic geometry and suggests a way to break the KashaevMurakamiMurakami volume conjecture into two simpler pieces.

30491

Wednesday 11/9 3:00 PM

Lubashan Pathirana Karunarathna, MSU

Limiting Theorems for Compositions of Stationary and Ergodic Random Maps With Applications in Quantum Processes
 Lubashan Pathirana Karunarathna, MSU
 Limiting Theorems for Compositions of Stationary and Ergodic Random Maps With Applications in Quantum Processes
 11/09/2022
 3:00 PM  3:50 PM
 C405 Wells Hall
 Dapeng Zhan (zhan@msu.edu)
A discrete parameter quantum process is represented by a sequence of quantum operations, which are completely positive maps that are trace nonincreasing. Given a stationary and ergodic sequence of such maps, an ergodic theorem describing convergence to equilibrium for a general class of such processes was recently obtained by Movassagh and Schenker. Under irreducibility conditions, we obtain a law of large numbers that describes the asymptotic behavior of the processes involving the Lyapunov exponent. Furthermore, a central limittype theorem is obtained under mixing conditions. These results do not require the sequences of quantum operations that describe the quantum process to be trace nonincreasing and hence can be applied to a larger class of compositions of random positive maps. In the continuoustime parameter, a quantum process is represented by a doubleindexed family of positive mapvalued random variables. For a stationary and ergodic family of such maps, we extend the results by Movassagh and Schenker to the continuous case.

29379

Wednesday 11/9 4:10 PM

Dimitris Vardakis, MSU

Buffon's needle problem for a random planar disklike Cantor set
 Dimitris Vardakis, MSU
 Buffon's needle problem for a random planar disklike Cantor set
 11/09/2022
 4:10 PM  5:00 PM
 C304 Wells Hall
 Willie WaiYeung Wong (wongwil2@msu.edu)
The Favard length of the planar $1/4$corner Cantor set is $0$. Estimates exists about the rate with which the Favard length of the previous steps goes to $0$, but the exact rate of decay is unknown. However, if one considers a random construction of the $1/4$corner Cantor set, things might seem better. In fact, Peres and Solomyak showed that the rate of decay for the average Favard length for the random $1/4$corner Cantor set is of order exactly $1/n$. We show that the rate of decay for a random disklike analogue has again order $1/n$. This suggests that any ``reasonable'' random Cantor set of positive and finite length might decay at the same rate.

30490

Thursday 11/10 3:00 PM

Keping Huang, MSU

Classical modular symbols
 Keping Huang, MSU
 Classical modular symbols
 11/10/2022
 3:00 PM  4:00 PM
 C204A Wells Hall
 Keping Huang (huangk23@msu.edu)
No abstract available.

30480

Monday 11/14 12:30 PM

Nicholas Ovenhouse, Yale University

Super Cluster Algebras from Surfaces
 Nicholas Ovenhouse, Yale University
 Super Cluster Algebras from Surfaces
 11/14/2022
 12:30 PM  1:30 PM
 C304 Wells Hall
 Linhui Shen (shenlin1@msu.edu)
One of the most wellknown examples of a cluster structure comes from Penner's lambdalength coordinates on the decorated Teichmuller space of a surface. In 2019, Penner and Zeitlin defined a supermanifold generalizing the decorated Teichmuller space, which involves new anticommuting variables. I wall talk about some recent work with Gregg Musiker and Sylvester Zhang, where we showed that the coordinates on the decorated super Teichmuller space have many of the nice properties associated to a cluster structure, such as a kind of Laurent phenomenon, positivity, and some interesting combinatorial interpretations of the Laurent expressions, involving double dimer covers of certain graphs.

31497

Monday 11/14 1:00 PM

Albert Chua, MSU

Wavelets, the Scattering Transform, and Generalizations
 Albert Chua, MSU
 Wavelets, the Scattering Transform, and Generalizations
 11/14/2022
 1:00 PM  2:00 PM
 C117 Wells Hall
(Virtual Meeting Link)
 Craig Gross (grosscra@msu.edu)
In this talk, we give an overview of some basic properties of wavelets. We then introduce the Windowed Scattering Transform and go over stability and invariance properties that make it desirable as a feature extractor. Finally, we provide a generalization of the Windowed Scattering Transform that is translation invariant and discuss other stability and invariance properties of our generalized Scattering Transform.
$\\$
This will be a hybrid seminar and take place in C117 Wells Hall and via Zoom at https://msu.zoom.us/j/99426648081?pwd=ZEljM3BPUXg2MjVUMVM5TnlzK2NQZz09 .

30495

Monday 11/14 1:30 PM

Higinio Dominguez, MSU; Tina Haselius, Teacher; Sofia Abreu, MSU; Melvin Peralta, MSU

Animating Mathematical Concepts…(and the learning of teachers, students, and researchers)
 Higinio Dominguez, MSU; Tina Haselius, Teacher; Sofia Abreu, MSU; Melvin Peralta, MSU
 Animating Mathematical Concepts…(and the learning of teachers, students, and researchers)
 11/14/2022
 1:30 PM  2:30 PM
 115 Erickson Hall
 Lisa Keller (kellerl@msu.edu)
Mathematics education research is overwhelmingly assimilationist in its desire
to change people, teachers, students, researchers, instead of changing the mathematics. In this teachingresearch collaboration, one teacher (Tina Haselius), two graduate research assistants (Sofía Abreu and Melvin Peralta), and one mathematics education researcher (Higinio Dominguez) will share their emerging experiences learning how to animate mathematical concepts. While one key goal in our collaboration has been to resist the violence of trying to change, assimilate, and colonize learners, the process of animating mathematical concepts has, in beautiful and nonviolent ways, allowed us to experience change in and among ourselves as we learn to (co)respond to the animacy and agency of the mathematical concepts that we set out to animate in our teachingresearch group.

29394

Monday 11/14 3:00 PM

Lena Ji, University of Michigan

Finite order birational automorphisms of Fano hypersurfaces
 Lena Ji, University of Michigan
 Finite order birational automorphisms of Fano hypersurfaces
 11/14/2022
 3:00 PM  4:00 PM
 C304 Wells Hall
 Joseph Waldron (waldro51@msu.edu)
The birational automorphism group is a natural birational invariant associated to an algebraic variety. In this talk, we study the specialization homomorphism for the birational automorphism group. As an application, building on work of Kollár and of Chen–Stapleton, we show that a very general ndimensional complex hypersurface X of degree ≥ 5⌈(n+3)/6⌉ has no finite order birational automorphisms. This work is joint with Nathan Chen and David Stapleton.

30496

Monday 11/14 4:00 PM

Brent Nelson, MSU

Free transport, II
 Brent Nelson, MSU
 Free transport, II
 11/14/2022
 4:00 PM  5:30 PM
 C517 Wells Hall
 Brent Nelson (banelson@msu.edu)
In operator algebras, specifically free probability, free transport is a technique for producing statepreserving isomorphisms between C* and von Neumann algebras that was developed by Guionnet and Shlyakhtenko in their 2014 Inventiones paper. The inspiration for their work comes from the field of optimal transport, specifically work of Brenier from 1991 who showed that under very mild assumptions one can push forward a probability measure on $\mathbb{R}^n$ to the Gaussian measure. In the noncommutative case, Guionnet and Shlyakhtenko showed that if $x_1,\ldots, x_n$ are selfadjoint operators in a tracial von Neumann algebra $(M,\tau)$ whose distribution satisfies an "integrationbyparts" formula up to a small perturbation, then these operators generate a copy of the free group factor $L(\mathbb{F}_n)$. In this series of talks, I will give an overview of their proof, discuss some applications of their result, and survey the current state of free transport theory.

29430

Tuesday 11/15 3:00 PM

LouisHadrien Robert, Université Clermont Auvergne

Symmetric link homology
 LouisHadrien Robert, Université Clermont Auvergne
 Symmetric link homology
 11/15/2022
 3:00 PM  4:00 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Vijay B Higgins (higgi231@msu.edu)
In this talk I will detail a construction of symmetric link
homology. In particular, this provides a nontrivial categorification of
1 and a finite dimensional categorification of the colored Jones
polynomial and a new categorification of the Alexander polynomial. I
will also explain how this relates to the triply graded homology and
knot Floer homology.

30497

Wednesday 11/16 3:00 PM

John Shareshian, Washington University

Coset lattices, invariable generation of simple groups, and a problem on binomial coefficients
 John Shareshian, Washington University
 Coset lattices, invariable generation of simple groups, and a problem on binomial coefficients
 11/16/2022
 3:00 PM  3:50 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Bruce E Sagan (bsagan@msu.edu)
In joint work with Russ Woodroofe, we showed that the order complex of the poset of all cosets of all proper subgroups of a finite group, ordered by inclusion, has noncontractible order complex using Smith Theory. A key part of our proof involves invariable generation of finite groups: two subsets $S,T$ of a group $G$ generate $G$ invariably if, for every $g,h \in G$, $g^{1}Sg$ and $h^{1}Th$ together generate $G$. It remains open whether the alternating group $A_n$ can be generated invariably by $\{s\}$ and $\{t\}$ with both $s,t$ having prime power order. This question is closely related to a (still open) question about prime divisors of binomial coefficients. I will discuss all of this, along with current work joint with Bob Guralnick and Russ Woodroofe about invariable generation of arbitrary simple groups by two elements of prime or prime power order.

29444

Wednesday 11/16 4:10 PM

Perry Kleinhenz, MSU

Energy decay for the damped wave equation
 Perry Kleinhenz, MSU
 Energy decay for the damped wave equation
 11/16/2022
 4:10 PM  5:00 PM
 C517 Wells Hall
 Willie WaiYeung Wong (wongwil2@msu.edu)
The damped wave equation models the behavior of vibrating systems exposed to some damping force, which causes the total energy to decay. In this talk, I will discuss classical results that give upper and lower bounds on decay, based on the dynamics of the geodesic flow and the support of the damping. I will discuss recent generalizations of these results to time dependent, unbounded, or anisotropic damping.
(Note location: this talk will be held in C517 due to hiring meeting in C304.)

30458

Thursday 11/17 2:30 PM

Wei Zhu , University of Massachusetts Amherst

1WMINDS talk (passcode is the first prime number > 100).
 Wei Zhu , University of Massachusetts Amherst
 1WMINDS talk (passcode is the first prime number > 100).
 11/17/2022
 2:30 PM  3:30 PM
 Online (virtual meeting)
 Mark A Iwen ()
See https://sites.google.com/view/mindsseminar/home

31496

Thursday 11/17 3:00 PM

Jie Yang

Modular symbols and modular forms
 Jie Yang
 Modular symbols and modular forms
 11/17/2022
 3:00 PM  4:00 PM
 C204A Wells Hall
 Jie Yang (yangji79@msu.edu)
We will define modular symbols and discuss its relation with modular forms.

31498

Monday 11/21 1:00 PM

Liping Yin, MSU

Long Range Constraints for Neural Texture Synthesis Using Sliced Wasserstein Loss
 Liping Yin, MSU
 Long Range Constraints for Neural Texture Synthesis Using Sliced Wasserstein Loss
 11/21/2022
 1:00 PM  2:00 PM
 C117 Wells Hall
(Virtual Meeting Link)
 Craig Gross (grosscra@msu.edu)
In the past decade, exemplarbased texture synthesis algorithms have seen strong gains in performance by matching statistics of deep convolutional neural networks. However, these algorithms require regularization terms or useradded spatial tags to capture long range constraints in images. Thus, we propose a new set of statistics for exemplar based texture synthesis based on Sliced Wasserstein Loss and create a multiscale algorithm to synthesize textures without any regularization terms or useradded spatial tags. Lastly, we study the ability of our proposed algorithm to capture long range constraints in images and compare our results to other exemplarbased neural texture synthesis algorithms.
$\\$
This will be a hybrid seminar and take place in C117 Wells Hall and via Zoom at https://msu.zoom.us/j/99426648081?pwd=ZEljM3BPUXg2MjVUMVM5TnlzK2NQZz09 .

31501

Monday 11/21 4:00 PM

Lucas Hall, MSU

Modular Stonevon Neumann Theorems
 Lucas Hall, MSU
 Modular Stonevon Neumann Theorems
 11/21/2022
 4:00 PM  5:30 PM
 C517 Wells Hall
 Brent Nelson (banelson@msu.edu)
I’ll talk about C*modules and representations on them, developing a loose parallel with the Hilbert space case. For specialized C*modules, much can be said, and a classification of these modules suggests a vast generalization of the Stonevon Neumann Theorem which accommodates all of the data of generalized C*dynamical systems.

31499

Monday 11/28 1:00 PM

Rolando Ramos, MSU

TBD
This will be a hybrid seminar and take place in C117 Wells Hall and via Zoom at https://msu.zoom.us/j/99426648081?pwd=ZEljM3BPUXg2MjVUMVM5TnlzK2NQZz09 .

30449

Monday 11/28 3:00 PM

Zijian Yao, University of Chicago

The eigencurve over the boundary of the weight space
 Zijian Yao, University of Chicago
 The eigencurve over the boundary of the weight space
 11/28/2022
 3:00 PM  4:00 PM
 C304 Wells Hall
 Preston Wake (wakepres@msu.edu)
The eigencurve is a rigid analytic curve that $p$adically interpolates eigenforms of finite slope. The global geometry of the eigencurve is somewhat mysterious. However, over the boundary, it is predicted to behave rather nicely (by the socalled Halo conjecture). This conjecture has been studied by LiuWanXiao for definite quaternion algebras. In this talk, we will report on some work in progress on this conjecture in the case of $\rm{GL}(2)$. If time permits, we will discuss some generalizations towards groups beyond $\rm{GL}(2)$. This is partially joint with H. Diao.

29441

Monday 11/28 4:00 PM

Matthew Lorentz, MSU

An Introduction to Ktheory
 Matthew Lorentz, MSU
 An Introduction to Ktheory
 11/28/2022
 4:00 PM  5:30 PM
 C517 Wells Hall
 Brent Nelson (banelson@msu.edu)
Based on the work of Grothendieck, in the 1960's Atiyah and Hirzebruch developed Ktheory as a tool for algebraic geometry. Adapted to the topological setting Ktheory can be regarded as the study of a ring generated by vector bundles. In the 1970's it was introduced as a tool in C*algebras. C*algebras are often considered to be "noncommutative topology", additionally they are an algebra over the complex numbers. In this setting the algebraic and topological definitions of Ktheory overlap giving us a powerful tool. Essential for the Elliott classification program, for certain classes of C*algebras, Ktheory is a complete invariant. Ktheory is also a natural setting for higher index theory.
We will begin by looking at different types of equivalence for projections. Then we will build a monoid where these types of equivalences are equivalent. We then use the Grothendieck construction to turn our monoid into an abelian group. This group is called the $K_0$ group of our algebra and can be thought of as the "connected components" of projections in our C*algebra.
Next, in a similar manner, we construct the $K_1$ group using unitaries from our C*algebra.
Once we have the $K_0$ and $K_1$ groups we will discuss Bott periodicity and the sixterm exact sequence, a tool used to calculate Ktheory.

29448

Tuesday 11/29 3:00 PM

Justin Lanier, University of Chicago

Mapping class groups and dense conjugacy classes
 Justin Lanier, University of Chicago
 Mapping class groups and dense conjugacy classes
 11/29/2022
 3:00 PM  4:00 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Peter Kilgore Johnson (john8251@msu.edu)
I’ll start by introducing infinitetype surfaces—those with infinite genus or infinitely many punctures—and the emerging study of their mapping class groups. One difference from the finitetype setting is that these mapping class groups come with natural nondiscrete topologies. I’ll discuss joint work with Nick Vlamis where we fully characterize which surfaces have mapping class groups with dense conjugacy classes, so that there exists an element that well approximates every mapping class, up to conjugacy.

31502

Tuesday 11/29 4:00 PM

Gus Schrader, Northwestern University

Decorated character varieties and their quantizations from factorization homology
 Gus Schrader, Northwestern University
 Decorated character varieties and their quantizations from factorization homology
 11/29/2022
 4:00 PM  5:00 PM
 C204A Wells Hall
 Linhui Shen (shenlin1@msu.edu)
I will report on joint work with D. Jordan, I. Le and A. Shapiro in which we construct categorical invariants of decorated surfaces using the stratified factorization homology of Ayala, Francis and Tanaka, together with the representation theory of quantum groups. The categories we obtain can be regarded as `quantizations' of the categories of quasicoherent sheaves on the stacks of decorated local systems on surfaces, and satisfy strong functoriality and locality properties reminiscent of those of a TQFT. I will give an overview of their construction, and explain how to recover FockGoncharovShen's cluster quantizations of related moduli spaces within this framework.

31503

Wednesday 11/30 3:00 PM

Laura Hernando Colmenarejo, North Carolina State University

Multiplying quantum Schubert polynomials using combinatorics
 Laura Hernando Colmenarejo, North Carolina State University
 Multiplying quantum Schubert polynomials using combinatorics
 11/30/2022
 3:00 PM  3:50 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Bruce E Sagan (bsagan@msu.edu)
Schubert polynomials are a very interesting family of polynomials in algebraic geometry due to their relation with the cohomology of the flag variety. Moreover, they are also very interesting from a combinatorial point of view because they can be considered generalizations of Schur functions. In this talk, we will talk about how to multiply a Schubert polynomial by a Schur function indexed by a hook and how we can extend this multiplication to the quantum world. This is a current work with C. Benedetti, N. Bergeron, F. Saliola, and F. Sottile.

30494

Wednesday 11/30 3:00 PM

Leslie Dietiker, Boston University

Characteristics of High School Mathematics Lessons that Increase Opportunities for Captivation
 Leslie Dietiker, Boston University
 Characteristics of High School Mathematics Lessons that Increase Opportunities for Captivation
 11/30/2022
 3:00 PM  4:30 PM
 252 EH
(Virtual Meeting Link)
 Lisa Keller (kellerl@msu.edu)
Why do some high school mathematics lessons captivate high school students and others not? This study explores this question by comparing how the content unfolds in the lessons that students rated highest with respect to their aesthetic affordances (e.g., using terms like “intriguing”, “surprising”) with those the same students rated lowest with respect to their aesthetic affordances (e.g., “just ok”, “dull”). Using a framework that interprets the unfolding content across a lesson as a mathematical story, we identified characteristics of lessons that provoked curiosity or enabled surprise. This talk will explain the methodological approach to studying this question, as well as share the lesson characteristics that related strongly to student experience. These findings point to the characteristics of future lesson designs that could enable more students to experience curiosity and wonder in secondary mathematics classrooms. Also on Zoom: https://msu.zoom.us/j/98171049554 Passcode: GOGREEN

30485

Thursday 12/1 2:30 PM

Zhaoran Wang, Northwestern University

1WMINDS talk (passcode is the first prime number > 100).
 Zhaoran Wang, Northwestern University
 1WMINDS talk (passcode is the first prime number > 100).
 12/01/2022
 2:30 PM  3:30 PM
 Online (virtual meeting)
 Mark A Iwen ()
See https://sites.google.com/view/mindsseminar/home

31500

Thursday 12/1 3:00 PM

Peikai Qi, MSU

Classic modular symbol over complex field
 Peikai Qi, MSU
 Classic modular symbol over complex field
 12/01/2022
 3:00 PM  4:00 PM
 C204A Wells Hall
 Peikai Qi (qipeikai@msu.edu)
We will move from the classic modular symbol form to modular symbol over complex field. And we will use a lot of theorem from previous chapter as black box.

31506

Friday 12/2 6:30 PM

Our undergraduate research teams!

Exchange Program REU Final Presentations
 Our undergraduate research teams!
 Exchange Program REU Final Presentations
 12/02/2022
 6:30 PM  9:45 PM
 C304 Wells Hall
(Virtual Meeting Link)
 Jeanne Wald (wald@msu.edu)
Linked Abstract
Exchange Program REU Final Presentations
Speakers: Our undergraduate research teams!
Title: See the program, which includes descriptions of the research projects
Date: Friday December 2, 2022
Time: 6:30 p.m. – 9:45 p.m.
https://msu.zoom.us/j/92801969144
Meeting ID: 928 0196 9144
Passcode: 112358

30479

Monday 12/5 4:00 PM

Alberto Takase, MSU

TBA
 Alberto Takase, MSU
 TBA
 12/05/2022
 4:00 PM  5:30 PM
 C517 Wells Hall
 Brent Nelson (banelson@msu.edu)
TBA

30463

Tuesday 12/6 11:00 AM

Ekaterina Shchetka, University of Michigan

TBA
 Ekaterina Shchetka, University of Michigan
 TBA
 12/06/2022
 11:00 AM  12:00 PM
 C304 Wells Hall
 Ilya Kachkovskiy (ikachkov@msu.edu)
No abstract available.

31508

Tuesday 12/6 2:00 PM

Yuping Ruan, University of Michigan

Boundary rigidity and filling minimality via the barycenter method
 Yuping Ruan, University of Michigan
 Boundary rigidity and filling minimality via the barycenter method
 12/06/2022
 2:00 PM  3:00 PM
 A136 Wells Hall
 Fan Yang (yangfa31@msu.edu)
A compact manifold with a smooth boundary is boundary rigid if its boundary and boundary distance function uniquely determine its interior up to boundary preserving isometries. Under certain natural conditions, the notion of boundary rigidity is closely related to Gromov's filling minimality. In this talk, we will first give a brief overview of BuragoIvanov's approach to prove filling minimality and boundary rigidity for almost Euclidean and almost real hyperbolic metrics. Then we will explain how we generalize their results to regions in a rank1 symmetric space equipped with an almost symmetric metric. We will also explain the relations to BessonCourtoisGallot's barycenter constructions used in their celebrated volume entropy rigidity theorem.

30446

Tuesday 12/6 3:00 PM

Cameron Gates Rudd, Max Planck Institute, Bonn

TBA
 Cameron Gates Rudd, Max Planck Institute, Bonn
 TBA
 12/06/2022
 3:00 PM  4:00 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Vijay B Higgins (higgi231@msu.edu)
TBA

31507

Wednesday 12/7 3:00 PM

Jinting Liang, Michigan State University

Enriched toric $[\vec{D}]$partitions
 Jinting Liang, Michigan State University
 Enriched toric $[\vec{D}]$partitions
 12/07/2022
 3:00 PM  3:50 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Bruce E Sagan (bsagan@msu.edu)
In this talk I will discuss the theory of enriched toric $[\vec{D}]$partitions. Whereas Stembridge's enriched $P$partitions give rises to the peak algebra which is a subring of the ring of quasisymmetric functions QSym, our enriched toric $[\vec{D}]$partitions will generate the cyclic peak algebra which is a subring of cyclic quasisymmetric functions cQSym. In the same manner as the peak set of linear permutations appears when considering enriched $P$partitions, the cyclic peak set of cyclic permutations plays an important role in our theory.

30459

Thursday 12/8 2:30 PM

Rongjie Lai , Rensselaer Polytechnic Institute

1WMINDS talk (passcode is the first prime number > 100).
 Rongjie Lai , Rensselaer Polytechnic Institute
 1WMINDS talk (passcode is the first prime number > 100).
 12/08/2022
 2:30 PM  3:30 PM
 Online (virtual meeting)
 Mark A Iwen ()
See https://sites.google.com/view/mindsseminar/home

29431

Monday 12/12 11:00 AM

Renaud Requipas, NYU

TBA
 Renaud Requipas, NYU
 TBA
 12/12/2022
 11:00 AM  12:00 PM
 C304 Wells Hall
 Jeffrey Hudson Schenker (schenke6@msu.edu)
No abstract available.
