• Speaker: Raymond Chan, City University of Hong Kong
• Title: TBA; zoom link @ https://sites.google.com/view/minds-seminar/home
• Date: 01/14/2021
• Time: 3:30 PM - 4:30 PM
• Place:  (Virtual Meeting Link)
• Contact: Olga Turanova (turanova@msu.edu)

TBA; (Note the unusual time: 4:30pm Shanghai, 10:30am Paris.)

• Speaker: Daniel Kane, University of California, San Diego
• Title: Point Location and Active Learning
• Date: 01/21/2021
• Time: 2:30 PM - 3:30 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Olga Turanova (turanova@msu.edu)

In the point location problem one is given a hyperplane arrangement and an unknown point. By making linear queries about that point one wants to determine which cell of the hyperplane arrangement it lies in. This problem has an unexpected connection to the problem in machine learning of actively learning a halfspace. We discuss these problems and their relationship and provide a new and nearly optimal algorithm for solving them.

• Speaker: 
• Title: Online large lectures and coordinated courses - challenges and opportunities
• Date: 01/26/2021
• Time: 10:00 AM - 11:00 AM
• Place:  (Virtual Meeting Link)
• Contact: Tsvetanka Sendova (tsendova@msu.edu)

No abstract available.

• Speaker: Luis Silvestre, University of Chicago
• Title: Integro-differential diffusion and the Boltzmann equation
• Date: 01/26/2021
• Time: 4:30 PM - 5:30 PM
• Place: Online (virtual meeting)
• Contact: Aaron D Levin (levina@msu.edu)

Integro-differential equations have been a very active area of research in the last 20 years. In this talk we will explain what they are and in what sense they are similar to more classical parabolic partial differential equations. We will discuss results on regularity estimates for the Boltzmann equation in this context.

• Speaker: Vaidehee Thatte, SUNY Binghamton
• Title: Arbitrary Valuation Rings and Wild Ramification
• Date: 01/27/2021
• Time: 4:00 PM - 5:00 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Preston Wake (wakepres@msu.edu)

We aim to develop ramification theory for arbitrary valuation fields, extending the classical theory of complete discrete valuation fields with perfect residue fields. By studying wild ramification, we hope to understand the mysterious phenomenon of the $\textit{defect}$ (or ramification deficiency) unique to the positive residue characteristic case and is one of the main obstacles in obtaining resolution of singularities. Extensions of degree $p$ in residue characteristic $p>0$ are building blocks of the general case. We present a generalization of ramification invariants for such extensions. These results enable us to construct an upper ramification filtration of the absolute Galois group of Henselian valuation fields (joint with K.Kato).

• Speaker: Zuowei Shen, National University of Singapore
• Title: Deep Approximation via Deep Learning
• Date: 01/28/2021
• Time: 3:30 AM - 4:30 AM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Olga Turanova (turanova@msu.edu)

The primary task of many applications is approximating/estimating a function through samples drawn from a probability distribution on the input space. The deep approximation is to approximate a function by compositions of many layers of simple functions, that can be viewed as a series of nested feature extractors. The key idea of deep learning network is to convert layers of compositions to layers of tuneable parameters that can be adjusted through a learning process, so that it achieves a good approximation with respect to the input data. In this talk, we shall discuss mathematical theory behind this new approach and approximation rate of deep network; how this new approach differs from the classic approximation theory, and how this new theory can be used to understand and design deep learning network.

• Speaker: Zheng Xiao, MSU
• Title: $ef$ Theorem, discriminant and different in function fields
• Date: 01/29/2021
• Time: 5:00 PM - 6:00 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Zheng Xiao (xiaozhen@msu.edu)

No abstract available.

• Speaker: Dogancan Karabas, Northwestern University
• Title: Wrapped Fukaya category via gluing sheaves, and the case of pinwheels
• Date: 02/02/2021
• Time: 2:50 PM - 3:40 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Honghao Gao (gaohongh@msu.edu)

In this talk, I will discuss some gluing techniques for microlocal sheaves, and calculate wrapped Fukaya category of some rational homology balls, which are quotients of $A_n$ Milnor fibres, via gluing sheaves on their skeleta, i.e. pinwheels.

• Speaker: Richard Stanley, MIT
• Title: Two Analogues of Pascal's Triangle
• Date: 02/03/2021
• Time: 3:00 PM - 3:50 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Bruce E Sagan (bsagan@msu.edu)

Pascal's triangle is closely associated with the expansion of the product $(1+x)^n$. We will discuss two analogous arrays of numbers that are associated with the products $\prod_{i=0}^{n-1} \left(1+x^{2^i}+x^{2^{i+1}}\right)$ and $\prod_{i=1}^n \left(1+x^{F_{i+1}}\right)$, where $F_{i+1}$ is a Fibonacci number. All three arrays are special cases of a two-parameter family that might be interesting to investigate further.

• Speaker: Tino Ullrich , TU Chemnitz
• Title: A New Subsampling Technique for Random Points and Optimal Least Squares Approximation of High-Dimensional Functions
• Date: 02/04/2021
• Time: 2:30 PM - 3:30 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Olga Turanova (turanova@msu.edu)

We provide a new general upper bound for the minimal L2-worst-case recovery error in the framework of RKHS, where only n function samples are allowed. This quantity can be bounded in terms of the singular numbers of the compact embedding into the space of square integrable functions. It turns out that in many relevant situations this quantity is asymptotically only worse by square root of log(n) compared to the singular numbers. The algorithm which realizes this behavior is a weighted least squares algorithm based on a specific set of sampling nodes which works for the whole class of functions simultaneously. These points are constructed out of a random draw with respect to distribution tailored to the spectral properties of the reproducing kernel (importance sampling) in combination with a sub-sampling procedure coming from the celebrated proof of Weaver's conjecture, which was shown to be equivalent to the Kadison-Singer problem. For the above multivariate setting, it is still a fundamental open problem whether sampling algorithms are as powerful as algorithms allowing general linear information like Fourier or wavelet coefficients. However, the gap is now rather small. As a consequence, we may study well-known scenarios where it was widely believed that sparse grid sampling recovery methods perform optimally. It turns out that this is not the case for dimensions d > 2. This is joint work with N. Nagel and M. Schaefer from TU Chemnitz.

• Speaker: Zheng Xiao, MSU
• Title: Function fields different theory continued
• Date: 02/05/2021
• Time: 5:00 PM - 6:00 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Zheng Xiao (xiaozhen@msu.edu)

No abstract available.

• Speaker: Irving Dai, MIT
• Title: Lattice homology and instantons
• Date: 02/09/2021
• Time: 2:50 PM - 3:40 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Honghao Gao (gaohongh@msu.edu)

We show that if Y is the boundary of an almost-rational plumbing, then the framed instanton Floer homology of Y is isomorphic to its Heegaard Floer homology. This class of 3-manifolds includes all Seifert fibered rational homology spheres. Our proof utilizes lattice homology, and relies on a decomposition theorem for instanton Floer cobordism maps established by John Baldwin and Steven Sivek. This is joint work with Antonio Alfieri, John Baldwin, and Steven Sivek.

• Speaker: Nicholas Ovenhouse, University of Minnesota
• Title: Laurent Polynomials from the Super Ptolemy Relation
• Date: 02/10/2021
• Time: 3:00 PM - 3:50 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Bruce E Sagan (bsagan@msu.edu)

In classical geometry, Ptolemy's theorem relates the lengths of the sides of a quadrilateral to the lengths of the diagonals. Fixing a triangulation of a polygon, the length of any diagonal can be expressed (using Ptolemy's theorem) as a Laurent polynomial in the lengths of diagonals in the triangulation. There is a combinatorial description of the terms in this Laurent polynomial due to Schiffler, in terms of "T-paths". Recently, Penner and Zeitlin constructed a super-algebra from a triangulation, and an analogue of the Ptolemy relation in this situation. I will describe a generalization of "T-paths" which enumerate the terms in the corresponding super Laurent polynomials. This is joint work with Gregg Musiker and Sylvester Zhang.

• Speaker: Massimo Fornasier , Technische Universität München
• Title: Consensus-based Optimization on the Sphere
• Date: 02/11/2021
• Time: 2:30 PM - 3:30 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Olga Turanova (turanova@msu.edu)

I present new stochastic multi-particle models for global optimization of nonconvex functions on the sphere. These models belong to the class of Consensus-Based Optimization methods. In fact, particles move over the manifold driven by a drift towards an instantaneous consensus point, computed as a combination of the particle locations weighted by the cost function according to Laplace's principle. The consensus point represents an approximation to a global minimizer. The dynamics is further perturbed by a random vector field to favor exploration, whose variance is a function of the distance of the particles to the consensus point. In particular, as soon as the consensus is reached, then the stochastic component vanishes. In the first part of the talk, I present the well-posedness of the model on the sphere and we derive rigorously its mean-field approximation for large particle limit. In the second part I address the proof of convergence of numerical schemes to global minimizers provided conditions of well-preparation of the initial datum. The proof combines the mean-field limit with a novel asymptotic analysis, and classical convergence results of numerical methods for SDE. We present several numerical experiments, which show that the proposed algorithm scales well with the dimension and is extremely versatile. To quantify the performances of the new approach, we show that the algorithm is able to perform essentially as good as ad hoc state of the art methods in challenging problems in signal processing and machine learning, namely the phase retrieval problem and the robust subspace detection. Joint work with H. Huang, L. Pareschi, and P. Sünnen

• Speaker: Chuangtian Guan, MSU
• Title: Etale cohomology
• Date: 02/12/2021
• Time: 1:00 PM - 2:00 PM
• Place: C117 Wells Hall
• Contact: Joshua Ruiter (ruiterj2@msu.edu)

We'll continue reading through Milne's notes on etale cohomology.

• Speaker: Rachael Lund
• Title: New technologies that worked and that didn't (Packback, Catme, FlipGrid)
• Date: 02/16/2021
• Time: 10:00 AM - 11:00 AM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Tsvetanka Sendova (tsendova@msu.edu)

No abstract available.

• Speaker: Walter Strauss, Brown University
• Title: Steady Water Waves
• Date: 02/16/2021
• Time: 4:00 PM - 5:00 PM
• Place: Online (virtual meeting)
• Contact: Aaron D Levin ()

The mathematical study of water waves began with the derivation of the basic mathematical equations of any fluid by Euler in 1752. Later, water waves, which have a free boundary at the air interface, played a central role in the work of Poisson, Cauchy, Stokes, Levi-Civita and many others. In the last quarter century it has become a particularly active mathematical research area. I will limit my discussion to classical 2D traveling water waves with vorticity. By means of local and global bifurcation theory using topological degree, we now know that there exist many such waves. They are exact smooth solutions of the Euler equations with the physical boundary conditions. Numerical computations provide insight into their properties. I will mention a number of properties that are the subjects of current research such as: their heights, their steepness, the possibility of self-intersection, and their stability or instability.

• Speaker: François Greer, IAS
• Title: A tale of two Severi curves
• Date: 02/17/2021
• Time: 4:00 PM - 5:00 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Laure Flapan (flapanla@msu.edu)

Let $(S,L)$ be a general polarized K3 surface with $c_1(L)^2=2g-2$. A general member of the linear system $|L|\simeq \mathbb P^g$ is a smooth curve of genus $g$. For $0\leq h\leq g$, define the Severi variety $V_h(S,L)\subset |L|$ to be the locus of curves with geometric genus $\leq h$. As expected, $V_h(S,L)$ has dimension $h$. We consider the case $h=1$, where the Severi variety is a (singular) curve. Our first result is that the geometric genus of $V_1(S,L)$ goes to infinity with $g$; we give a lower bound $\sim e^{c\sqrt{g}}$. Next we consider the analogous question for Severi curves of a rational elliptic surface, and give a polynomial upper bound instead. Modular forms play a central role in both arguments. Passcode: MSUALG

• Speaker: Shen Yu, MSU
• Title: Serre's GAGA
• Date: 02/19/2021
• Time: 1:00 PM - 2:00 PM
• Place: C117 Wells Hall (Virtual Meeting Link)
• Contact: Joshua Ruiter (ruiterj2@msu.edu)

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

• Speaker: Shelley Kandola, MSU
• Title: Strengthening the Quality of Mathematical Writing for Math Majors at the University of Minnesota
• Date: 02/23/2021
• Time: 10:00 AM - 11:00 AM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Tsvetanka Sendova (tsendova@msu.edu)

No abstract available.

• Speaker: Sarah Mason, Wake Forest University
• Title: Quasisymmetric Macdonald polynomials
• Date: 02/24/2021
• Time: 3:00 PM - 3:50 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Bruce E Sagan (bsagan@msu.edu)

We introduce a quasisymmetric analogue of Macdonald polynomials, originating from work by Corteel, Mandelshtam, and Williams on multiline queues. Along the way we produce a new and compactified combinatorial formula for Macdonald polynomials. This is joint work with Corteel, Haglund, Mandelshtam, and Williams.

• Speaker: Zaiwen Wen, Peking University, China
• Title: Stochastic Second-Order Methods For Deep Learning
• Date: 02/25/2021
• Time: 3:30 AM - 4:30 AM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Olga Turanova (turanova@msu.edu)

Stochastic methods are widely used in deep learning. In this talk, we first review the state-of-the-art methods such as KFAC. Then we present a structured stochastic quasi-Newton method and a sketchy empirical natural gradient method. Numerical results on deep convolution networks illustrate that our methods are quite competitive to SGD and KFAC.

• Speaker: Keping Huang, Michigan State University
• Title: Carlitz exponentials and Carlitz modules
• Date: 02/26/2021
• Time: 5:00 PM - 6:00 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Keping Huang (huangk23@msu.edu)

No abstract available.

• Speaker: Willie Wong
• Title: Experiences with promoting student collaboration in undergraduate math classes via software tools.
• Date: 03/02/2021
• Time: 10:00 AM - 11:00 AM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Tsvetanka Sendova (tsendova@msu.edu)

No abstract available.

• Speaker: Rankeya Datta, University of Illinois at Chicago
• Title: Openness of splinter loci in prime characteristic.
• Date: 03/03/2021
• Time: 4:00 PM - 5:00 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Joe Waldron (waldro51@msu.edu)

A splinter is a notion of singularity that has seen numerous applications of late, especially in connection with the direct summand theorem, the mixed characteristic minimal model program, Cohen-Macaulayness of absolute integral closures and vanishing theorems. However, many basic questions about splinters remain elusive. One such problem is whether the splinter condition spreads from a point to an open neighborhood of a noetherian scheme. In this talk, we will address this question in prime characteristic and show that a locally noetherian scheme whose associated absolute Frobenius is finite map has an open splinter locus. In particular, all varieties over perfect fields of positive characteristic have open splinter loci. If time permits, we will show how our methods also give openness of splinter loci for a large class of schemes that do not necessarily have finite Frobenius. This talk is based on joint work in progress with Kevin Tucker.

• Speaker: Peter Liljedahl, Simon Fraser University
• Title: Building Thinking Classrooms
• Date: 03/05/2021
• Time: 11:00 AM - 12:00 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Lisa Keller (kellerl@msu.edu)

Much of how classrooms look and much of what happens in them today is guided by institutional norms laid down at the inception of an industrial-age model of public education. These norms have enabled a culture of teaching and learning that is often devoid of student thinking. In this session I present some of the results of over 15 years of research into how K-12 and post-secondary teachers can transform their classrooms from a space where students mimic to where students think. The practiced discussed will intertwine with, and make extensive references to, the recently published book, Building Thinking Classrooms in Mathematics: 14 Teaching Practices for Enhancing Learning. Register in advance for the colloquium: https://bit.ly/3bafgVE After registering, you will receive a confirmation email containing information about joining the meeting.

• Speaker: Keping Huang, MSU
• Title: Carlitz modules and Drinfeld modules
• Date: 03/05/2021
• Time: 5:00 PM - 6:00 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Keping Huang (huangk23@msu.edu)

No abstract available.

• Speaker: Roger Casals, UC Davis
• Title: Lagrangian Fillings of Legendrian links: Two Constructions in Floer Theory
• Date: 03/09/2021
• Time: 2:50 PM - 3:40 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Honghao Gao (gaohongh@msu.edu)

In this talk I will review our current understanding in the classification of Lagrangian fillings for Legendrian links in the standard contact 3-sphere. The talk will present two illustrative constructions: one explaining how to build and detect infinitely many Lagrangian fillings using the Legendrian Contact DGA, and the other explaining how to classify fillings for the Hopf link using pseudo-holomorphic foliations. First, I will present the basic objects of interest and survey the recent developments in the field (work with H. Gao, and work with E. Zaslow). Then I will delve into new and in-progress results on the Legendrian Contact DGA (work with L. Ng). Finally, I will report on how pseudo-holomorphic curves might help us classify Lagrangian fillings in certain cases. During the course of the talk, I will try to highlight some of the interesting open questions and new methods that arise from our current work as well as future directions.

• Speaker: Andrea Nahmod, University of Massachusetts Amherst
• Title: Propagation of randomness under the flow of nonlinear dispersive equations
• Date: 03/09/2021
• Time: 4:00 PM - 5:00 PM
• Place: Online (virtual meeting)
• Contact: Aaron D Levin ()

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

• Speaker: Joe Waldron, MSU
• Title: Minimal model program for threefolds of mixed characteristic
• Date: 03/10/2021
• Time: 4:00 PM - 5:00 PM
• Place: Online (virtual meeting)
• Contact: Laure Flapan (flapanla@msu.edu)

A major obstacle to extending the minimal model program away from characteristic zero is the lack of cohomology vanishing theorems such as Kodaira vanishing. In this talk we describe the minimal model program and then discuss a new way to overcome this difficulty in the arithmetic situation, which has enabled the development of the minimal model program for arithmetic threefolds of residue characteristic greater than 5. This is joint work with Bhatt, Ma, Patakfalvi, Schwede, Tucker and Witaszek.

• Speaker: Qi Peikai, MSU
• Title: Student algebra seminar
• Date: 03/12/2021
• Time: 1:00 PM - 2:00 PM
• Place: C117 Wells Hall (Virtual Meeting Link)
• Contact: Joshua Ruiter (ruiterj2@msu.edu)

Continue reading Milne's notes on etale cohomology

• Speaker: Keping Huang, MSU
• Title: Drinfeld modules, continued
• Date: 03/12/2021
• Time: 5:00 PM - 6:00 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Keping Huang (huangk23@msu.edu)

No abstract available.

• Speaker: Luis Scoccola, Michigan State University
• Title: Approximate and discrete vector bundles in theory and in applications
• Date: 03/15/2021
• Time: 2:00 PM - 3:00 PM
• Place: Online (virtual meeting)
• Contact: Shelley Kandola (kandola2@msu.edu)

Synchronization problems, such as the problem of reconstructing a 3D shape from a set of 2D projections, can often be modeled by principal bundles. Similarly, the application of local PCA to a point cloud concentrated around a manifold approximates the tangent bundle of the manifold. In the first case, the characteristic classes of the bundle provide obstructions to global synchronization, while, in the second case, they provide obstructions to dimensionality reduction. I will describe joint work with Jose Perea in which we propose several notions of approximate and discrete vector bundle, study the extent to which they determine true vector bundles, and give algorithms for the stable and consistent computation of low-dimensional characteristic classes directly from these combinatorial representations. No previous knowledge of the theory of vector bundles will be assumed.

• Speaker: 
• Title: Coffee hour and hands on experience with Gather.town
• Date: 03/16/2021
• Time: 10:00 AM - 11:00 AM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Tsvetanka Sendova (tsendova@msu.edu)

No abstract available.

• Speaker: Martin Olsson, UC Berkeley
• Title: The Zariski topology, linear systems, and reconstruction of algebraic varieties
• Date: 03/16/2021
• Time: 4:00 PM - 5:00 PM
• Place: Online (virtual meeting)
• Contact: Aaron D Levin ()

The classical Veblen-Young theorem characterizes axiomatically projective spaces over fields. It is natural to ask for generalizations of this fundamental result to arbitrary algebraic varieties. In this colloquium I will survey work in this direction, and discuss recent progress characterizing algebraic varieties in terms of their Zariski topological spaces. The main new results are joint with János Kollár, Max Lieblich, and Will Sawin.

• Speaker: Tristan Wells, Michigan State University
• Title: Crash Course on Handles and 4 Manifolds
• Date: 03/17/2021
• Time: 4:00 PM - 5:00 PM
• Place: 
• Contact: Danika Vanniel (vannield@msu.edu)

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

• Speaker: Roberto Imbuzeiro Oliveira, IMPA, Rio de Janeiro
• Title: Sample average approximation with heavier tails
• Date: 03/18/2021
• Time: 2:30 PM - 3:30 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Olga Turanova (turanova@msu.edu)

Consider an "ideal" optimization problem where constraints and objective function are defined in terms of expectations over some distribution P. The sample average approximation (SAA) -- a fundamental idea in stochastic optimization -- consists of replacing the expectations by an average over a sample from P. A key question is how much the solutions of the SAA differ from those of the original problem. Results by Shapiro from many years ago consider what happens asymptotically when the sample size diverges, especially when the solution of the ideal problem lies on the boundary of the feasible set. In joint work with Philip Thompson (Purdue), we consider what happens with finite samples. As we will see, our results improve upon the nonasymptotic state of the art in various ways: we allow for heavier tails, unbounded feasible sets, and obtain bounds that (in favorable cases) only depend on the geometry of the feasible set in a small neighborhood of the optimal solution. Our results combine "localization" and "fixed-point" type arguments inpired by the work of Mendelson with chaining-type inequalities. One of our contributions is showing what can be said when the SAA constraints are random.

• Speaker: Ivan So, MSU
• Title: Student algebra seminar
• Date: 03/19/2021
• Time: 1:00 PM - 2:00 PM
• Place: C117 Wells Hall (Virtual Meeting Link)
• Contact: Joshua Ruiter (ruiterj2@msu.edu)

Continue reading Milne's notes on etale cohomology

• Speaker: Keping Huang, MSU
• Title: Endomorphisms of Drinfeld modules
• Date: 03/19/2021
• Time: 5:00 PM - 6:00 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Keping Huang (huangk23@msu.edu)

No abstract available.

• Speaker: Sarah Klanderman , Marian University
• Title: Mastery-Based Grading in Calculus
• Date: 03/23/2021
• Time: 10:00 AM - 11:00 AM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Tsvetanka Sendova (tsendova@msu.edu)

No abstract available.

• Speaker: Jo Ellis-Monaghan, Korteweg-de Vries Instituut voor Wiskunde, Universiteit van Amsterdam
• Title: Graph theoretical tools for DNA self-assembly
• Date: 03/24/2021
• Time: 3:00 PM - 3:50 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Bruce E Sagan (bsagan@msu.edu)

Applications of immediate concern have driven some of the most interesting questions in the field of graph theory, for example graph drawing and computer chip layout problems, random graph theory and modeling the internet, graph connectivity measures and ecological systems, etc. Currently, scientists are engineering self-assembling DNA molecules to serve emergent applications in biomolecular computing, nanoelectronics, biosensors, drug delivery systems, and organic synthesis. Often, the self-assembled objects, e.g. lattices or polyhedral skeletons, may be modeled as graphs. Thus, these new technologies in self-assembly are now generating challenging new design problems for which graph theory is a natural tool. We will present some new applications in DNA self-assembly and describe some of the graph-theoretical design strategy problems arising from them. We will see how finding optimal design strategies leads to developing new algorithms for graphs, addressing new computational complexity questions, and finding new graph invariants corresponding to the minimum number of components necessary to build a target structure under various laboratory settings.

• Speaker: Stefan Patrikis, Ohio State University
• Title: Lifting Galois representations
• Date: 03/24/2021
• Time: 4:00 PM - 5:00 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Igor Rapinchuk (rapinchu@msu.edu)

I will survey joint work with Najmuddin Fakhruddin and Chandrashekhar Khare in which we prove in many cases existence of geometric p-adic lifts of "odd" mod p Galois representations, valued in general reductive groups. Then I will discuss applications to modularity of reducible mod p Galois representations, including most cases of a generalization of Serre's modularity conjecture to reducible (but not necessarily indecomposable) odd two-dimensional representations of the Galois group of Q. Passcode: MSUALG

• Speaker: Joe Melby
• Title: The Figure Eight Knot (The Friendliest Knot)
• Date: 03/26/2021
• Time: 3:00 PM - 4:00 PM
• Place:  (Virtual Meeting Link)
• Contact: Keshav Sutrave (sutravek@msu.edu)

Even on its laziest days, the figure-eight knot keeps climbers from falling and a boat's sails in place better than the measly trefoil overhand knot (totally inferior knot). Does the figure-eight save lives? Many would say so. We will discuss the topology and geometry of this life-saving knot, which is the unique 4-crossing and the simplest hyperbolic knot. Our friend the figure-eight knot will guide us as we introduce some important classical concepts and techniques in the fields of knot theory and low-dimensional topology. This is a BYOR (Bring Your Own Rope) event due to COVID-19.

• Speaker: Jiahui Chen, MSU
• Title: Evolutionary de Rham-Hodge method
• Date: 03/29/2021
• Time: 2:00 PM - 3:00 PM
• Place: Online (virtual meeting)
• Contact: Shelley Kandola (kandola2@msu.edu)

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

• Speaker: CRLT Players , https://crlt.umich.edu/crltplayers
• Title: Shoulda, Woulda, Coulda: Moving Beyond Failure and Actively Cultivating a More Equitable Academy
• Date: 03/30/2021
• Time: 4:00 PM - 5:30 PM
• Place: Online (virtual meeting)
• Contact: Aaron D Levin ()

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

• Speaker: Peter Yuditskii, Johannes Kepler University Linz
• Title: The Deift conjecture
• Date: 03/31/2021
• Time: 4:00 PM - 5:00 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Dapeng Zhan (zhan@msu.edu)

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

• Speaker: Yi Ma , University of California, Berkeley
• Title: Deep Networks from First Principles
• Date: 04/01/2021
• Time: 2:30 PM - 2:30 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Olga Turanova (turanova@msu.edu)

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

• Speaker: Gabriel Nagy, MSU
• Title: Embedding interactive graphs (GeoGebra) in Webwork
• Date: 04/06/2021
• Time: 10:00 AM - 11:00 AM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Tsvetanka Sendova (tsendova@msu.edu)

No abstract available.

• Speaker: Emily Riehl, Johns Hopkins University
• Title:  Elements of ∞-Category Theory
• Date: 04/06/2021
• Time: 4:00 PM - 5:00 PM
• Place: Online (virtual meeting)
• Contact: Aaron D Levin ()

Confusingly for the uninitiated, experts in weak infinite-dimensional category theory make use of different definitions of an ∞-category, and theorems in the ∞-categorical literature are often proven "analytically", in reference to the combinatorial specifications of a particular model. In this talk, we present a new point of view on the foundations of ∞-category theory, which allows us to develop the basic theory of ∞-categories --- adjunctions, limits and colimits, co/cartesian fibrations, and pointwise Kan extensions --- "synthetically" starting from axioms that describe an ∞-cosmos, the infinite-dimensional category in which ∞-categories live as objects. We demonstrate that the theorems proven in this manner are "model-independent", i.e., invariant under change of model. Moreover, there is a formal language with the feature that any statement about ∞-categories that is expressible in that language is also invariant under change of model, regardless of whether it is proven through synthetic or analytic techniques. This is joint work with Dominic Verity.

• Speaker: Dapeng Zhan, MSU
• Title: Schramm-Loewner evolution and hypergeometric functions
• Date: 04/07/2021
• Time: 4:00 PM - 5:00 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Dapeng Zhan (zhan@msu.edu)

Schramm-Loewner evolution (SLE for short) is a family of random fractal curves, which describe the scaling limits of some lattice models. When one studies SLE with additional marked points, and requires that those SLE satisfy certain nice properties, some special functions come into play. They arise as the solution of some second-order partial differential equations. In this talk, I will describe how the one-variable and multi-variable hypergeometric functions are used to study the time-reversal of SLE$_\kappa(\rho_1,\dots,\rho_m)$ curves. We use the same zoom link ant passcode as before.  

• Speaker: Mahdi Soltanolkotabi, University of Southern California
• Title: Precise Tradeoffs for Adversarial Training
• Date: 04/08/2021
• Time: 2:30 PM - 3:30 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Olga Turanova (turanova@msu.edu)

Despite breakthrough performance, modern learning models are known to be highly vulnerable to small adversarial perturbations in their inputs. While a wide variety of recent adversarial training methods have been effective at improving robustness to perturbed inputs (robust accuracy), often this benefit is accompanied by a decrease in accuracy on benign inputs (standard accuracy), leading to a tradeoff between often competing objectives. Complicating matters further, recent empirical evidence suggests that a variety of other factors (size and quality of training data, model size, etc.) affect this tradeoff in somewhat surprising ways. In this talk we will provide a precise and comprehensive understanding of the role of adversarial training in the context of linear regression with Gaussian features and binary classification in a mixture model. We precisely characterize the standard/robust accuracy and the corresponding tradeoff achieved by a contemporary mini-max adversarial training approach in a high-dimensional regime where the number of data points and the parameters of the model grow in proportion to each other. Our theory for adversarial training algorithms also facilitates the rigorous study of how a variety of factors (size and quality of training data, model overparametrization etc.) affect the tradeoff between these two competing accuracies.

• Speaker: Nick Krupansky
• Title: Home Economics 400: Basic financial concepts for entering the working world.
• Date: 04/09/2021
• Time: 3:00 PM - 4:00 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Keshav Sutrave (sutravek@msu.edu)

While we have undoubtedly mastered quantitative problem solving, in the coming months many of us will deal with some very common and personal quantitative decisions that we haven't encountered before: retirement benefits. The sooner you have a basic grasp of what benefits are available to you and their impact, the sooner you can make informed decisions and potential compare employment opportunities. As potential new employees, learn the basics of common retirement offerings for US employment and associated tax implications from a student with first-hand experience.

• Speaker: Haibin Hang, University of Delaware
• Title: Correspondence modules and their diagrams
• Date: 04/12/2021
• Time: 2:00 PM - 3:00 PM
• Place: Online (virtual meeting)
• Contact: Shelley Kandola (kandola2@msu.edu)

In this talk, I will introduce correspondence modules (c-modules), which generalize persistence and zigzag modules. I also will introduce the persistence sheaf of sections of a c-module, which is used to analyze its structure and prove an interval decomposition theorem. Several applications in which c-modules arise naturally will be discussed.

• Speaker: Susan Richter, MSU
• Title: Impact of Math Gateway Reforms on Student Success
• Date: 04/13/2021
• Time: 10:00 AM - 11:00 AM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Tsvetanka Sendova (tsendova@msu.edu)

No abstract available.

• Speaker: Adrian Ioana, UC San Diego
• Title: Classification and rigidity for group von Neumann algebras
• Date: 04/13/2021
• Time: 4:00 PM - 5:00 PM
• Place: Online (virtual meeting)
• Contact: Aaron D Levin ()

Any countable group G gives rise to a von Neumann algebra L(G). The classification of these group von Neumann algebras is a central theme in operator algebras. I will survey recent rigidity results which provide instances when various algebraic properties of groups, such as the presence or absence of a direct product decomposition, are remembered by their von Neumann algebras. I will also explain the strongest such rigidity results, where L(G) completely remembers G, and discuss some of the open problems in the area.

• Speaker: Ilya Kachkovskiy, MSU
• Title: Spectral bands of two-dimensional periodic elliptic operators
• Date: 04/14/2021
• Time: 3:00 PM - 4:00 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Dapeng Zhan (zhan@msu.edu)

I will give an overview of spectral theory of second order elliptic operators on $\mathbb R^2$ on the example of Schrodinger operators and explain the main steps of the proof that spectral band edged are attained at finitely many values of the quasimomenta. If time permits, I will discuss related result and work in progress. The talk is based on joint work with N. Filonov. Note: The meeting time is 3:00 pm instead of 4:00 pm. We use the same zoom link and passcode as before.

• Speaker: Michael Wakin, Colorado School of Mines
• Title: Spectral Properties of Time-limited Toeplitz Operators and Applications in Signal Processing
• Date: 04/15/2021
• Time: 2:30 PM - 3:30 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Olga Turanova (turanova@msu.edu)

Toeplitz operators are fundamental and ubiquitous in signal processing and information theory as models for convolutional (filtering) systems. Due to the fact that any practical system can access only signals of finite duration, however, time-limited restrictions of Toeplitz operators are also of interest. In the discrete-time case, time-limited Toeplitz operators are simply Toeplitz matrices. In this talk we survey existing and present new bounds on the eigenvalues (spectra) of time-limited Toeplitz operators, and we discuss applications of these results in various signal processing contexts. As a special case, we discuss time-frequency limiting operators, which alternatingly limit a signal in the time and frequency domains. Slepian functions arise as eigenfunctions of these operators, and we describe applications of Slepian functions in spectral analysis of multiband signals, super-resolution SAR imaging, and blind beamforming in antenna arrays. This talk draws from joint work with numerous collaborators including Zhihui Zhu from the University of Denver.

• Speaker: Paula Mercurio
• Title: An Introduction to Network Embedding for Data Clustering
• Date: 04/16/2021
• Time: 3:00 PM - 4:00 PM
• Place:  (Virtual Meeting Link)
• Contact: Keshav Sutrave (sutravek@msu.edu)

I will introduce some of the basic ideas behind network embedding, and show how a complicated or high-dimensional graph can be represented as a collection of points in a lower-dimensional vector space. This will be an expository talk focusing on random walk-based methods, and how these methods are related to certain matrix-based methods and diffusion maps. Throughout the talk, I'll show how these techniques are useful for machine learning tasks like social network analysis and image recognition.

• Speaker: Sarah Tymochko, MSU
• Title: Bifurcation Detection using Zigzag Persistence
• Date: 04/19/2021
• Time: 2:00 PM - 3:00 PM
• Place: Online (virtual meeting)
• Contact: Shelley Kandola (kandola2@msu.edu)

No abstract available.

• Speaker: Reshma Menon, Harvard
• Title: A year-long introduction to calculus (integrated with functions)
• Date: 04/20/2021
• Time: 10:00 AM - 11:00 AM
• Place: Online (virtual meeting)
• Contact: Tsvetanka Sendova (tsendova@msu.edu)

No abstract available.

• Speaker: Nicolas Addington, University of Oregon
• Title: Cubic fourfolds
• Date: 04/20/2021
• Time: 4:00 PM - 5:00 PM
• Place: Online (virtual meeting)
• Contact: Aaron D Levin ()

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

• Speaker: Seonghyeon Jeong, MSU
• Title: The Kantorovich duality and c-convexity
• Date: 04/21/2021
• Time: 4:00 PM - 5:00 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Dapeng Zhan (zhan@msu.edu)

The Kantorovich duality was a big breakthrough in the optimal transportation problem. The Kantorovich duality provides information of the transportation plan. In this talk, I present two proofs of the Kantorovich duality. The first proof uses the c-convex functions and Arzela-Ascoli to construct a solution of the dual problem. The second proof uses a geometric property of the support of the transportation plan which is called c-cyclical monotonicity. We are going to use the same zoom link and passcode as before.

• Speaker: Shahar Mendelson, Australian National University
• Title: TBA
• Date: 04/22/2021
• Time: 4:30 AM - 5:30 AM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Olga Turanova (turanova@msu.edu)

No abstract available.

• Speaker: Rami Fakhry, MSU
• Title: Multi-point Boundary Green's function for Chordal SLE curves
• Date: 04/28/2021
• Time: 4:00 PM - 5:00 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Dapeng Zhan (zhan@msu.edu)

For a Chordal SLE$_\kappa$ ($\kappa \in (0,8)$) curve in a simply connected domain $D$ with smooth boundary, the $n$-point boundary Green's function valued at distinct points $z_1, ..., z_n\in \partial{D}$ is defined by} \[ G(z_1,...,z_n)= \lim_{r_1,...,r_n \to 0+} \prod_{j=1}^{n} {r_j}^ {- \alpha} \mathbb{P} \left[ dist(\gamma, z_k) \leqq r_k, 1 \leqq k \leqq n \right] ,\]where $ \alpha = \frac{8}{\kappa} - 1 $ is the boundary exponent of SLE$_\kappa$, provided that the limit converges. In this talk, we will show that such Green's function exists for any finite number of points. Along the way we provide the rate of convergence and modulus of continuity for Green's functions as well. Finally, we give up-to-constant bounds for them. We use the same zoom link and passcode as before.