• Speaker: Lucas Hall, MSU
• Title: Skew Products: Coactions You Can See
• Date: 09/06/2022
• Time: 11:00 AM - 11:50 AM
• Place: C304 Wells Hall
• Contact: 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.

• Speaker: Sasha Volberg, MSU
• Title: Heat smoothing conjecture and Bernstein--Markov inequalities on Hamming cube
• Date: 09/07/2022
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall
• Contact: Willie Wai-Yeung 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 Bernstein--Markov inequalities, here the novelty is in getting rid of some irritating logarithms.

• Speaker: Leonid Parnovski, University College London
• Title: Floating mats and sloping beaches: spectral asymptotics of the Steklov problem on polygons
• Date: 09/08/2022
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall
• Contact: Joseph Waldron (waldro51@msu.edu)

I will discuss asymptotic behaviour of the eigenvalues of the Steklov problem (aka Dirichlet-to-Neumann operator) on curvilinear polygons. The answer is completely unexpected and depends on the arithmetic properties of the angles of the polygon.

• Speaker: Brent Nelson, MSU
• Title: Making Weight
• Date: 09/12/2022
• Time: 4:00 PM - 5:30 PM
• Place: C517 Wells Hall
• Contact: 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 non-discrete 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.

• Speaker: Brendon Rhoades, UCSD
• Title: Superspace, Vandermondes, and representations
• Date: 09/14/2022
• Time: 3:00 PM - 3:50 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: 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.

• Speaker: Jenny Wilson, University of Michigan
• Title: Stability patterns in configuration spaces
• Date: 09/15/2022
• Time: 4:10 PM - 5:00 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: 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.

• Speaker: Alexander Vainshtein, Haifa University
• Title: Cluster structures on SL_n and the Belavin-Drinfeld classification
• Date: 09/19/2022
• Time: 12:30 PM - 1:30 PM
• Place: C304 Wells Hall
• Contact: 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 Poisson-Lie 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 Belavin-Drinfeld classification of Poisson-Lie structures on SL_n. Based on a joint work with M.~Gekhtman (Notre Dame) and M.~Shapiro (MSU).

• Speaker: Brent Nelson, MSU
• Title: Worth Their Weight
• Date: 09/19/2022
• Time: 4:00 PM - 5:30 PM
• Place: C517 Wells Hall
• Contact: 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 semi-cyclic representations and Tomita-Takesaki theory. I will conclude with a detailed examination of Plancherel weights on locally compact groups.

• Speaker: Bin Sun, Oxford
• Title: $L^2$-Betti numbers of fiber bundles
• Date: 09/20/2022
• Time: 3:00 PM - 4:00 PM
• Place: C304 Wells Hall (Virtual Meeting Link)
• Contact: 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 non-positively curved $3-$manifold. This is a joint work with Dawid Kielak.

• Speaker: Alex Wilson, Dartmouth
• Title: A Diagram-Like Basis for the Multiset Partition Algebra
• Date: 09/21/2022
• Time: 3:00 PM - 3:50 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: 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 Schur-Weyl 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 well-known basis indexed by graph-theoretic 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.

• Speaker: Rayan Saab, University of California, San Diego (UCSD)
• Title: Quantizing neural networks
• Date: 09/22/2022
• Time: 2:30 PM - 3:30 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Mark A Iwen (iwenmark@msu.edu)

Neural networks are highly non-linear 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 data-driven 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 multi-layer networks, to illustrate the performance of our methods. Time permitting, we will also discuss open problems and related areas of research.

• Speaker: Chenyang Xu, Princeton University
• Title: K-stability and birational geometry
• Date: 09/22/2022
• Time: 4:10 PM - 5:00 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Joseph Waldron (waldro51@msu.edu)

The notion of K-stability for a Fano varieties was introduced by differential geometers in late 90s, to capture the existence of a Kähler-Einstein metric. In the last decade, it has gradually become clear to algebraic geometers that K-stability 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 K-stability 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 K-stability and the existence of a Kähler-Einstein metric, i.e. the Yau-Tian-Donaldson Conjecture, for all Fano varieties. If time permits, I want to also discuss the construction of K-moduli spaces parametrizing Fano varieties, and how the recipe given by K-stability can be used to resolve the issues that mystify people for a long time.

• Speaker: Remy Liu, MSU
• Title: Understanding dataset characteristics via diffusion on graph
• Date: 09/26/2022
• Time: 1:00 PM - 2:00 PM
• Place: C117 Wells Hall (Virtual Meeting Link)
• Contact: 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 graph-related 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 low-frequency signals; on the contrary, heterophilic datasets, such as WebKB, rely more heavily on high-frequency 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 task-specific 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 .

• Speaker: Aldo Garcia Guinto, MSU
• Title: Conjugate Variables and Dual Systems
• Date: 09/26/2022
• Time: 4:00 PM - 5:30 PM
• Place: C517 Wells Hall
• Contact: Brent Nelson (banelson@msu.edu)

In free probability, the semi-circular operators are the analogue of the Gaussian distribution in classical probability. We will be using the semi-circular 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.

• Speaker: Shi-Zhuo Looi, UC Berkeley
• Title: Asymptotics for odd- and even-dimensional waves
• Date: 09/28/2022
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall
• Contact: Willie Wai-Yeung 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 odd-dimensional 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.

• Speaker: Nam Le, Indiana University Bloomington
• Title: Hessian eigenvalues and hyperbolic polynomials
• Date: 09/29/2022
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall
• Contact: 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, max-min principle, global smoothness, Brunn-Minkowski 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 Monge-Ampere 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.

• Speaker: Bin Sun, University of Oxford
• Title: Generalized wreath products and rigidity of their von Neumann algebras
• Date: 10/04/2022
• Time: 11:00 AM - 11:50 AM
• Place: C304 Wells Hall
• Contact: 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 group-theoretic 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.

• Speaker: Peter Johnson, Michigan State University
• Title: Knot lattice homology and the Gukov-Manolescu 2-variable series
• Date: 10/04/2022
• Time: 3:00 PM - 4:00 PM
• Place: C304 Wells Hall (Virtual Meeting Link)
• Contact: 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 3-manifolds, 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 Gukov-Pei-Putrov-Vafa, is a power series coming from a physical theory and is conjectured to recover quantum invariants of 3-manifolds at roots of unity. In this talk, I will discuss work in progress relating knot lattice homology and the Gukov-Manolescu 2-variable series, the knot theoretic counterparts to lattice homology and $\widehat{Z}$. This is joint work with Ross Akhmechet and Sunghyuk Park.

• Speaker: Weijie Su, University of Pennsylvania
• Title: 1W-MINDS talk (passcode is the first prime number > 100).
• Date: 10/06/2022
• Time: 2:30 PM - 3:30 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Mark A Iwen (iwenmark@msu.edu)

What Should a Good Deep Neural Network Look Like? Insights from a Layer-Peeled Model and the Law of Equi-Separation See https://sites.google.com/view/minds-seminar/home

• Speaker: Vijay Higgins, Michigan State University
• Title: TBA
• Date: 10/10/2022
• Time: 3:00 PM - 4:00 PM
• Place: C204A Wells Hall
• Contact: Linhui Shen (shenlin1@msu.edu)

No abstract available.

• Speaker: Lucas Hall, MSU
• Title: TBA
• Date: 10/10/2022
• Time: 4:00 PM - 5:30 PM
• Place: C517 Wells Hall
• Contact: Brent Nelson (banelson@msu.edu)

TBA

• Speaker: Daniel Douglas, Yale
• Title: TBA
• Date: 10/11/2022
• Time: 3:00 PM - 4:00 PM
• Place: C304 Wells Hall (Virtual Meeting Link)
• Contact: Vijay B Higgins (higgi231@msu.edu)

TBA

• Speaker: Patricia Hersh, University of Oregon
• Title: Generalized recursive atom ordering and equivalence to CL-shellability
• Date: 10/13/2022
• Time: 3:00 PM - 3:50 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Bruce E Sagan (bsagan@msu.edu)

When Björner and Wachs introduced one of the main forms of lexicographic shellability, namely CL-shellability, they also introduced the notion of recursive atom ordering, and they proved that a finite bounded poset is CL-shellable 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 ``CC-shellable'' by way of a CC-labeling which is self-consistent in a certain sense. This allows us to conclude that CL-shellability is equivalent to self-consistent CC-shellability. As an application, we prove that the uncrossing orders, namely the face posets for stratified spaces of planar electrical networks, are dual CL-shellable. 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

• Speaker: Evzenie Coupkova, Purdue
• Title: Unique generalization properties of a dense set of classifiers based on one-dimensional random projections
• Date: 10/17/2022
• Time: 1:00 PM - 2:00 PM
• Place: C117 Wells Hall (Virtual Meeting Link)
• Contact: 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 low-complexity classifiers consisting of thresholding a random one-dimensional feature. The feature is obtained by projecting the data on a random line after embedding it into a higher-dimensional space parametrized by monomials of order up to k. More specifically, the extended data is projected n-times 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 low-complexity 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 .

• Speaker: Juan Muñoz-Echániz, Columbia University
• Title: TBA
• Date: 10/18/2022
• Time: 3:00 PM - 4:00 PM
• Place: C304 Wells Hall
• Contact: Peter Kilgore Johnson (john8251@msu.edu)

No abstract available.

• Speaker: Ken Ribet, UC Berkeley
• Title: The Unreasonable Effectiveness of Elliptic Curves
• Date: 10/20/2022
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall
• Contact: 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.

• Speaker: Nathan Chen, Columbia University
• Title: TBA
• Date: 10/24/2022
• Time: 3:00 PM - 4:00 PM
• Place: C304 Wells Hall
• Contact: Laure Flapan (flapanla@msu.edu)

TBA

• Speaker: Victor Reiner, University of Minnesota
• Title: TBA
• Date: 10/27/2022
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall
• Contact: Joseph Waldron (waldro51@msu.edu)

No abstract available.

• Speaker: Giorgio Young, University of Michigan
• Title: TBA
• Date: 11/01/2022
• Time: 11:00 AM - 12:00 PM
• Place: C304 Wells Hall
• Contact: Jeffrey Hudson Schenker (schenke6@msu.edu)

No abstract available.

• Speaker: Alex Townsend , Cornell University
• Title: 1W-MINDS talk (passcode is the first prime number > 100).
• Date: 11/03/2022
• Time: 2:30 PM - 3:30 PM
• Place: Online (virtual meeting)
• Contact: Mark A Iwen ()

See https://sites.google.com/view/minds-seminar/home

• Speaker: Qingjing Chen, University of California Santa Barbara
• Title: TBA
• Date: 11/07/2022
• Time: 3:00 PM - 4:00 PM
• Place: C304 Wells Hall
• Contact: Laure Flapan (flapanla@msu.edu)

TBA

• Speaker: Dimitris Vardakis, MSU
• Title: Buffon's needle problem for a random planar disk-like Cantor set
• Date: 11/09/2022
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall
• Contact: Willie Wai-Yeung 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 disk-like 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.

• Speaker: Louis-Hadrien Robert, Université Clermont Auvergne
• Title: TBA
• Date: 11/15/2022
• Time: 3:00 PM - 4:00 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Vijay B Higgins (higgi231@msu.edu)

TBA

• Speaker: Wei Zhu , University of Massachusetts Amherst
• Title: 1W-MINDS talk (passcode is the first prime number > 100).
• Date: 11/17/2022
• Time: 2:30 PM - 3:30 PM
• Place: Online (virtual meeting)
• Contact: Mark A Iwen ()

See https://sites.google.com/view/minds-seminar/home

• Speaker: Zijian Yao, University of Chicago
• Title: TBA
• Date: 11/28/2022
• Time: 3:00 PM - 4:00 PM
• Place: C304 Wells Hall
• Contact: Preston Wake (wakepres@msu.edu)

No abstract available.

• Speaker: Justin Lanier, University of Chicago
• Title: TBA
• Date: 11/29/2022
• Time: 3:00 PM - 4:00 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Peter Kilgore Johnson (john8251@msu.edu)

No abstract available.

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

TBA