Talk_id  Date  Speaker  Title 
26803

Thursday 8/20 2:30 PM

Helmut Bolcskei, ETH Zurich

Fundamental limits of learning in deep neural networks; zoom link @ https://sites.google.com/view/mindsseminar/home
 Helmut Bolcskei, ETH Zurich
 Fundamental limits of learning in deep neural networks; zoom link @ https://sites.google.com/view/mindsseminar/home
 08/20/2020
 2:30 PM  3:30 PM

(Part of One World MINDS seminar:
https://sites.google.com/view/mindsseminar/home)
\[
\]
We develop a theory that allows to characterize the fundamental limits of learning in deep neural networks. Concretely, we consider Kolmogorovoptimal approximation through deep neural networks with the guiding theme being a relation between the epsilonentropy of the hypothesis class to be learned and the complexity of the approximating network in terms of connectivity and memory requirements for storing the network topology and the quantized weights and biases. The theory we develop educes remarkable universality properties of deep networks. Specifically, deep networks can Kolmogorovoptimally learn essentially any hypothesis class. In addition, we find that deep networks provide exponential approximation accuracy—i.e., the approximation error decays exponentially in the number of nonzero weights in the network—of widely different functions including the multiplication operation, polynomials, sinusoidal functions, general smooth functions, and even onedimensional oscillatory textures and fractal functions such as the Weierstrass function, both of which do not have any known methods achieving exponential approximation accuracy. We also show that in the approximation of sufficiently smooth functions finitewidth deep networks require strictly smaller connectivity than finitedepth wide networks. We conclude with an outlook on the further role our theory could play.

26815

Thursday 8/27 2:30 PM

Nir Sochen, University of Tel Aviv

Unsupervised deep learning of forward and inverse solutions for PDEbased imaging; zoom link @ https://sites.google.com/view/mindsseminar/home
 Nir Sochen, University of Tel Aviv
 Unsupervised deep learning of forward and inverse solutions for PDEbased imaging; zoom link @ https://sites.google.com/view/mindsseminar/home
 08/27/2020
 2:30 PM  3:30 PM

(Part of One World MINDS seminar: https://sites.google.com/view/mindsseminar/home)
\[
\]
Many imaging modalities are based on inverse problems of physical processes that are given as PDEs. Traditional methods for solving these PDEbased forward and inverse problems are based on discretizations of the domain. Deep learning methods are based on an excessive amount of inputoutput pairs. Both approaches encounter problems either by numerical instabilities and by being limited to low dimensions or by the lack of sufficient data. We suggest an alternative method of unsupervised deep learning method were the network parametrizes the solution and the loss function minimizes the deviation from the PDE. The input set are points sampled randomly in the domain and the output is the deviation from the PDE, namely zero. One key issue in the loss function is the introduction of the L_infty term that guaranty the uniform convergence of the network to the solution. We demonstrate our method on the Electrical Impedance Tomography (EIT).

26849

Tuesday 9/1 4:00 PM

Dmitry Chelkak, École Normale Supérieure

Bipartite dimer model and minimal surfaces in the Minkowski space
 Dmitry Chelkak, École Normale Supérieure
 Bipartite dimer model and minimal surfaces in the Minkowski space
 09/01/2020
 4:00 PM  5:00 PM
 Online (virtual meeting)
We discuss a new approach to the convergence of height fluctuations in the bipartite dimer model considered on big planar graphs. This viewpoint is based upon special embeddings of weighted planar graphs into the complex plane known under the name Coulomb gauges or, equivalently, tembeddings. The longterm motivation comes from trying to understand fluctuations on irregular graphs, notably on random planar maps equipped with the dimer (or, similarly, the critical Ising) model.
When the dimer model is considered on subgraphs of refining lattices, a classical conjecture due to KenyonOkounkov predicts the convergence of fluctuations to the Gaussian Free Field in a certain conformal structure. However, the latter is defined via a latticedependent entropy functional, which makes the analysis of irregular graphs highly problematic. To overcome this difficulty, we introduce a notion of 'perfect tembeddings' of abstract weighted bipartite graphs and develop new discrete complex analysis techniques to handle correlation functions of the dimer model on tembeddings. Though in full generality the existence of perfect embeddings remains an open question, we prove that  at least in some concrete cases  they reveal the relevant conformal structure in a latticeindependent way: as that of a related Lorentzminimal surface in the Minkowski space.
Based upon joint works with Benoît Laslier, Sanjay Ramassamy and Marianna Russkikh.

26816

Thursday 9/3 2:30 PM

Daniel Potts, TU Chemnitz

High dimensional approximation with trigonometric polynomials; zoom link @ https://sites.google.com/view/mindsseminar/home
 Daniel Potts, TU Chemnitz
 High dimensional approximation with trigonometric polynomials; zoom link @ https://sites.google.com/view/mindsseminar/home
 09/03/2020
 2:30 PM  3:30 PM

(Part of One World MINDS seminar: https://sites.google.com/view/mindsseminar/home)
\[
\]
In this talk, we present fast Fourier based methods for the approximation of multivariate functions. Our aim is to learn the support of the Fourier coefficients in the frequency domain of highdimensional functions. We are interested in two different approximation scenarios. The first case is blackbox approximation where the user is allowed to sample the unknown function at any point and in the second case we are working with fixed scattered data. For blackbox approximation we employ quasi MonteCarlo methods on rank1 lattice points. The fast algorithms are then based on onedimensional fast Fourier transforms (FFT). In the second case, which is much more difficult, we will couple truncated ANOVA (analysis of variance) decompositions with the fast Fourier transform on nonequispaced data (NFFT). In both cases, we present error estimates and numerical results. The presented methods can be understood as sparse high dimensional FFT’s.
This talk based on joint work with Lutz Kämmerer, Michael Schmischke, Manfred Tasche, and Toni Volkmer.

26852

Monday 9/7 5:00 PM

Zheng Xiao, MSU

Polynomials over finite fields. Zoom https://msu.zoom.us/j/6171365526
 Zheng Xiao, MSU
 Polynomials over finite fields. Zoom https://msu.zoom.us/j/6171365526
 09/07/2020
 5:00 PM  6:00 PM
 Online (virtual meeting)
Finite fields introduction and congruence equations of polynomials over finite fields.

26817

Tuesday 9/8 3:00 PM

Yi Ni, Caltech

Thurston norm minimizing Seifert surfaces
 Yi Ni, Caltech
 Thurston norm minimizing Seifert surfaces
 09/08/2020
 3:00 PM  4:00 PM
 Online (virtual meeting)
Let K be a nullhomologous knot in a closed 3manifold Y, and F be a Seifert surface. One can cap off the boundary of F with a disk in the zero surgery on K to get a closed surface F_0. If we know that F is Thurston norm minimizing, we can ask whether F_0 is also Thurston norm minimizing. A classical theorem of Gabai says that the answer is Yes when Y is the 3sphere. Gabai's theorem can be generalized to many other 3manifolds using Heegaard Floer homology. In this talk, we will discuss a sufficient condition for F_0 to be Thurston norm minimizing which relates this property to the 4genus of the knot.
Zoom: https://msu.zoom.us/j/92550015779?pwd=azRER2p1Sm5CWWRML3lHbVQyWDU1QT09

26842

Tuesday 9/8 8:00 PM

Tatsuki Kuwagaki, Osaka

Sheaf quantization from spectral network
 Tatsuki Kuwagaki, Osaka
 Sheaf quantization from spectral network
 09/08/2020
 8:00 PM  9:00 PM
 Online (virtual meeting)
A sheaf quantization is a sheaf associated to a Lagrangian brane. This sheaf conjecturally has information as much as Floer theory of the Lagrangian. On the other hand, exact WKB analysis is an analysis of differential equations containing the Planck constant hbar.
In this talk, I will explain how to construct a sheaf quantization over the Novikov ring of the spectral curve of an hbardifferential equation, by using the ideas of exact WKB analysis and spectral network. In the construction, one can see how (conjecturally) the convergence in WKB analysis are related to the convergence of Fukaya category. In degree 2, the sheaf quantization associates a cluster coordinate which is the same as Fock—Goncharov coordinate. I will also mention about some relationships to Riemann—Hilbert correspondence of D’Agnolo—Kashiwara and Kontsevich—Soibelman.
https://msu.zoom.us/j/95159415920?pwd=bUlETkdpazdiWGNjZnNkUWNIaXRFQT09

26839

Wednesday 9/9 4:10 PM

Sheila Sundaram

On the homology of subword order. Zoom https://msu.zoom.us/j/5476724571
 Sheila Sundaram
 On the homology of subword order. Zoom https://msu.zoom.us/j/5476724571
 09/09/2020
 4:10 PM  5:00 PM

In this talk we examine the homology representation of the symmetric group $S_n$ on rankselected subposets of subword order. We show that the action on the rankselected chains is a nonnegative integer combination of tensor powers of the reflection representation $S_{(n1,1)}$ indexed by the partition $(n1,1)$, and that its Frobenius characteristic is $h$positive and supported on the set $T_{1}(n)=\{h_\lambda: \lambda=(nr, 1^r), r\ge 1\}.$
We give an explicit formula for the homology module for words of bounded length, as a sum of tensor powers of $S_{(n1,1)}$. This recovers, as a special case, a theorem of Bj\"orner and Stanley for words of length at most $k.$ We exhibit a curious duality in homology in the case when one rank is deleted. We also show that in many cases, the rankselected homology modules, modulo one copy of the reflection representation, are $h$positive and supported on the set $T_{2}(n)=\{h_\lambda: \lambda=(nr, 1^r), r\ge 2\}.$
Our analysis of the homology also uncovers curious enumerative formulas that may be interesting to investigate combinatorially.

26851

Thursday 9/10 1:00 PM

Joshua Ruiter, MSU

Galois descent. Zoom link: https://msu.zoom.us/j/96111069403
 Joshua Ruiter, MSU
 Galois descent. Zoom link: https://msu.zoom.us/j/96111069403
 09/10/2020
 1:00 PM  2:00 PM
 Online (virtual meeting)
We'll introduce and motivate techniques of Galois descent for classifying twisted forms of algebras, using nonabelian group cohomology. We'll also describe a connection to relative Brauer groups.
Zoom link: https://msu.zoom.us/j/96111069403

26825

Thursday 9/10 2:30 PM

Rima Alaifari, ETH Zurich

The phase factor: recovery from magnitudes of signal representations; zoom link @ https://sites.google.com/view/mindsseminar/home
 Rima Alaifari, ETH Zurich
 The phase factor: recovery from magnitudes of signal representations; zoom link @ https://sites.google.com/view/mindsseminar/home
 09/10/2020
 2:30 PM  3:30 PM

We study the problem of phase retrieval from a deterministic viewpoint, in which the magnitudes of a timefrequency or timescale representation of a signal are known. From an inverse problems perspective, the questions of uniqueness and stability are crucial to theoretically guarantee meaningful reconstruction. In this talk, we present results on these two questions for Gabor frames and wavelet frames and conclude by discussing some open problems.

26853

Monday 9/14 5:00 PM

Zheng Xiao, MSU

Arithmetic functions and Zeta functions over finite fields. Zoom https://msu.zoom.us/j/6171365526
 Zheng Xiao, MSU
 Arithmetic functions and Zeta functions over finite fields. Zoom https://msu.zoom.us/j/6171365526
 09/14/2020
 5:00 PM  6:00 PM
 Online (virtual meeting)
No abstract available.

26821

Tuesday 9/15 3:00 PM

Tian Yang, Texas A&M University

Relative ReshetikhinTuraev invariants and hyperbolic cone metrics on 3manifolds
 Tian Yang, Texas A&M University
 Relative ReshetikhinTuraev invariants and hyperbolic cone metrics on 3manifolds
 09/15/2020
 3:00 PM  4:00 PM
 Online (virtual meeting)
We propose the Volume Conjecture for the relative ReshetikhinTuraev invariants of a closed oriented 3manifold with a colored framed link inside it whose asymptotic behavior is related to the volume and the ChernSimons invariant of the hyperbolic cone metric on the manifold with singular locus the link and cone angles determined by the coloring, and prove the conjecture for a number of families of examples. This provides a possible approach of solving the Volume Conjecture for the ReshetikhinTuraev invariants of closed oriented hyperbolic 3manifolds. A large part of this work is joint with Ka Ho Wong. https://msu.zoom.us/j/92550015779?pwd=azRER2p1Sm5CWWRML3lHbVQyWDU1QT09

26855

Tuesday 9/15 4:00 PM

Martin Hairer, Imperial College London

Taming infinities
 Martin Hairer, Imperial College London
 Taming infinities
 09/15/2020
 4:00 PM  5:00 PM
 Online (virtual meeting)
Some physical and mathematical theories have the unfortunate feature that if one takes them at face value, many quantities of interest appear to be infinite! What's worse, this doesn't just happen for some exotic theories, but in the standard theories describing some of the most fundamental aspects of nature. Various techniques, usually going under the common name of “renormalisation” have been developed over the years to address this, allowing mathematicians and physicists to tame these infinities. We will dip our toes into some of the conceptual and mathematical aspects of these techniques and we will see how they have recently been used in probability theory to study equations whose meaning was not even clear until now.

26857

Wednesday 9/16 3:00 PM

Samantha Dahlberg, Arizona State University

Diameters of Graphs of Reduced Words of Permutations, Zoom https://msu.zoom.us/j/5476724571
 Samantha Dahlberg, Arizona State University
 Diameters of Graphs of Reduced Words of Permutations, Zoom https://msu.zoom.us/j/5476724571
 09/16/2020
 3:00 PM  3:50 PM
 Online (virtual meeting)
It is a classical result that any two reduced words of a permutation in the symmetric group can be transformed into one another by a sequence of long braid moves and commutation moves. In this talk we will discuss the diameters of these connected graphs formed from the reduced words connected by single moves. Recently, the diameter has been calculated for the longest permutation $n\ldots 21$ by Reiner and Roichman as well as Assaf. In this talk we present our results on diameters for certain classes or permutation . We also make progress on conjectured bounds of the diameter by Reiner and Roichman, which are based on the underlying hyperplane arrangement.

26864

Thursday 9/17 1:00 PM

Chuangtian Guan, MSU

Dieudonne Theory and Its Application
 Chuangtian Guan, MSU
 Dieudonne Theory and Its Application
 09/17/2020
 1:00 PM  2:00 PM
 Online (virtual meeting)
Classical (contravariant) Dieudonne theory establishes an antiequivalence of categories between finite commutative group schemes over a perfect field $k$ and Dieudonne modules. In this talk we will talk about this antiequivalence and some simple applications of it.

26826

Thursday 9/17 2:30 PM

Mauro Maggioni, Johns Hopkins University

Learning Interaction laws in particle and agentbased systems; zoom link @ https://sites.google.com/view/mindsseminar/home
 Mauro Maggioni, Johns Hopkins University
 Learning Interaction laws in particle and agentbased systems; zoom link @ https://sites.google.com/view/mindsseminar/home
 09/17/2020
 2:30 PM  3:30 PM

Interacting agentbased systems are ubiquitous in science, from modeling of particles in Physics to preypredator and colony models in Biology, to opinion dynamics in economics and social sciences. Oftentimes the laws of interactions between the agents are quite simple, for example they depend only on pairwise interactions, and only on pairwise distance in each interaction. We consider the following inference problem for a system of interacting particles or agents: given only observed trajectories of the agents in the system, can we learn what the laws of interactions are? We would like to do this without assuming any particular form for the interaction laws, i.e. they might be “any” function of pairwise distances. We consider this problem both the meanfield limit (i.e. the number of particles going to infinity) and in the case of a finite number of agents, with an increasing number of observations, albeit in this talk we will mostly focus on the latter case. We cast this as an inverse problem, and study it in the case where the interaction is governed by an (unknown) function of pairwise distances. We discuss when this problem is wellposed, and we construct estimators for the interaction kernels with provably good statistically and computational properties. We measure their performance on various examples, that include extensions to agent systems with different types of agents, secondorder systems, and families of systems with parametric interaction kernels. We also conduct numerical experiments to test the large time behavior of these systems, especially in the cases where they exhibit emergent behavior. This is joint work with F. Lu, J.Miller, S. Tang and M. Zhong.

26859

Monday 9/21 2:00 PM

Roy Araiza, Purdue University

Operator Spaces and Operator Systems: An Exposition
 Roy Araiza, Purdue University
 Operator Spaces and Operator Systems: An Exposition
 09/21/2020
 2:00 PM  2:50 PM
 Online (virtual meeting)
During this lecture I will give an overview of the history and theory of operator spaces and operator systems. These "matrix normed spaces'' and "matrix ordered $*$vector spaces'' arose in a somewhat natural fashion and the study of these objects is motivated by problems that arise when studying the "classical'' theory such as C*algebras. After going over necessary background for both objects I will discuss how operator space and operator system theory were applied to approaching and solving problems in operator algebras.
Join via Zoom: https://msu.zoom.us/j/95716797501

26865

Monday 9/21 3:00 PM

Roy Araiza, Purdue University

An Abstract Characterization for Projections in Operator Systems
 Roy Araiza, Purdue University
 An Abstract Characterization for Projections in Operator Systems
 09/21/2020
 3:00 PM  3:50 PM
 Online (virtual meeting)
Given an abstract operator system V it is not clear how one would go about defining the notion of a projection. During this talk I will present an answer and some recent results on this question. This is done by first considering abstract compression operator systems associated with a positive contraction in V and then determining when we have a realization of V in such an abstract compression operator system. It then follows that there is a onetoone correspondence between abstract and concrete projections, and in particular, that every abstract projection is a concrete projection in the C*envelope of V. I will then conclude with some applications to quantum information theory. In particular, the study of certain correlation sets. This is joint work with Travis Russell (West Point).
Join via Zoom: https://msu.zoom.us/j/95716797501

26861

Monday 9/21 5:00 PM

Keping Huang, MSU; Zheng Xiao, MSU

The reciprocity law over function fields. Zoom https://msu.zoom.us/j/6171365526
 Keping Huang, MSU; Zheng Xiao, MSU
 The reciprocity law over function fields. Zoom https://msu.zoom.us/j/6171365526
 09/21/2020
 5:00 PM  6:00 PM
 Online (virtual meeting)
No abstract available.

26837

Tuesday 9/22 3:00 PM

Jeffrey Case, Penn State

A geometric approach to fractional powers of the Laplacian and sharp Sobolev trace inequalities
 Jeffrey Case, Penn State
 A geometric approach to fractional powers of the Laplacian and sharp Sobolev trace inequalities
 09/22/2020
 3:00 PM  4:00 PM
 Online (virtual meeting)
A seminal paper of Caffarelli and Silvestre identifies fractional powers of the Laplacian on Euclidean space as DirichlettoNeumann operators. In this talk, I will use conformal geometry to generalize their approach to Riemannian manifolds. More specifically, I will present multiple (equivalent) definitions of (conformally covariant) operators with principal symbol that of a fractional power of the Laplacian. I will also discuss how these operators lead to a simple derivation of a broad family of sharp Sobolev trace inequalities.
https://msu.zoom.us/j/92550015779?pwd=azRER2p1Sm5CWWRML3lHbVQyWDU1QT09

26856

Tuesday 9/22 4:00 PM

John Lesieutre, Penn State University

Polynomial interpolation is harder than it sounds
 John Lesieutre, Penn State University
 Polynomial interpolation is harder than it sounds
 09/22/2020
 4:00 PM  5:00 PM
 Online (virtual meeting)
Suppose that $(x_1,y_1),\ldots,(x_r,y_r)$ is a set of points in the plane. Given a degree $d$ and multiplicities $m_i$, does there a nonzero polynomial in two variables of degree at most $d$ which vanishes to order at least $m_i$ at $(x_i,y_i)$? What is the dimension of the space of such polynomials, and how does it vary with the parameters? I will explain some of the basic results and conjectures and show how this problem is connected to some questions of current interest in algebraic geometry.

26854

Tuesday 9/22 8:00 PM


Let's gather!

 Let's gather!
 09/22/2020
 8:00 PM  9:00 PM
 Online (virtual meeting)
https://gather.town/app/zn0JbuYdRh4QqZ6h/MSUGT
Firefox or Chrome only. No password.
G&T community activity. Open to MSU faculties and students.

26858

Wednesday 9/23 3:00 PM

Samin Aref, Max Planck Institute for Demographic Research

Structural analysis of signed graphs: a talk on methods and applications, Zoom https://msu.zoom.us/j/5476724571
 Samin Aref, Max Planck Institute for Demographic Research
 Structural analysis of signed graphs: a talk on methods and applications, Zoom https://msu.zoom.us/j/5476724571
 09/23/2020
 3:00 PM  3:50 PM
 Online (virtual meeting)
This talk focuses on positive and negative ties in networks (signed graphs) resulting in a common structural configuration. We analyze signed networks from the perspective of balance theory which predicts structural balance as a stable configuration. A signed network is balanced iff its set of vertices can be partitioned into two groups such that positive edges are within the groups and negative edges are between the groups.
The scarcity of balanced configurations in networks inferred from empirical data (real networks) requires us to define the notion of partial balance in order to quantify the extent to which a network is balanced. After evaluating several numerical measures of partial balance, we recommend using the frustration index, which equals the minimum number of edges whose removal results in a balanced network [arxiv.org/abs/1509.04037].
We use the definition of balance to optimally partition nodes of signed networks into two internally solidary but mutually hostile groups. An optimal partitioning leads to an exact value for the frustration index. We tackle the intensive computations of finding an optimal partition by developing efficient mathematical models and algorithms [arxiv.org/abs/1710.09876] [arxiv.org/abs/1611.09030]. We then extend the concepts of balance and frustration in signed networks to applications beyond the classic friendenemy interpretation of balance theory in the social context. Using a highperformance computer, we analyze large networks to investigate a range of applications from biology, chemistry and physics to finance, international relations, and political science [arxiv.org/abs/1712.04628].
In another project manly focused on a political science application, we focus on the challenge of quantifying political polarization in the US Congress, and analyzing its relationship to the fraction of introduced bills that are passed into law (bill passage rate). We use signed graph models of political collaboration among legislators to show that changes in bill passage rates are better explained by the partisanship of a chamber's largest coalition, which we identify by partitioning signed networks of legislators according to balance theory [arxiv.org/abs/1906.01696].
In another project, we expand the evaluation of balance to incorporate directionality of the edges and consider three levels of analysis: triads, subgroups, and the whole network. Through extensive computational analysis, we explore common structural patterns across a range of social settings from college students and Wikipedia editors to philosophers and Bitcoin traders. We then apply our multilevel framework of analysis to examine balance in temporal and multilayer networks which leads to new observations on balance with respect to time and layer dimensions [arxiv.org/abs/2005.09925].

26862

Wednesday 9/23 4:00 PM

Igor Rapinchuk, MSU

Algebraic groups with good reduction. Zoom https://msu.zoom.us/j/97573873209
 Igor Rapinchuk, MSU
 Algebraic groups with good reduction. Zoom https://msu.zoom.us/j/97573873209
 09/23/2020
 4:00 PM  5:00 PM
 Online (virtual meeting)
Techniques involving reduction are very common in number theory and arithmetic geometry. In particular, elliptic curves and general abelian varieties having good reduction have been the subject of very intensive investigations over the years. The purpose of this talk is to report on recent work that focuses on good reduction in the context of reductive linear algebraic groups over finitely generated fields. In addition, we will highlight some applications to the study of localglobal principles and the analysis of algebraic groups having the same maximal tori. (Parts of this work are joint with V. Chernousov and A. Rapinchuk.)

26867

Thursday 9/24 1:00 PM

Nick Rekuski, MSU

Simply Connectedness in Algebraic Geometry
 Nick Rekuski, MSU
 Simply Connectedness in Algebraic Geometry
 09/24/2020
 1:00 PM  2:00 PM
 Online (virtual meeting)
A path connected topological space is simply connected if the space of based paths is path connected. Equivalently, the fundamental group is zero or any connected covering space is trivial. However, these notions do not capture the correct notion in the world of algebraic geometry. For example, if $X$ is a Riemann surface then the Zariski topology (the usual topology in algebraic geometry) on $X$ is equivalent to the cofinite topology, so $X$ is simply connected.
In this talk, we will introduce a few definitions of simply connectedness in algebraic geometry  each corresponding to one of the equivalent definitions above. We will then compare these definitions and discuss how their consequences differ from their topological counterparts.

26827

Thursday 9/24 2:30 PM

Rebecca Willett, University of Chicago

Regularization in InfiniteWidth ReLU Networks; zoom link @ https://sites.google.com/view/mindsseminar/home
 Rebecca Willett, University of Chicago
 Regularization in InfiniteWidth ReLU Networks; zoom link @ https://sites.google.com/view/mindsseminar/home
 09/24/2020
 2:30 PM  3:30 PM
 Online (virtual meeting)
A growing body of research illustrates that neural network generalization performance is less dependent on the network size (i.e. number of weights or parameters) and more dependent on the magnitude of the weights. That is, generalization is not achieved by limiting the size of the network, but rather by explicitly or implicitly controlling the magnitude of the weights. To better understand this phenomenon, we will explore how neural networks represent functions as the number of weights in the network approaches infinity. Specifically, we characterize the norm required to realize a function f as a single hiddenlayer ReLU network with an unbounded number of units (infinite width), but where the Euclidean norm of the weights is bounded, including precisely characterizing which functions can be realized with finite norm. This was settled for univariate functions in Savarese et al. (2019), where it was shown that the required norm is determined by the L1norm of the second derivative of the function. We extend the characterization to multivariate functions (i.e., networks with d input units), relating the required norm to the L1norm of the Radon transform of a (d+1)/2power Laplacian of the function. This characterization allows us to show that all functions in certain Sobolev spaces can be represented with bounded norm and to obtain a depth separation result. These results have important implications for understanding generalization performance and the distinction between neural networks and more traditional kernel learning.

26860

Monday 9/28 2:00 PM

Krishnendu Kahn, University of Iowa

Fundamental groups of certain property (T) factors
 Krishnendu Kahn, University of Iowa
 Fundamental groups of certain property (T) factors
 09/28/2020
 2:00 PM  2:50 PM
 Online (virtual meeting)
Calculation of fundamental groups of type $\rm II_1$ factor is, in general, an extremely hard and central problem in the field of von Neumann algebras. In this direction, a conjecture due to A. Connes states that the fundamental group of the group von Neumann algebra $L(\Gamma)$ associated to any icc property (T) group $\Gamma$ is trivial. Up to now, there was no single example of property (T) group factor satisfying the conjecture. In this talk, I shall provide the first examples of property (T) group factors with trivial fundamental group. This talk is based on a joint work with Ionut Chifan, Sayan Das and Cyril Houdayer.
Join via Zoom: https://msu.zoom.us/j/98441498789

26818

Tuesday 9/29 3:00 PM

David Jordan, Edinburgh

Skein theory in the geometric Langlands TFT
 David Jordan, Edinburgh
 Skein theory in the geometric Langlands TFT
 09/29/2020
 3:00 PM  4:00 PM
 Online (virtual meeting)
I will overview several appearances (some recently established, some conjectural) of skein theory in the socalled quantum geometric Langlands fully extended TFT. The talk will be mostly elementary, and I'll highlight an application to a conjecture of Witten concerning the finitedimensionality of skein modules of 3manifolds at generic values of the quantum parameter. https://msu.zoom.us/j/92550015779?pwd=azRER2p1Sm5CWWRML3lHbVQyWDU1QT09

26869

Tuesday 9/29 4:00 PM

Ruixiang Zhang, IAS

Kakeya type problems and analysis
 Ruixiang Zhang, IAS
 Kakeya type problems and analysis
 09/29/2020
 4:00 PM  5:00 PM
 Online (virtual meeting)
Informally, Kakeya type problems ask whether tubes with different positions and directions can overlap a lot. One usually expects the answer to be no in an appropriate sense. Thanks to the uncertainty principle, such a quantified nonoverlapping theorem would often see powerful applications in analysis problems that have Fourier aspects. Perhaps the most wellknown Kakeya type problem is the Kakeya conjecture. It remains widely open in $\Bbb{R}^n (n>2)$ as of today. Nevertheless, in the recent few decades people have been able to prove new Kakeya type theorems that led to improvements or complete solutions to analysis problems that appeared out of reach before. I will give an introduction to Kakeya type problems/theorems and analysis problems that see their applications. Potentially reporting some recent progress joint with Du, Guo, Guth, Hickman, Iosevich, Ou, Rogers, Wang and Wilson.

26863

Wednesday 9/30 3:00 PM

Josh Hallam, Loyola Marymount University

Whitney Duals of Graded Posets, Zoom https://msu.zoom.us/j/5476724571
 Josh Hallam, Loyola Marymount University
 Whitney Duals of Graded Posets, Zoom https://msu.zoom.us/j/5476724571
 09/30/2020
 3:00 PM  3:50 PM
 Online (virtual meeting)
To each graded poset one can associate two sequences of numbers; the Whitney numbers of the first kind and the Whitney numbers of the second kind. One sequence keeps track of the Möbius function at each rank level and the other keeps track of the number of elements at each rank level. The Whitney numbers appear in many contexts in combinatorics. For example, they appear as the coefficients of the chromatic polynomial of a graph and can be used to compute the number of regions in a real hyperplane arrangement.
We say that posets P and Q are Whitney duals if the Whitney numbers of the first kind of P are the Whitney numbers of the second kind of Q and viceversa. In this talk, we will discuss a method to construct Whitney duals using edge labelings and quotient posets. We will also discuss some applications of Whitney duals.
This is joint work with Rafael S. González D'León.

26866

Wednesday 9/30 4:10 PM

Yilin Wang, MIT

Multichordal Loewner potential https://msu.zoom.us/j/99389628054
 Yilin Wang, MIT
 Multichordal Loewner potential https://msu.zoom.us/j/99389628054
 09/30/2020
 4:10 PM  5:00 PM
 Online (virtual meeting)
SchrammLoewner evolutions (SLE) are probabilistic models of simple planar curves. They first arise as interfaces in scaling limits of 2D statistical mechanics lattice models which exhibit conformal invariance. In this talk, I will explain how asymptotic behaviors of SLE give rise to an interesting quantity (multichordal Loewner potential), which connects to rational function, zetaregularized determinants of Laplacian, and BelavinPolyakovZamolodchikov equations in conformal field theory. This is a joint work with Eveliina Peltola (Bonn).

26828

Thursday 10/1 2:30 PM

Rene Vidal, Johns Hopkins University

TBA; zoom link @ https://sites.google.com/view/mindsseminar/home
 Rene Vidal, Johns Hopkins University
 TBA; zoom link @ https://sites.google.com/view/mindsseminar/home
 10/01/2020
 2:30 PM  3:30 PM

No abstract available.

26820

Tuesday 10/6 3:00 PM

Jesse Huang, UIUC

TBA
 Jesse Huang, UIUC
 TBA
 10/06/2020
 3:00 PM  4:00 PM
 Online (virtual meeting)
TBA

26870

Tuesday 10/6 4:00 PM

Colin McLarty, Case Western Reserve University

Grothendieck's personal idea of a topos as a space
 Colin McLarty, Case Western Reserve University
 Grothendieck's personal idea of a topos as a space
 10/06/2020
 4:00 PM  5:00 PM
 Online (virtual meeting)
In 33 hours of tape recordings in 1973 Grothendieck described his view of topos beyond what is in the collective volume Théorie des topos et cohomologie étale (SGA 4). In particular, this shows how Grothendieck got his idea of a "generalized topological space" simultaneously with what became etale cohomology during a 1958 talk by JeanPierre Serre.

26829

Thursday 10/8 2:30 PM

Jun Kitagawa, Michigan State University

TBA; zoom link @ https://sites.google.com/view/mindsseminar/home
 Jun Kitagawa, Michigan State University
 TBA; zoom link @ https://sites.google.com/view/mindsseminar/home
 10/08/2020
 2:30 PM  3:30 PM

No abstract available.

26822

Tuesday 10/13 3:00 PM

Josh Wang, Harvard

TBA
 Josh Wang, Harvard
 TBA
 10/13/2020
 3:00 PM  4:00 PM
 Online (virtual meeting)
TBA

26873

Wednesday 10/14 4:00 PM

Lennart Gehrmann, Universität DuisburgEssen

TBA
 Lennart Gehrmann, Universität DuisburgEssen
 TBA
 10/14/2020
 4:00 PM  5:00 PM
 Online (virtual meeting)
No abstract available.

26838

Tuesday 10/20 3:00 PM

Jeremy Van HornMorris, U Arkansas

TBA
 Jeremy Van HornMorris, U Arkansas
 TBA
 10/20/2020
 3:00 PM  4:00 PM
 Online (virtual meeting)
TBA

26871

Tuesday 10/20 4:00 PM

Alexander Volberg, Michigan State University

Metric properties of Banach spaces, Enflo's problem, Pisier's inequality and quantum random variables
 Alexander Volberg, Michigan State University
 Metric properties of Banach spaces, Enflo's problem, Pisier's inequality and quantum random variables
 10/20/2020
 4:00 PM  5:00 PM
 Online (virtual meeting)
A nonlinear analogue of the Rademacher type of a Banach space was introduced in classical work of Enflo. The key feature of Enflo type is that its definition uses only the metric structure of the Banach space, while the definition of Rademacher type relies on its linear structure.
In the joint paper with Paata Ivanisvili and Ramon Van Handel we prove that Rademacher type and Enflo type coincide, settling a longstanding open problem in Banach space theory. The proof is based on a novel dimensionfree analogue of Pisier's inequality on the discrete cube, which, in its turn, is based on a certain formula that we used before in improving the constants in the scalar Poincaré inequality on the Hamming cube. I will also show several extensions of Pisier's inequality with ultimate assumptions on a Banach space structure.
Some of our results use approach via quantum random variables.

26824

Tuesday 10/27 3:00 PM

Lenny Ng, Duke

TBA
 Lenny Ng, Duke
 TBA
 10/27/2020
 3:00 PM  4:00 PM
 Online (virtual meeting)
TBA

26844

Thursday 10/29 4:30 AM

Yang Wang, Hong Kong University of Science and Technology

TBA; zoom link @ https://sites.google.com/view/mindsseminar/home
 Yang Wang, Hong Kong University of Science and Technology
 TBA; zoom link @ https://sites.google.com/view/mindsseminar/home
 10/29/2020
 4:30 AM  5:30 AM

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

26836

Tuesday 11/3 3:00 PM

Eric Samperton, UIUC

Finite gauge groups, TQFT, and the computational complexity of 3manifold invariants
 Eric Samperton, UIUC
 Finite gauge groups, TQFT, and the computational complexity of 3manifold invariants
 11/03/2020
 3:00 PM  4:00 PM
 Online (virtual meeting)
I will give an overview of some relations between finite group theory, Gequivariant topological quantum field theory, and the computational complexity of invariants of 3manifolds, both classical and quantum. We will start with one of the simplest kinds of invariants in knot theory: the coloring invariants, introduced by Fox when giving a talk to undergraduates in the 1950s. We will then build up to the idea of Gequivariant TQFT (aka homotopy QFT with target K(G,1)), which mathematically describes the topological order determined by a symmetryenriched topological phase of matter. Physicists have studied these in part motivated by the search for new universal topological quantum computing architectures.
Our goal will be to convey two complexitytheoretic lessons. First, when G is sufficiently complicated (nonabelian simple), the simpletodefine coloring invariants associated to G are, in fact, very difficult to compute, even on a quantum computer. Second, no matter what finite group G one uses, a 3dimensional Gequivariant TQFT can not be used for universal topological quantum computation if the underlying nonequivariant theory is not already universal. This talk is based on joint works with Greg Kuperberg and Colleen Delaney.

26830

Thursday 11/5 2:30 PM

Rachel Ward, University of Texas at Austin

TBA; zoom link @ https://sites.google.com/view/mindsseminar/home
 Rachel Ward, University of Texas at Austin
 TBA; zoom link @ https://sites.google.com/view/mindsseminar/home
 11/05/2020
 2:30 PM  3:30 PM

No abstract available.

26868

Monday 11/9 3:30 PM

Ben Hayes, University of Virginia

TBA
 Ben Hayes, University of Virginia
 TBA
 11/09/2020
 3:30 PM  4:20 PM
 Online (virtual meeting)
TBA

26841

Tuesday 11/10 3:00 PM

Josh Howie, UC Davis

TBA
 Josh Howie, UC Davis
 TBA
 11/10/2020
 3:00 PM  4:00 PM
 Online (virtual meeting)
TBA

26872

Wednesday 11/11 4:10 PM

Ben Hayes, University of Virginia

TBD
 Ben Hayes, University of Virginia
 TBD
 11/11/2020
 4:10 PM  5:00 PM
 Online (virtual meeting)
TBD

26831

Thursday 11/12 2:30 PM

Hrushikesh Mhaskar, Claremont Graduate University

TBA; zoom link @ https://sites.google.com/view/mindsseminar/home
 Hrushikesh Mhaskar, Claremont Graduate University
 TBA; zoom link @ https://sites.google.com/view/mindsseminar/home
 11/12/2020
 2:30 PM  3:30 PM

No abstract available.

26819

Tuesday 11/17 3:00 PM

Yu Pan

TBA
 Yu Pan
 TBA
 11/17/2020
 3:00 PM  4:00 PM
 Online (virtual meeting)
TBA

26886

Wednesday 11/18 1:00 PM

Dimitris Vardakis, MSU

TBD
 Dimitris Vardakis, MSU
 TBD
 11/18/2020
 1:00 PM  2:00 PM
 C517 Wells Hall
No abstract available.

26832

Thursday 11/19 2:30 PM

Yonina Eldar, Weizmann Institute of Science

TBA; zoom link @ https://sites.google.com/view/mindsseminar/home
 Yonina Eldar, Weizmann Institute of Science
 TBA; zoom link @ https://sites.google.com/view/mindsseminar/home
 11/19/2020
 2:30 PM  3:30 PM

No abstract available.

26874

Tuesday 11/24 11:00 AM

Stéphane Guillermou, Institut Fourier

TBA
 Stéphane Guillermou, Institut Fourier
 TBA
 11/24/2020
 11:00 AM  11:59 AM
 Online (virtual meeting)
TBA

26875

Tuesday 11/24 3:00 PM

Pyongwon Suh, Northwestern University

TBA
 Pyongwon Suh, Northwestern University
 TBA
 11/24/2020
 3:00 PM  4:00 PM
 Online (virtual meeting)
TBA

26845

Thursday 11/26 3:30 AM

ManCho Anthony So, Chinese University of Hong Kong

TBA; zoom link @ https://sites.google.com/view/mindsseminar/home
 ManCho Anthony So, Chinese University of Hong Kong
 TBA; zoom link @ https://sites.google.com/view/mindsseminar/home
 11/26/2020
 3:30 AM  4:30 AM

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

26840

Tuesday 12/1 3:00 PM

Christine Lee, U of South Alabama

TBA
 Christine Lee, U of South Alabama
 TBA
 12/01/2020
 3:00 PM  4:00 PM
 Online (virtual meeting)
TBA

26846

Thursday 12/3 3:30 AM

DingXua Zhou, City University of Hong Kong

TBA; zoom link @ https://sites.google.com/view/mindsseminar/home
 DingXua Zhou, City University of Hong Kong
 TBA; zoom link @ https://sites.google.com/view/mindsseminar/home
 12/03/2020
 3:30 AM  4:30 AM

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

26850

Tuesday 12/8 3:00 PM

Shea VelaVick, Louisiana State University

TBA
 Shea VelaVick, Louisiana State University
 TBA
 12/08/2020
 3:00 PM  4:00 PM
 Online (virtual meeting)
TBA

26843

Tuesday 12/8 8:00 PM

Corey Bregman, Brandeis

TBA
 Corey Bregman, Brandeis
 TBA
 12/08/2020
 8:00 PM  9:00 PM
 Online (virtual meeting)
TBA

26833

Thursday 12/10 2:30 PM

Anna Little, University of Utah

TBA; zoom link @ https://sites.google.com/view/mindsseminar/home
 Anna Little, University of Utah
 TBA; zoom link @ https://sites.google.com/view/mindsseminar/home
 12/10/2020
 2:30 PM  3:30 PM

No abstract available.

26823

Tuesday 12/15 3:00 PM

Inbar Klang, Columbia

TBA
 Inbar Klang, Columbia
 TBA
 12/15/2020
 3:00 PM  4:00 PM
 Online (virtual meeting)
TBA

26834

Thursday 12/17 2:30 PM

David P. Woodruff , Carnegie Mellon University

TBA; zoom link @ https://sites.google.com/view/mindsseminar/home
 David P. Woodruff , Carnegie Mellon University
 TBA; zoom link @ https://sites.google.com/view/mindsseminar/home
 12/17/2020
 2:30 PM  3:30 PM

No abstract available.
