• Speaker: Anna Weigandt, Massachusetts Institute of Technology
• Title: Combinatorial Aspects of Determinantal Varieties
• Date: 01/09/2023
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall (Virtual Meeting Link)
• Contact: Sabrina M Walton (waltons3@msu.edu)

Schubert calculus has its origins in enumerative questions asked by the geometers of the 19th century, such as “how many lines meet four fixed lines in three-space?”  These problems can be recast as questions about the structure of cohomology rings of geometric spaces such as flag varieties.  Borel’s isomorphism identifies the cohomology of the complete flag variety with a simple quotient of a polynomial ring.  Lascoux and Schützenberger (1982) defined Schubert polynomials, which are coset representatives for the Schubert basis of this ring. However, it was not clear if this choice was geometrically natural.  Knutson and Miller (2005) provided a justification for the naturality of Schubert polynomials via antidiagonal Gröbner degenerations of matrix Schubert varieties, which are generalized determinantal varieties. Furthermore, they showed that pre-existing combinatorial objects called pipe dreams govern this degeneration.  In this talk, we study the dual setting of diagonal Gröbner degenerations of matrix Schubert varieties, interpreting these limits in terms of the “bumpless pipe dreams” of Lam, Lee, and Shimozono (2021).  We then use the combinatorics of K-theory representatives for Schubert classes to compute the Castelnuovo-Mumford regularity of matrix Schubert varieties, which gives a bound on the complexity of their coordinate rings.

• Speaker: Nathaniel Bottman, Max Planck Institute
• Title: What analysis, combinatorics, and quilted spheres can tell us about symplectic geometry
• Date: 01/10/2023
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall (Virtual Meeting Link)
• Contact: Sabrina M Walton (waltons3@msu.edu)

A central tool for studying symplectic manifolds is the Fukaya category. In this talk, I will describe my program to relate the Fukaya categories of different symplectic manifolds. The key objects are "witch balls", which are coupled systems of PDEs whose domain is the Riemann sphere decorated with circles and points, and "2-associahedra", the configuration spaces of these domains. I will describe applications to symplectic geometry and algebraic geometry, and highlight the role of degenerating families of elliptic PDEs.

• Speaker: Simon Foucart, Texas A&M University
• Title: ZOOM TALK (Passcode: the smallest prime > 100 ): Three uses of semidefinite programming in approximation theory
• Date: 01/12/2023
• Time: 2:30 PM - 3:30 PM
• Place: C304 Wells Hall (Virtual Meeting Link)
• Contact: Mark A Iwen (iwenmark@msu.edu)

In this talk, modern optimization techniques are publicized as fitting computational tools to attack several extremal problems from Approximation Theory which had reached their limitations based on purely analytical approaches. Three such problems are showcased: the first problem---minimal projections---involves minimization over measures and exploits the moment method; the second problem---constrained approximation---involves minimization over polynomials and exploits the sum-of-squares method; and the third problem---optimal recovery from inaccurate observations---is highly relevant in Data Science and exploits the S-procedure. In each of these problems, one ends up having to solve semidefinite programs.

• Speaker: Alexander Watson, University of Minnesota
• Title: Mathematics of novel materials from atomic to macroscopic scales
• Date: 01/13/2023
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall (Virtual Meeting Link)
• Contact: Sabrina M Walton (waltons3@msu.edu)

Materials' electronic properties arise from the complex dynamics of electrons flowing through the material. These dynamics are quantum mechanical and present many surprising phenomena without classical analogues. I will present analytical and numerical work clarifying these dynamics in three novel materials which have attracted intense theoretical and experimental attention in recent years: graphene, the first ``2D'' material, whose electronic properties can be captured by an effective Dirac equation, topological insulators, whose edges host surprising one-way edge currents, and twisted bilayer graphene, an aperiodic material whose properties can be captured by an effective system of Dirac equations with periodic coefficients. I will then present ongoing and future work focused on further clarifying the properties of twisted bilayer graphene, which was recently shown to superconduct when twisted to the ``magic'' twist angle 1 degree.

• Speaker: Charles Ouyang, UMass Amherst
• Title: Compactifications of Hitchin components
• Date: 01/18/2023
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall (Virtual Meeting Link)
• Contact: Sabrina M Walton (waltons3@msu.edu)

Hitchin components are natural generalizations of the classical Teichmüller space. In the setting of SL(3,R), the Hitchin component parameterizes the holonomies of convex real projective structures, which are related to hyperbolic affine spheres. By studying Blaschke metrics, which are Riemannian metrics associated to hyperbolic affine spheres, along with their limits, we obtain a compactification of the SL(3,R)-Hitchin component. We show the boundary objects are hybrid structures, which are in part flat metric and in part laminar. These hybrid objects are natural generalizations of measured laminations, which are the boundary objects in Thurston's compactification of Teichmüller space.

• Speaker: March Tian Boedihardjo, ETH Zurich
• Title: Freeness and matrices
• Date: 01/19/2023
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall (Virtual Meeting Link)
• Contact: Sabrina M Walton (waltons3@msu.edu)

I will begin by giving some background on Free Probability motivated by the freeness in free groups. I will then demonstrate how Free Probability can be used to obtain a sharp non-asymptotic random matrix estimate for general use. This talk will be concluded by a recent application of our result to the Matrix Spencer Conjecture. Joint work with Afonso Bandeira and Ramon van Handel.

• Speaker: Zhongshan An, University of Michigan
• Title:  Geometric boundary conditions for the Einstein equations and quasi-local mass
• Date: 01/23/2023
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall (Virtual Meeting Link)
• Contact: Sabrina M Walton (waltons3@msu.edu)

The Einstein equations are the most fundamental equations for spacetimes in general relativity. They relate the geometry (curvatures) of a spacetime with its physical property. When a spacetime has nonempty boundary, it is natural to ask what geometric boundary conditions are well-posed for the Einstein equations. The investigation of geometric boundary conditions both gives rise to interesting geometric PDE problems in differential geometry, and also plays an important role in the study of quasi-local mass for compact spacetimes in general relativity. In this talk, we will discuss geometric boundary conditions for the vacuum Einstein equations, from both the hyperbolic and elliptic aspects. Furthermore, we will talk about applications of these geometric boundary value problems in the construction of quasi-local mass.

• Speaker: Wlodzimierz Bryc, University of Cincinnati
• Title: Stationary measures of the Kardar-Parisi-Zhang equation and their limits
• Date: 01/25/2023
• Time: 3:00 PM - 3:50 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Konstantin Matetski (matetski@msu.edu)

I will overview recent results of [Corwin and Knizel, 2021] on the existence of stationary measures for the KPZ equation on an interval and [Barraquand and Le Doussal, 2022], [B.-Kuznetsov-Wang-Wesolowski, 2022] who found two different probabilistic descriptions of the stationary measures as a Markov process and as a measure with explicit Radon-Nikodym derivative with respect to the Brownian motion. The Markovian description leads to rigorous proofs of some of the limiting results claimed in [Barraquand and Le Doussal, 2022]. I shall discuss how the stationary measures of the KPZ equation on [0,L] behave at large scale as L goes to infinity which according to [Barraquand and Le Doussal, 2022] depending on the normalization, should correspond to stationary measures of a hypothetical KPZ fixed point on [0,1], to the stationary measure for the KPZ equation on the half-line, and to the stationary measure of a hypothetical KPZ fixed point on the half-line. The talk is based mostly on a joint work with Alexey Kuznetsov (ALEA 2022).

• Speaker: Katie Lewis, University of Washington
• Title: Disability Equity in Mathematics Education: Accessibility, Re-mediation, and CompensationAbstract
• Date: 01/25/2023
• Time: 3:30 PM - 5:00 PM
• Place: 252 EH (Virtual Meeting Link)
• Contact: Lisa Keller (kellerl@msu.edu)

Equity in mathematics education research has only recently begun to consider students with disabilities. In this talk, I focus specifically on students with mathematics disabilities – students who have a neurological difference in how their brains process numerical information. Prior research on mathematics disabilities (i.e., dyscalculia) has predominantly taken up a deficit frame, documenting the ways in which students with dyscalculia are deficient in terms of speed and accuracy. In my work, I argue that this deficit orientation is problematic, and I offer an alternative. I take up an explicitly anti-deficit framing and draw upon sociocultural learning theories and Disability Studies to orient my work. In this talk I use multiple case studies to explore ideas about accessibility, re-mediation, and compensation across a range of mathematical topics. This anti-deficit work provides an alternative vantage point to understand disability in mathematics education and suggests avenues to work towards equity. I close by considering ways that mathematics education equity research can be in service of and in partnership with the populations that we study. Zoom option: https://msu.zoom.us/j/95059549382 Passcode: PRIME

• Speaker: Theodore Voronov, University of Manchester
• Title:  From homotopy Lie brackets to thick morphisms of supermanifolds and non-linear functional-algebraic duality (NOTE UNUSUAL DAY)
• Date: 01/31/2023
• Time: 3:00 PM - 4:00 PM
• Place: C204A Wells Hall
• Contact: Michael Shapiro (mshapiro@msu.edu)

I will give a motivation for homotopy Lie brackets and the corresponding morphisms preserving brackets "up to homotopy" (more precisely, for L-infinity morphisms and L-infinity algebras), and show how to describe them using supergeometry. So, instead of a single Poisson or Lie bracket, there is a whole sequence of operations with n arguments, n=1,2,3,..., satisfying a linked infinite sequence of identities replacing the familiar Jacobi identity for a Lie bracket; and, instead of a morphism as a linear map mapping a bracket to a bracket, there is a sequence of multi-linear mappings mixing brackets with different numbers of arguments, and, in particular, the binary bracket is preserved only up to an (algebraic) homotopy. Geometrically, such a sequence of multi-linear mappings assembles into one non-linear map of supermanifolds. For the case of homotopy brackets of functions ("higher Poisson" or "homotopy Poisson" structure), this leads us to the question about a natural construction of non-linear mappings between algebras of smooth functions generalizing the usual pull-backs. I discovered such a construction some years ago. These are "thick morphisms" of (super)manifolds generalizing ordinary smooth maps. From a more general perspective, we arrive in this way at a non-linear analog of the classical functional-algebraic duality between spaces and algebras.

• Speaker: Igor Rapinchuk, MSU
• Title: Profinite groups and infinite Galois theory
• Date: 02/01/2023
• Time: 3:00 PM - 4:00 PM
• Place: C329 Wells Hall
• Contact: Igor Rapinchuk (rapinchu@msu.edu)

No abstract available.

• Speaker: James Murphy, Tufts University
• Title: ZOOM TALK (password the smallest prime > 100) - Towards Intrinsically Low-Dimensional Models in Wasserstein Space: Geometry, Statistics, and Learning
• Date: 02/02/2023
• Time: 2:30 PM - 3:30 PM
• Place: C304 Wells Hall
• Contact: Mark A Iwen ()

We consider the problems of efficient modeling and representation learning for probability distributions in Wasserstein space. We consider a general barycentric coding model in which data are represented as Wasserstein-2 (W2) barycenters of a set of fixed reference measures. Leveraging the Riemannian structure of W2-space, we develop a tractable optimization program to learn the barycentric coordinates when given access to the densities of the underlying measures. We provide a consistent statistical procedure for learning these coordinates when the measures are accessed only by i.i.d. samples. Our consistency results and algorithms exploit entropic regularization of the optimal transport problem, thereby allowing our barycentric modeling approach to scale efficiently. We also consider the problem of learning reference measures given observed data. Our regularized approach to dictionary learning in Wasserstein space addresses core problems of ill-posedness and in practice learns interpretable dictionary elements and coefficients useful for downstream tasks. Applications to image and natural language processing will be shown throughout the talk.

• Speaker: Amitesh Datta, Princeton University
• Title: Does the Jones polynomial of a knot detect the unknot? A novel approach via braid group representations and class numbers of number fields.
• Date: 02/07/2023
• Time: 3:30 PM - 4:30 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Peter Kilgore Johnson (john8251@msu.edu)

How good of an invariant is the Jones polynomial? The question is closely tied to studying braid group representations since the Jones polynomial can be defined as a (normalized) trace of a braid group representation. In this talk, I will present my work developing a new theory to precisely characterize the entries of classical braid group representations, which leads to a generic faithfulness result for the Burau representation of B_4 (the faithfulness is a longstanding question since the 1930s and is equivalent to whether B_4 is a group of 3 x 3 matrices). In forthcoming work, I use this theory to furthermore explicitly characterize the Jones polynomial of all 3-braid closures and generic 4-braid closures. I will also describe my work which uses the class numbers of quadratic number fields to show that the Jones polynomial detects the unknot for 3-braid links - this work also answers (in a strong form) a question of Vaughan Jones. I will discuss all of the relevant background from scratch and illustrate my techniques through simple examples.

• Speaker: Igor Rapinchuk, MSU
• Title: Profinite groups and infinite Galois theory
• Date: 02/08/2023
• Time: 3:00 PM - 4:00 PM
• Place: C329 Wells Hall
• Contact: Igor Rapinchuk (rapinchu@msu.edu)

No abstract available.

• Speaker: Alexander Volberg, MSU
• Title: Noncommutative Bohnenblust--Hille inequalities and application to learning the quantum observables
• Date: 02/08/2023
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall (Virtual Meeting Link)
• Contact: Willie Wai-Yeung Wong (wongwil2@msu.edu)

Bohnenblust--Hille inequalities for Boolean cubes have been proven with dimension-free constants that grow sub-exponentially in the degree (Defant—Mastylo—Peres). Such inequalities have found great applications in learning low degree Boolean functions (Eskenazis—Ivanisvili). Motivated by learning quantum observables, a quantum counterpart of Bohnenblust--Hille inequality for Boolean cubes was recently conjectured in Cambyse Rouz\’e, Melchior Wirth, and Haonan Zhang: ``Quantum Talagrand, KKL and Friedgut’s theorems and the learnability of quantum Boolean functions.” arXiv preprint, arXiv:2209.07279, 2022. Haonan Zhang and myself prove such noncommutative Bohnenblust--Hille inequalities with constants that are dimension-free and of exponential growth in the degree. As applications, we study learning problems of quantum observables. (Speaker will present remotely)

• Speaker: Peikai Qi, MSU
• Title: Banach space over Qp
• Date: 02/09/2023
• Time: 2:10 PM - 3:10 PM
• Place: C204A Wells Hall
• Contact: Peikai Qi (qipeikai@msu.edu)

No abstract available.

• Speaker: Fan Yang, Michigan State University
• Title: Foliations and transverse invariant measures from a dynamical systems point of view
• Date: 02/09/2023
• Time: 3:00 PM - 4:00 PM
• Place: C117 Wells Hall
• Contact: Fan Yang (yangfa31@msu.edu)

In this talk, we will discuss foliations and their transverse invariant measures (i.e., measures on cross-sections that are invariant under the holonomy maps) from a dynamical systems point of view. We will show that for a large family of diffeomorphisms, the unstable foliations admit families of transverse measures that are naturally related to certain probability measures invariant under the dynamics. Given an unstable leaf, we will consider a dynamically defined average that captures its intersection with cross-sections and prove that this averaging will converge exponentially fast to the transverse invariant measures. This is a joint work with Ures, Viana and J. Yang.

• Speaker: Keerthi Madapusi, Boston College
• Title: Derived cycles on Shimura varieties
• Date: 02/13/2023
• Time: 3:00 PM - 4:00 PM
• Place: C304 Wells Hall
• Contact: Georgios Pappas (pappasg@msu.edu)

I’ll explain how methods from derived algebraic geometry can be applied to give a uniform definition of special cycle classes on integral models of Shimura varieties of Hodge type, verifying some consequences of Kudla’s conjectures on the modularity of generating series of cycles on Shimura varieties of Hermitian type.

• Speaker: Frank Sottile, Texas A and M Univeristy
• Title: CANCELLED: A Murnaghan-Nakayama formula in quantum Schubert calculus
• Date: 02/15/2023
• Time: 3:00 PM - 3:50 PM
• Place: C517 Wells Hall
• Contact: Bruce E Sagan (bsagan@msu.edu)

The Murnaghan-Nakayama formula expresses the product of a Schur function with a Newton power sum in the basis of Schur functions. An important generalization of Schur functions are Schubert polynomials (both classical and quantum). For these, a Murnaghan-Nakayama formula is geometrically meaningful. In previous work with Morrison, we established a Murnaghan-Nakayama formula for Schubert polynomials and conjectured a quantum version. In this talk, I will discuss some background and then some recent work proving this quantum conjecture. This is joint work with Benedetti, Bergeron, Colmenarejo, and Saliola.

• Speaker: Patel Coupek, MSU
• Title: Property (Pr) and completed tensor product
• Date: 02/16/2023
• Time: 2:10 PM - 3:10 PM
• Place: C204A Wells Hall
• Contact: Peikai Qi (qipeikai@msu.edu)

No abstract available.

• Speaker: Ian Montague , Brandeis University
• Title: Seiberg-Witten Floer K-Theory and Cyclic Group Actions
• Date: 02/21/2023
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall
• Contact: Peter Kilgore Johnson (john8251@msu.edu)

Given a spin rational homology sphere equipped with a cyclic group action, I will introduce equivariant refinements of Manolescu's kappa invariant, derived from the equivariant K-theory of the Seiberg--Witten Floer spectrum. These invariants give rise to equivariant relative 10/8-ths type inequalities for equivariant spin cobordisms between rational homology spheres. I will explain how these inequalities provide applications to knot concordance, obstruct cyclic group actions on spin fillings, and give genus bounds for knots in punctured 4-manifolds. If time permits I will explain how these invariants are related to equivariant eta-invariants of the Dirac operator, and describe work-in-progress which provides explicit formulas for the $S^1$-equivariant eta-invariants on Seifert-fibered spaces.

• Speaker: Himchan Jeong, Department of Statistics and Actuarial Science at Simon Fraser University in Canada
• Title: Integration of Traditional and Telematics Data for Efficient Insurance Claims Predictions
• Date: 02/21/2023
• Time: 4:00 PM - 5:00 PM
• Place: C304 Wells Hall
• Contact: Amanda Nickols (nickols2@msu.edu)

Linked Abstract

While driver telematics has gained attention for risk classification in auto insurance, scarcity of observations with telematics features has been problematic, which could be owing to either privacy concern or adverse selection compared to the data points with traditional features. To handle this issue, we propose a data integration technique based on calibration weights. It is shown that the proposed technique can efficiently integrate the so-called traditional data and telematics data and also cope with possible adverse selection issues on the availability of telematics data. Our findings are supported by a simulation study and empirical analysis on a synthetic telematics dataset.

• Speaker: Hemanshu Kaul, Illinois Institute of Technology
• Title: Polynomials and DP-coloring of Graphs
• Date: 02/22/2023
• Time: 3:00 PM - 3:50 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Bruce E Sagan (bsagan@msu.edu)

DP-coloring (also called correspondence coloring) of graphs is a generalization of list coloring of graphs that has been widely studied in recent years after its introduction by Dvorak and Postle in 2015. Intuitively, DP-coloring is a variation on list coloring where each vertex in the graph still gets a list of colors, but identification of which colors are different can change from edge to edge. DP-coloring has been investigated from both the extremal (DP-chromatic number) and the enumerative (DP-color function) perspectives. In this talk, we will give an overview of questions arising with regard to when the DP-color function equals the chromatic polynomial (or any polynomial), and how the polynomial method, through the Combinatorial Nullstellensatz and the Alon-Furedi theorem for the number of non-zeros of a polynomial, can be applied to both extremal and enumerative problems in DP-coloring. Many open problems and conjectures will be presented.

• Speaker: Pavel Coupek, MSU
• Title: Property(Pr) and completed tensor product
• Date: 02/23/2023
• Time: 2:10 PM - 3:10 PM
• Place: C204A Wells Hall
• Contact: Peikai Qi (qipeikai@msu.edu)

No abstract available.

• Speaker: Zhenqi Wang, Michigan State University
• Title: Periodic data and smooth rigidity for hyperbolic automorphisms on torus
• Date: 02/23/2023
• Time: 3:00 PM - 4:00 PM
• Place: A126 Wells Hall
• Contact: Fan Yang (yangfa31@msu.edu)

We study the regularity of the conjugacy between an irreducible Anosov automorphism $A$ on torus and its small perturbation $f$. We say that $f$ and $A$ has the same periodic data if the derivatives of the return maps of $f$ and $A$ at the corresponding periodic points are conjugate. We demonstrate that if $f$ is a $C^s$ diffeomorphism with $s$ sufficiently large and has the same periodic data as $A$, then the conjugacy is $C^{s-\epsilon}$. This completes the characterization of the most elementary $C^1$-invariant for local smooth rigidity. We also give the first example of cocycle rigidity over fibers with conjugate periodic data.

• Speaker: Yuehaw Khoo, U Chicago
• Title: New approaches in simulation of transition paths
• Date: 02/24/2023
• Time: 4:00 PM - 5:00 PM
• Place: C304 Wells Hall
• Contact: Mark A Iwen (iwenmark@msu.edu)

Tensor method can be used for compressing high-dimensional functions arising from partial differential equations (PDE). In this talk, we focus on using these methods for the simulation of transition processes between metastable states in chemistry applications, for example in molecular dynamics. To this end, we also propose a novel generative modeling procedure using tensor-network without the use of any optimization.

• Speaker: Chamila Malagoda Gamage, MSU
• Title: Capacity Constrained Barycenter Problem and its Duality
• Date: 02/27/2023
• Time: 2:00 PM - 3:00 PM
• Place: C329 Wells Hall (Virtual Meeting Link)
• Contact: Craig Gross (grosscra@msu.edu)

The problem of finding a barycenter in the Wasserstein space is a nonlinear interpolation between several probability measures. In this talk we will discuss the notion of barycenters in the Wasserstein space under a capacity constraint on the mass transported and its dual formulation. $\\$ This will be a hybrid seminar and take place in C329 Wells Hall and via Zoom at https://msu.zoom.us/j/99426648081?pwd=ZEljM3BPUXg2MjVUMVM5TnlzK2NQZz09 .

• Speaker: Francis Bonahon, MSU
• Title: The quantum trace for skein algebras of surfaces (continued)
• Date: 02/27/2023
• Time: 4:00 PM - 4:30 PM
• Place: C204A Wells Hall
• Contact: Michael Shapiro (mshapiro@msu.edu)

I will discuss the technical details of the construction of the quantum trace homomorphism, going from the SL_2-skein algebra to the quantum Teichmüller space of Chekhov-Fock.

• Speaker: Ryan Stees, Indiana University
• Title: Milnor's invariants for knots and links in closed orientable 3-manifolds
• Date: 02/28/2023
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall
• Contact: Peter Kilgore Johnson (john8251@msu.edu)

Early in his career, John Milnor defined his seminal link invariants, now called Milnor's $\overline{\mu}$-invariants. They are topological concordance invariants of links in $S^3$, and much is known about them. However, until recently, few results have extended Milnor's work to links in other closed orientable 3-manifolds, and such extensions have done so for special classes of 3-manifolds or specific types of links. In this talk, I will discuss an extension of these invariants to concordance invariants of knots and links in any closed orientable 3-manifold, discuss some theorems that justify calling them ``Milnor's invariants", and study their properties.

• Speaker: Igor Rapinchuk, MSU
• Title: Profinite groups and infinite Galois theory
• Date: 03/01/2023
• Time: 3:00 PM - 4:00 PM
• Place: C304 Wells Hall
• Contact: Igor Rapinchuk (rapinchu@msu.edu)

No abstract available.

• Speaker: Zhongshan An, U. Mich
• Title: Quasi-local Hamiltonians for compact initial data sets
• Date: 03/01/2023
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall
• Contact: Willie Wai-Yeung Wong (wongwil2@msu.edu)

In general relativity, one of the most interesting ways to construct notions of energy is the method of Hamiltonian analysis. For asymptotically flat spacetimes, this approach yields the well-known ADM mass. In order to define quasi-local energy/mass for compact initial data sets, one would like to apply the Hamiltonian analysis of GR on compact spacetimes with time-like boundary. Traditionally, this has been done based on fixing the Dirichlet boundary condition of the spacetimes — one of the most well-known work along this thread is the Brown-York quasi-local mass. In this talk we will discuss in detail the relation between the study of initial boundary value problem for vacuum Einstein equations and the Hamiltonian analysis on compact spacetimes. Then we will construct a notion of quasi-local Hamiltonian (energy) based on a well-posed initial boundary value problem.

• Speaker: Yuejie Chi, Carnegie Mellon University
• Title: ZOOM TALK (password the smallest prime > 100) - The Non-asymptotics of Reinforcement Learning
• Date: 03/02/2023
• Time: 2:30 PM - 3:30 PM
• Place: C304 Wells Hall (Virtual Meeting Link)
• Contact: Mark A Iwen ()

Reinforcement learning (RL) is garnering significant interest in recent years due to its success in a wide variety of modern applications. However, theoretical understandings on the non-asymptotic sample and computational efficiencies of RL algorithms remain elusive, and are in imminent need to cope with the ever-increasing problem dimensions. In this talk, we discuss our recent progress that sheds light on understanding the efficacy of popular RL algorithms in finding the optimal policy in tabular Markov decision processes.

• Speaker: Katy Craig, UCSB
• Title: Optimal Transport in Machine Learning and Partial Differential Equations
• Date: 03/02/2023
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall
• Contact: Olga Turanova (turanova@msu.edu)

Over the past ten years, optimal transport has become a fundamental tool in statistics and machine learning: the 2-Wasserstein metric provides a new notion of distance for classifying distributions and a rich geometry for interpolating between them. In parallel, optimal transport has gained mathematical significance by providing new tools for studying stability and limiting behavior of partial differential equations, through the theory of 2-Wasserstein gradient flows. In fact, the success optimal transport in each of these contexts ultimately relies on the same fundamental property of the 2-Wasserstein metric: as originally discovered by Otto, the 2-Wasserstein metric is unique among classical optimal transport metrics in that it has a formal Riemannian structure. In my talk, I will introduce the theory of optimal transport, explain the special geometric structure of the 2-Wasserstein metric, and illustrate the essential role it plays in how optimal transport is used in both machine learning and partial differential equations.

• Speaker: Ivan Loseu, Yale University
• Title: Unipotent representations and quantization
• Date: 03/13/2023
• Time: 3:00 PM - 4:00 PM
• Place: C304 Wells Hall
• Contact: Igor Rapinchuk (rapinchu@msu.edu)

This talk is aimed more at the general audience. A fundamental question in the representation theory of semisimple Lie groups is to classify their irreducible unitary representations. A guiding principle here is the Orbit method, first discovered by Kirillov in the 60's for nilpotent Lie groups. It states that the irreducible unitary representations should be related to coadjoint orbits, i.e., the orbits of the Lie group action in the dual of its Lie algebra. Passing from orbits to representations could be thought of as a quantization problem and it is known that in this setting this is very difficult. For semisimple Lie groups it makes sense to speak about nilpotent orbits, and one could try to study representations that should correspond to these orbits via the yet undefined Orbit method. These representations are called unipotent: they are expected to be nicer than general ones, while one hopes to reduce the study of general representations to that of unipotent ones. I will concentrate on the case of complex Lie groups. I will explain how recent advances in the study of deformation quantizations of singular symplectic varieties allow to define unipotent representations and obtain some results about them. The talk is based on the joint work with Lucas Mason-Brown and Dmytro Matvieievskyi.

• Speaker: Peixue Wu, University of Illinois Urbana Champaign
• Title: Driving open quantum systems to a subspace: stability and large deviations.
• Date: 03/14/2023
• Time: 10:30 AM - 11:30 AM
• Place: C304 Wells Hall
• Contact: Jeffrey Hudson Schenker (schenke6@msu.edu)

Abstract: Preparation of entangled states via engineered open quantum systems is proven to be successful. In our work, we initiate a study of engineered open quantum systems which drive the states to a subspace. In other word, our system will be non-ergodic. We prove some stability results and large deviation phenomenon in this setting, under some symmetry condition on the Liouvillian. This is joint work with Marius Junge and Nicholas Laracuente.

• Speaker: John Baldwin, Boston College
• Title: Small Dehn surgery and SU(2)-representations
• Date: 03/14/2023
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall
• Contact: Matthew Edward Hedden (heddenma@msu.edu)

In their celebrated proof of the Property P Conjecture and its sequel, Kronheimer and Mrowka proved that the fundamental group of r-surgery on a nontrivial knot in the 3-sphere admits an irreducible SU(2)-representation whenever r is at most 2 in absolute value (which implies in particular that surgery on a nontrivial knot is never a homotopy 3-sphere). They asked whether the same is true for other small values of r -- in particular, for r = 3 and 4 -- noting that it's false for r = 5 since 5-surgery on the right-handed trefoil is a lens space. I'll describe recent work which answers their question in the affirmative. Our proof involves Floer homology and also the dynamics of surface homeomorphisms. All of this work is joint with Steven Sivek, and significant parts are also joint with Zhenkun Li and Fan Ye.

• Speaker: Igor Rapinchuk, MSU
• Title: Grothendieck's Galois Theory
• Date: 03/15/2023
• Time: 3:00 PM - 4:00 PM
• Place: C304 Wells Hall
• Contact: Igor Rapinchuk (rapinchu@msu.edu)

No abstract available.

• Speaker: Peikai Qi, MSU
• Title: Everywhere convergent formal series and Riesz’s theory II
• Date: 03/16/2023
• Time: 2:10 PM - 3:10 PM
• Place: C204A Wells Hall
• Contact: Peikai Qi (qipeikai@msu.edu)

No abstract available.

• Speaker: Fan Yang, MSU
• Title: A countable partition for singular flows
• Date: 03/16/2023
• Time: 3:00 PM - 4:00 PM
• Place: A126 Wells Hall
• Contact: Fan Yang (yangfa31@msu.edu)

In this talk we consider the entropy theory for singular vector fields with all singularities hyperbolic and non-degenerate. We will construct a countable partition with the property that the metric entropy for any ergodic invariant measure is finite. For singular star flows, we will show that this partition is generating. This is a joint work with Yi Shi and Jiagang Yang.

• Speaker: Menglun Wang, Food and Drug Administration
• Title: Regulatory Perspective on Artificial Intelligence Integrated Drug Development
• Date: 03/17/2023
• Time: 3:00 PM - 4:00 PM
• Place: C304 Wells Hall
• Contact: Mark A Iwen (iwenmark@msu.edu)

The application of Artificial Intelligence/Machine Learning (AI/ML) in drug development is expanding rapidly. AI/ML have the potential to improve the efficiency of drug development and advance precision medicine. However, there are unique challenges. The presentation will mainly focus on the topic of AI/ML applications in clinical trials, including the following parts: 1. The increasing numbers of submissions over years. 2. Hot therapeutic areas of AI/ML submissions. 3. Types of analysis and objectives in AI/ML in submissions. 4. Case examples. 5. Challenges and outlooks. In the end of the presentation, opportunities of FDA-ORISE fellowship will be introduced to senior PhD students.

• Speaker: Siddhi Krishna, Columbia University
• Title: RTG Seminar: Fibered knots: what, why and how
• Date: 03/20/2023
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall
• Contact: Peter Kilgore Johnson (john8251@msu.edu)

Fibered knots show up all over low-dimensional topology, as they provide a robust way to investigate interactions between phenomena of different dimensions. In this talk, I'll survey what they are, why you should care, and how to identify them. Then, as time permits, I'll also sketch a proof that positive braid knots are fibered. I will assume very little background for this talk -- all are welcome!

• Speaker: John Sheridan, Princeton University
• Title: Torelli theorems for certain Steiner bundles on projective space
• Date: 03/20/2023
• Time: 3:00 PM - 4:00 PM
• Place: C304 Wells Hall
• Contact: Francois Greer (greerfra@msu.edu)

A vector bundle on projective space is called "Steiner" if it can be recognized simply as the cokernel of a map given by a matrix of linear forms. Such maps arise from various geometric setups and one can ask: from the Steiner bundle, can we recover the geometric data used to construct it? In this talk, we will mention an interesting Torelli-type result of Dolgachev and Kapranov from 1993 that serves as an origin of this story, as well as other work that this inspired. We'll then indicate our contribution which amounts to analogous Torelli-type statements for certain tautological bundles on the very ample linear series of a polarized smooth projective variety. This is joint work with R. Lazarsfeld.

• Speaker: Patrick DeBonis, Purdue University
• Title: Properties of the Actions and von Neumann algebras of Thompson-Like Groups from Cloning Systems
• Date: 03/21/2023
• Time: 10:30 AM - 11:20 AM
• Place: C304 Wells Hall
• Contact: Brent Nelson (banelson@msu.edu)

Cloning systems are a method for generalizing Thompson's groups, for example $V_d$, that result in a family of groups, $\mathcal{T}_d(G_*)$, whose group von Neumann algebras have been intensely studied by Bashwinger and Zarmesky in recent years. We consider the group actions of a large class of $\mathcal{T}_d(G_*)$ and show they are stable, that is, $G \sim_{OE} G \times \mathbb{Z}.$ As a corollary, we answer Bashwinger and Zaremsky question about when $\mathcal{T}_d(G_*)$ is a McDuff Group in the sense of Deprez and Vaes. As a contrasting result, we show $L(V_d)$ is a prime II$_1$ factor. This is joint work with Rolando de Santiago and Krishnendu Khan.

• Speaker: Anup Poudel, Ohio State
• Title: A comparison between $SL_n$ spider categories.
• Date: 03/21/2023
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall
• Contact: Vijay B Higgins (higgi231@msu.edu)

In this talk, we will explore and make comparisons between various models that exist for spherical tensor categories associated to the category of representations of the quantum group $U_q(sl_n).$ In particular, we will discuss the combinatorial model of Murakami-Ohtsuki-Yamada (MOY), the n-valent ribbon model of Sikora and the trivalent spider category of Cautis-Kamnitzer-Morrison (CKM). We conclude by showing that the full subcategory of the spider category from CKM, whose objects are monoidally generated by the standard representation and its dual, is equivalent as a spherical braided category to Sikora's quotient category. This proves a conjecture of Le and Sikora and also answers a question from Morrison's Ph.D. thesis.

• Speaker: Swee Hong Chan, University of California, Los Angeles
• Title: Log-concavity, cross product conjectures, and FKG inequalities in order theory
• Date: 03/22/2023
• Time: 3:00 PM - 3:50 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Bruce E Sagan (bsagan@msu.edu)

Given a finite poset that is not completely ordered, is it always possible to find two elements x and y, such that the probability that x is less than y in the random linear extension of the poset, is bounded away from 0 and 1? Kahn-Saks gave an affirmative answer and showed that this probability falls between 3/11 (0.273) and 8/11 (0.727). The currently best known bound is 0.276 and 0.724 by Brightwell-Felsner-Trotter, and it is believed that the optimal bound should be 1/3 and 2/3, also known as the 1/3-2/3 Conjecture. Most notably, log-concave and cross product inequalities played the central role in deriving both bounds. In this talk we will discuss various generalizations of these results together with related open problems. This talk is joint work with Igor Pak and Greta Panova, and is intended for the general audience.

• Speaker: Patel Coupek, MSU
• Title: Rigid analytic geometry
• Date: 03/23/2023
• Time: 2:00 PM - 3:00 PM
• Place: C204A Wells Hall
• Contact: Peikai Qi (qipeikai@msu.edu)

No abstract available.

• Speaker: Leonid Rybnikov, HSE and Harvard University
• Title: Gaudin model and arc diagrams
• Date: 03/23/2023
• Time: 3:00 PM - 4:00 PM
• Place: C204A Wells Hall
• Contact: Michael Shapiro (mshapiro@msu.edu)

We define a natural, purely geometrical bijection between the set solutions of Bethe ansatz equations for the Gaudin magnet chain and the set of arc diagrams of Frenkel-Kirillov-Varchenko. The former set is in natural bijection with monodromy-free sl_2-opers (aka projective structures) on the projective line with the prescribed type of regular singularities at prescribed real marked points (according to Feigin and Frenkel), while the latter indexes the canonical base in a tensor product of U_q(sl_2)-modules (via the Schechtman-Varchenko isomorphism). Both sets carry a natural action of the cactus group, i.e., the fundamental group of the real Deligne-Mumford space of stable rational curves with marked points (by monodromy of solutions to Bethe ansatz equations on the former and by crystal commuters on the latter). We prove that our bijection is compatible with this cactus group action. This is joint work with Nikita Markarian.

• Speaker: Sung-Jin Oh, UC Berkeley
• Title: TBA
• Date: 03/29/2023
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall
• Contact: Willie Wai-Yeung Wong (wongwil2@msu.edu)

TBA

• Speaker: Dan Le, Purdue
• Title: TBA
• Date: 04/03/2023
• Time: 3:00 PM - 4:00 PM
• Place: C304 Wells Hall
• Contact: Preston Wake (wakepres@msu.edu)

No abstract available.

• Speaker: David Chan, Vanderbilt University
• Title: TBA
• Date: 04/04/2023
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall
• Contact: Peter Kilgore Johnson (john8251@msu.edu)

No abstract available.

• Speaker: Alexander Strang, University of Chicago
• Title: Strategic Feature Extraction and Low Dimensional Representation of Games - ZOOM TALK (password the smallest prime > 100)
• Date: 04/06/2023
• Time: 2:30 PM - 3:30 PM
• Place: C304 Wells Hall (Virtual Meeting Link)
• Contact: Mark A Iwen ()

Games are widely used to test reinforcement learning paradigms, to study competitive systems in economics and biology, and to model decision tasks. Empirical game theory studies games through observation of populations of interacting agents. We introduce a generic low-dimensional embedding scheme that maps agents into a latent space which enables visualization, interpolation, and strategic feature extraction. The embedding can be used for feature extraction since it represents a generic game as a combination of simpler low dimensional games. Through examples, we illustrate that these components may correspond to basic strategic trade-offs. We then show that the embedding scheme can represent all games with bounded payout, or whose payout has finite variance when two agents are sampled at random. We develop a formal approximation theory for the representation, study the stability of the embedding, provide sufficient sampling guidelines, and suggest regularizers which promote independence in the identified features.

• Speaker: Sam Gunningham, Montana State
• Title: RTG Seminar: TBA
• Date: 04/10/2023
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall
• Contact: Vijay B Higgins (higgi231@msu.edu)

TBA

• Speaker: Sam Gunningham, Montana State
• Title: TBA
• Date: 04/11/2023
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall
• Contact: Vijay B Higgins (higgi231@msu.edu)

TBA

• Speaker: Marina Meila , University of Washington
• Title: ZOOM TALK (password the smallest prime > 100) - TBA
• Date: 04/13/2023
• Time: 2:30 PM - 3:30 PM
• Place: C304 Wells Hall (Virtual Meeting Link)
• Contact: Mark A Iwen ()

No abstract available.

• Speaker: Shiwen Zhang, University of Massachusetts Lowell
• Title: TBA
• Date: 04/17/2023
• Time: 10:30 AM - 11:30 AM
• Place: C304 Wells Hall
• Contact: Jeffrey Hudson Schenker (schenke6@msu.edu)

No abstract available.

• Speaker: Pierre-Louis Blayac, University of Michigan
• Title: TBA
• Date: 04/18/2023
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall
• Contact: Vijay B Higgins (higgi231@msu.edu)

TBA

• Speaker: Robert Pollack, Boston University
• Title: TBA
• Date: 04/20/2023
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall
• Contact: Joseph Waldron (waldro51@msu.edu)

No abstract available.

• Speaker: Guosheng Fu, University of Notre Dame
• Title: High-order variational Lagrangian schemes for compressible fluids
• Date: 04/21/2023
• Time: 4:00 PM - 5:00 PM
• Place: C304 Wells Hall
• Contact: Mark A Iwen ()

We present a class of high-order variational Lagrangian schemes for compressible fluids using the tool of energetic variational approach (EnVarA). This is the first time that the EnVarA framework has been applied to non isothermal models where temperature effects are non-negligible. We illustrate the main idea using the classical ideal gas model, and construct variational Lagrangian schemes that are conservative and entropy stable using EnVarA. Efficient implicit time stepping is designed so that the time step size is not restricted by the sound speed and the model is robust in the low Mach number case. Ample numerical examples will be presented to show the good performance of the proposed schemes for problems including strong shocks, low Mach number flows and multimaterial flows. This is a joint work with Prof. Chun Liu from IIT.

• Speaker: Ján Mináč, University of Western Ontario
• Title: TBA
• Date: 04/24/2023
• Time: 3:00 PM - 4:00 PM
• Place: Online (virtual meeting)
• Contact: Preston Wake (wakepres@msu.edu)

No abstract available.

• Speaker: Sarah Petersen, University of Colorado, Boulder
• Title: TBA
• Date: 04/25/2023
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall
• Contact: Peter Kilgore Johnson (john8251@msu.edu)

No abstract available.

• Speaker: Yulong Xing, Ohio State University
• Title: TBA
• Date: 04/28/2023
• Time: 4:00 PM - 5:00 PM
• Place: C304 Wells Hall
• Contact: Mark A Iwen ()

TBA