• Speaker: Linhui Shen, Michigan State University
• Title: Cluster structures on braid varieties
• Date: 10/31/2022
• Time: 12:30 PM - 1:30 PM
• Place: C304 Wells Hall
• Contact: Linhui Shen (shenlin1@msu.edu)

Let G be a complex simple group. Let $\beta$ be a positive braid whose Demazure product is the longest Weyl group element. The braid variety X($\beta$) generalizes many well known varieties, including positroid cells, open Richardson varieties, and double Bott-Samelson cells. We provide a concrete construction of the cluster structure on X($\beta$), using the weaves of Casals and Zaslow. We show that the coordinate ring of X($\beta$) is a cluster algebra, which confirms a conjecture of Leclerc as special cases. As an application, we show that X($\beta$) admits a natural Poisson structure and can be further quantized. If time permits, I will explain several of its applications on representation theory and knot theory, including its connections with the Kazhdan-Lusztig R-polynomials and a geometric interpretation of the Khovanov-Rozansky homology (following the work of Lam-Speyer and Galashin-Lam). This talk is based on joint work with Roger Casals, Eugene Gorsky, Mikhail Gorsky, Ian Le, and Jose Simental (arXiv:2207.11607).

• Speaker: Liping Yin, MSU
• Title: Exemplar-Based Texture Synthesis: Past and Current Approaches
• Date: 10/31/2022
• Time: 1:00 PM - 2:00 PM
• Place: C117 Wells Hall (Virtual Meeting Link)
• Contact: Craig Gross (grosscra@msu.edu)

In this talk, we will give an overview of exemplar-based texture synthesis. For the first part of the talk, we will discuss a classical approach via matching statistics of wavelet coefficients and its shortcomings. In the second part of the talk, we will discuss more recent work using statistics of deep convolutional neural networks for more realistic texture synthesis. $\\$ This will be a hybrid seminar and take place in C117 Wells Hall and via Zoom at https://msu.zoom.us/j/99426648081?pwd=ZEljM3BPUXg2MjVUMVM5TnlzK2NQZz09 .

• Speaker: Stephanie Chan, UMich
• Title: Integral points in families of elliptic curves
• Date: 10/31/2022
• Time: 3:00 PM - 4:00 PM
• Place: C304 Wells Hall
• Contact: Preston Wake (wakepres@msu.edu)

Given an elliptic curve over a number field with its Weierstrass model, we can study the integral points on the curve. Taking an infinite family of elliptic curves and imposing some ordering, we may ask how often a curve has an integral point and how many integral points there are on average. We expect that elliptic curves with any non-trivial integral points are generally very sparse. In certain quadratic and cubic twist families, we prove that almost all curves contain no nontrivial integral points.

• Speaker: Giorgio Young, University of Michigan
• Title: Ballistic Transport for Limit-periodic Schrödinger Operators in One Dimension
• Date: 11/01/2022
• Time: 11:00 AM - 12:00 PM
• Place: C304 Wells Hall
• Contact: Jeffrey Hudson Schenker (schenke6@msu.edu)

Abstract: In this talk, I will discuss some results on the transport properties of the class of limit-periodic continuum Schr\"odinger operators whose potentials are approximated exponentially quickly by a sequence of periodic functions. For such an operator $H$, and $X_H(t)$ the Heisenberg evolution of the position operator, we show the limit of $\frac{1}{t}X_H(t)\psi$ as $t\to\infty$ exists and is nonzero for $\psi\ne 0$ belonging to a dense subspace of initial states which are sufficiently regular and of suitably rapid decay. This is viewed as a particularly strong form of ballistic transport, and this is the first time it has been proven in a continuum almost periodic non-periodic setting. In particular, this statement implies that for the initial states considered, the second moment grows quadratically in time.

• Speaker: Ka Ho Wong, Texas A&M
• Title: On the 1-loop conjecture of fundamental shadow link complements
• Date: 11/01/2022
• Time: 3:00 PM - 4:00 PM
• Place: C304 Wells Hall (Virtual Meeting Link)
• Contact: Vijay B Higgins (higgi231@msu.edu)

The 1-loop conjecture proposed by Dimofte and Garoufalidis suggests a simple and explicit formula to compute the adjoint twisted Reidemeister torsion of hyperbolic 3-manifolds with toroidal boundary in terms of the shape parameters of any ideal triangulation of the manifolds. In this talk, I will give a brief overview of the conjecture and present our recent result on the 1-loop conjecture for fundamental shadow link complements. This is a joint work with Tushar Pandey.

• Speaker: Zhenqi Wang, Michigan State University
• Title: Local rigidity of higher rank partially hyperbolic algebraic actions
• Date: 11/01/2022
• Time: 3:00 PM - 4:00 PM
• Place: A136 Wells Hall
• Contact: Huyi Hu (hhu@msu.edu)

We give a complete solution to the local classification program of higher rank partially hyperbolic algebraic actions. We show $C^\infty$ local rigidity of abelian ergodic algebraic actions for symmetric space examples, twisted symmetric space examples and automorphisms on nilmanifolds. The method is a combination of representation theory, harmonic analysis and a KAM iteration. A striking feature of the method is no specific information from representation theory is needed. It is the first time local rigidity for non-accessible partially hyperbolic actions has ever been obtained other than torus examples. Even for Anosov actions, our results are new: it is the first time twisted spaces with non-abelian nilradical have been treated in the literature.

• Speaker: James Propp, University of Massachusetts, Lowell
• Title: A Pentagonal Number Theorem for Tribone Tilings
• Date: 11/02/2022
• Time: 3:00 PM - 3:50 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Bruce E Sagan (bsagan@msu.edu)

Conway and Lagarias used combinatorial group theory to show that certain roughly triangular regions in the hexagonal grid cannot be tiled by the shapes Thurston later dubbed tribones. The ideas of Conway, Lagarias, and Thurston have found many applications in the study of tilings in the plane. Today I'll discuss a two-parameter family of roughly hexagonal regions in the hexagonal grid I call benzels. A variant of Gauss’ shoelace formula allows one to compute the signed area (aka algebraic area) enclosed by a closed polygonal path, and by “twisting” the formula one can compute the values of the Conway-Lagarias invariant for all benzels. It emerges that the (a,b)-benzel can be tiled by tribones if and only if a and b are the paired pentagonal numbers k(3k+1)/2, k(3k-1)/2. This is joint work with Jesse Kim.

• Speaker: Shlomo Levental, MSU
• Title: FORMULAS FOR THE DIVERGENCE OPERATOR IN ISONORMAL GAUSSIAN SPACE
• Date: 11/02/2022
• Time: 3:00 PM - 3:50 PM
• Place: C405 Wells Hall
• Contact: Dapeng Zhan (zhan@msu.edu)

In this joint paper with P. Vellaisamy, we first derive some explicit formulas for the computation of the n-th order divergence operator in Malliavin calculus in the one-dimensional case. We then extend these results to the case of isonormal Gaussian space. Our results generalize some of the known results for the divergence operator. Our approach in deriving the formulas is new and simple.

• Speaker: Christopher Potvin, MSU
• Title: Escapism in Math: The Mathematics of Escapes
• Date: 11/02/2022
• Time: 5:00 PM - 6:00 PM
• Place: C517 Wells Hall
• Contact: Chris David Stclair (stclai22@msu.edu)

Abstract: There comes a time in every mathematician's life when they are detained by an evil dictator or warden with a soft spot for riddles. Fortunately for us, these riddles are often rooted in simple mathematics. This talk will prepare you for that inevitable occurrence by going over the mathematics involved in several prominent riddles. Along the way, we'll pick up some tricks of the trade that you can use when facing a logic puzzle to make an escape of your own.

• 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: Dr. Harvey Stein, Senior VP, Labs Group, Two Sigma
• Title: Model Invariants and Functional Regularization
• Date: 11/03/2022
• Time: 2:30 PM - 3:30 PM
• Place: C304 Wells Hall

Linked Abstract

When modeling data, we would like to know that our models are extracting facts about the data itself, and not about something arbitrary, like the order of the factors used in the model-ing. Formally speaking, this means we want the model to be invariant with respect to certain transformations. Here we look at different models and the nature of their invariants. We find that regression, MLE and Bayesian estimation all are invariant with respect to linear transformations, whereas regularized regressions have a far more limited set of invariants. As a result, regularized regressions produce results that are less about the data itself and more about how it is parameterized. To correct this, we propose an alternative expression of regularization which we call functional regularization. Ridge regression and lasso can be recast in terms of functional regularization, as can Bayesian estimation. But functional regularization preserves model invariance, whereas ridge and lasso do not. It is also more flexible, easier to understand, and can even be applied to non-parametric models.

• Speaker: Keping Huang, MSU
• Title: Eigenalgebras over DVR, continued
• Date: 11/03/2022
• Time: 3:00 PM - 4:00 PM
• Place: C204A Wells Hall
• Contact: Keping Huang (huangk23@msu.edu)

No abstract available.

• Speaker: Tasho Kaletha, University of Michigan
• Title: Representations of reductive groups over local fields
• Date: 11/03/2022
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall
• Contact: Joseph Waldron (waldro51@msu.edu)

The pioneering work of Langlands has established the theory of reductive algebraic groups and their representations as a key part of modern number theory. I will survey classical and modern results in the representation theory of reductive groups over local fields (the fields of real, complex, or p-adic numbers, or of Laurent series over finite fields) and discuss how they relate to Langlands' ideas, as well as to the various reflections of the basic mathematical idea of symmetry in arithmetic and geometry.

• Speaker: Dr. Harvey Stein, Senior VP, Labs Group, Two Sigma
• Title: Current Issues in Financial Risk Management
• Date: 11/03/2022
• Time: 6:00 PM - 8:00 PM
• Place: 3202 STEM

Linked Abstract

Innovations and changes in financial markets do not come without risks. We will discuss some recent innovations and changes and discuss their implications for risk management, such as the risks associated with cryptocurrency, and the impact on finance of machine learning.