• Speaker: Deanna Needell, UCLA
• Title: On the topic of topic modeling: enhancing machine learning approaches with topic features
• Date: 08/26/2021
• Time: 2:30 PM - 2:30 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Olga Turanova (turanova@msu.edu)

In this talk we touch on several problems in machine learning that can benefit from the use of topic modeling. We present topic modeling based approaches for online prediction problems, computer vision, text generation, and others. While these problems have classical machine learning approaches that work well, we show that by incorporating contextual information via topic features, we obtain enhanced and more realistic results. These classical methods include non-negative matrix and tensor factorization, generative adversarial networks, and even traditional epidemiological SIR models for prediction. In this talk we provide a brief overview of these problems and show how topic features can be used in these settings. We include supporting theoretical and experimental evidence that showcases the broad use of our approaches.

• Speaker: Joshua Ruiter, MSU
• Title: Organizing meeting for student algebra seminar
• Date: 09/03/2021
• Time: 3:00 PM - 4:00 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Joshua Ruiter (ruiterj2@msu.edu)

We'll discuss plans for the student algebra seminar this semester, e.g. choosing our first few speakers.

• Speaker: Emily Gunawan, Oklahoma University
• Title: Box-ball systems and Robinson-Schensted-Knuth tableaux
• Date: 09/08/2021
• Time: 3:00 PM - 3:50 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Bruce E Sagan (bsagan@msu.edu)

The Robinson-Schensted (RS) correspondence is a famous bijection between permutations and pairs (P,Q) of standard tableaux of the same shape, called the RS partition. The RS partition and its conjugate record certain permutation statistics called Greene’s theorem statistics. A box-ball system is a discrete dynamical system which can be thought of as a collection of time states. A permutation on n objects gives a box-ball system state by assigning its one-line notation to n consecutive boxes. After a finite number of steps, a box-ball system will reach a steady state. From any steady state, we can construct a tableau (not necessarily standard) called the soliton decomposition. The shape of the soliton decomposition is called the BBS partition. An exciting discovery (made in 2019 by Lewis, Lyu, Pylyavskyy, and Sen) is that the BBS partition and its conjugate record a localized version of Greene’s theorem statistics. We will discuss a few new results: (1) The Q tableau of a permutation completely determines the dynamics of the corresponding box-ball system. (2) The permutations whose BBS partitions are L-shaped have steady-state time at most 1. This large class of permutations include column reading words and noncrossing involutions. (3) If the soliton decomposition of a permutation is a standard tableau or if its BBS partition coincides with its RS partition, then its soliton decomposition and its P tableau are equal. (4) Finally, we study the permutations whose P tableaux and soliton decompositions coincide and refer to them as “good". These “good” permutations are closed under consecutive pattern containment. Furthermore, we conjecture that the “good” Q tableaux are counted by the Motzkin numbers. This talk is based on REU projects with Ben Drucker, Eli Garcia, Aubrey Rumbolt, Rose Silver (UConn Math REU 2020) and Marisa Cofie, Olivia Fugikawa, Madelyn Stewart, David Zeng (SUMRY 2021).

• Speaker: Anna Ma, University of California, Irvine
• Title: The Kaczmarz Algorithm: Greed, Randomness, and Tensors
• Date: 09/09/2021
• Time: 2:30 PM - 3:30 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Olga Turanova (turanova@msu.edu)

The Kaczmarz algorithm is an iterative method for solving linear systems of equations of the form Ax=y. Owing to its low memory footprint, the Kaczmarz algorithm has gained popularity for its practicality in applications to large-scale data, acting only on single rows of A at a time. In this talk, we discuss selecting rows of A randomly (Randomized Kaczmarz), selecting rows in a greedy fashion (Motzkin's Method), and selecting rows in a partially greedy fashion (Sampling Kaczmarz-Motzkin algorithm). Despite their variable computational costs, these algorithms have been proven to have the same theoretical upper bound on the convergence rate. Here we present an improvement upon previous known convergence bounds of the Sampling Kaczmarz-Motzkin algorithm, capturing the benefit of partially greedy selection schemes. Time permitting, we also will discuss an extension of the Kaczmarz algorithm to the setting where data takes on the form of a tensor and make connections between the new Tensor Kaczmarz algorithm and previously established algorithms. This presentation contains joint work with Jamie Haddock and Denali Molitor.

• Speaker: Matthew Lorentz, Michigan State University
• Title: Derivations and the Hochschild Cohomology of Uniform Roe Algebras, Part 1
• Date: 09/14/2021
• Time: 11:10 AM - 12:00 PM
• Place: C304 Wells Hall
• Contact: Brent Nelson (banelson@msu.edu)

In this series of talks we show a necessary and sufficient condition for the vanishing of the Hochschild cohomology of a uniform Roe algebra. Specifically, the n-dimensional continuous Hochschild cohomology vanishes if and only if every norm continuous n-linear map from the uniform Roe algebra to itself is equivalent to a weakly continuous n-linear map. In our first talk we will begin defining and discussing derivations as they are an important building block of Hochschild cohomology. Motivated by the needs of mathematical physics and the study of one-parameter automorphism groups, it is interesting to study whether all derivations are inner (i.e. given by the commutator bracket) for a particular C*-algebra. In the 1970s, a complete solution to this problem was obtained in the separable case via the work of several authors. For non-separable C*-algebras the picture is murkier. Our main goal in this talk is to give a new class of examples that only have inner derivations: uniform Roe algebras, which are separable only in the trivial finite dimensional case. Uniform Roe algebras were originally introduced for index-theoretic purposes but are now studied for their own sake as a bridge between C*-algebra theory and coarse geometry, as well as having interesting applications to single operator theory. Lastly, we will briefly explain how the uniform Roe algebra only having inner derivations is equivalent to the first Hochschild cohomology vanishing.

• Speaker: Oliver Pechenik, University of Waterloo
• Title: What is the degree of a Grothendieck polynomial?
• Date: 09/15/2021
• Time: 3:00 PM - 3:50 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Bruce E Sagan (bsagan@msu.edu)

Jenna Rajchgot observed that the Castelnuovo-Mumford regularity of matrix Schubert varieties is computed by the degrees of the corresponding Grothendieck polynomials. We give a formula for these degrees. Indeed, we compute the leading terms of the top degree pieces of Grothendieck polynomials and give a complete description of when two Grothendieck polynomials have the same top degree piece (up to scalars). Our formulas rely on some new facts about major index of permutations. (Joint work with David Speyer and Anna Weigandt.)

• Speaker: Yoonjoo Kim, Stony Brook University
• Title: The dual Lagrangian fibration of compact hyper-Kahler manifolds
• Date: 09/15/2021
• Time: 4:00 PM - 5:00 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Laure Flapan (flapanla@msu.edu)

A compact hyper-Kahler manifold is a higher dimensional generalization of a K3 surface. An elliptic fibration of a K3 surface correspondingly generalizes into the so-called Lagrangian fibration of a compact hyper-Kahler manifold. It is known that an elliptic fibration of a K3 surface is always "self-dual" in a certain sense. This turns out to be not the case for higher-dimensional Lagrangian fibrations. In this talk, we will explicitly construct the dual of Lagrangian fibrations of all currently known examples of compact hyper-Kahler manifolds. Passcode: MSUALG

• Speaker: Chen Zhang, Michigan State University
• Title: An introduction to Instanton Floer homology
• Date: 09/16/2021
• Time: 3:00 PM - 4:00 PM
• Place: C304 Wells Hall
• Contact: Danika Keala Van Niel ()

Instanton Floer homology is a three-manifold invariant connected to Donaldson theory introduced by Floer himself which turns out to be a powerful tool to study 3-manifolds. In today’s talk, I will first briefly review the (ordinary) Morse background and to introduce basic notions about connections. Then we will see the definition and basic properties of the Chern-Simons invariant, and a sketch of the construction of the instanton homology of a homology 3-sphere. Lastly, we will see some applications of the Instanton Floer homology and some other versions of Instanton Floer homology if time permits.

• Speaker: Matthew Lorentz, Michigan State University
• Title: Derivations and the Hochschild Cohomology of Uniform Roe Algebras, Part 2
• Date: 09/21/2021
• Time: 11:10 AM - 12:00 PM
• Place: C304 Wells Hall
• Contact: Brent Nelson (banelson@msu.edu)

In this series of talks we show a necessary and sufficient condition for the vanishing of the Hochschild cohomology of a uniform Roe algebra. Specifically, the n-dimensional continuous Hochschild cohomology vanishes if and only if every norm continuous n-linear map from the uniform Roe algebra to itself is equivalent to a weakly continuous n-linear map. In our second talk we will continue discussing derivations as they are an important building block of Hochschild cohomology. Motivated by the needs of mathematical physics and the study of one-parameter automorphism groups, it is interesting to study whether all derivations are inner (i.e. given by the commutator bracket) for a particular C*-algebra. In the 1970s, a complete solution to this problem was obtained in the separable case via the work of several authors. For non-separable C*-algebras the picture is murkier. Our main goal in this talk is to give a new class of examples that only have inner derivations: uniform Roe algebras, which are separable only in the trivial finite dimensional case. Uniform Roe algebras were originally introduced for index-theoretic purposes but are now studied for their own sake as a bridge between C*-algebra theory and coarse geometry, as well as having interesting applications to single operator theory. We will then briefly explain how the uniform Roe algebra only having inner derivations is equivalent to the first Hochschild cohomology vanishing. Lastly, we will discuss the Hochschild cohomology in higher dimensions.

• Speaker: Einar Steingrímsson, University of Strathclyde
• Title: Permutation statistics and moment sequences
• Date: 09/22/2021
• Time: 3:00 PM - 3:50 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Bruce E Sagan (bsagan@msu.edu)

Which combinatorial sequences correspond to moments of probability measures on the real line? We present a generating function, as a continued fraction, for a 14-parameter family of integer sequences and interpret these in terms of statistics on permutations and other combinatorial objects. Special cases include several classical and noncommutative probability laws, and a substantial subset of the orthogonalizing measures in the q-Askey scheme of orthogonal polynomials. This continued fraction captures a variety of combinatorial sequences. In particular, it characterizes the moment sequences associated to the numbers of permutations avoiding (classical and vincular) patterns of length three. This connection between pattern avoidance and classical and noncommutative probability is among several consequences that generalize and unify previous results in the literature. The fourteen combinatorial statistics further generalize to colored permutations, and, as an infinite family of statistics, to the k-arrangements: permutations with k-colored fixed points, introduced here. This is joint work with Natasha Blitvić, Lancaster University.

• Speaker: Joel Tropp, California Institute of Technology
• Title: Scalable semidefinite programming
• Date: 09/23/2021
• Time: 2:30 PM - 3:30 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Olga Turanova (turanova@msu.edu)

Semidefinite programming (SDP) is a powerful framework from convex optimization that has striking potential for data science applications. This talk describes a provably correct randomized algorithm for solving large, weakly constrained SDP problems by economizing on the storage and arithmetic costs. Numerical evidence shows that the method is effective for a range of applications, including relaxations of MaxCut, abstract phase retrieval, and quadratic assignment problems. Running on a laptop equivalent, the algorithm can handle SDP instances where the matrix variable has over 10^14 entries. This talk will highlight the ideas behind the algorithm in a streamlined setting. The insights include a careful problem formulation, design of a bespoke optimization method, and use of randomized matrix computations. Joint work with Alp Yurtsever, Olivier Fercoq, Madeleine Udell, and Volkan Cevher. Based on arXiv 1912.02949 (Scalable SDP, SIMODS 2021) and other papers (SketchyCGM in AISTATS 2017, Nyström sketch in NeurIPS 2017).

• Speaker: Jie Yang, MSU
• Title: An introduction to Fermat's Last Theorem
• Date: 09/24/2021
• Time: 3:00 PM - 4:00 PM
• Place:  (Virtual Meeting Link)
• Contact: Joshua Ruiter (ruiterj2@msu.edu)

In this talk, I will first introduce some motivations and historical works for FLT, then sketch modern ideas to attack this problem.

• Speaker: Peng Zhou, Berkeley
• Title: Homological Mirror Symmetry for A_n-type cluster varieties
• Date: 09/28/2021
• Time: 4:00 PM - 5:00 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Honghao Gao (gaohongh@msu.edu)

The A_n type cluster variety, denoted by X_n, is the affine scheme associated to the upper cluster algebra of the A_n quiver (of n unfrozen vertices and one frozen vertex). The dual of X_n is denoted as Y_n, and is isomorphic but not canonically to X_n. For example, the variety X_1 is given by the equation {x y = 1 + q} where x, y are in \C and q is in \C^*. We prove that the homological mirror symmetry (HMS) conjecture for X_n, Y_n: the coherent sheaf category of Coh(X_n) is equivalent to the wrapped Fukaya category WFuk(Y_n), generalizing the known case for n=1 and 2. This is based on a recent work of Gammage-Le on HMS for truncated cluster variety, by putting back the 'truncated' part. This is work in progress, and is joint with Linhui Shen and Zhe Sun.

• Speaker: Keshav Sutrave, Michigan State University
• Title: Connections: a meditation in three parts
• Date: 09/30/2021
• Time: 3:00 PM - 4:00 PM
• Place: C304 Wells Hall
• Contact: Danika Keala Van Niel ()

No abstract available.

• Speaker: Daniel López Neumann, Indiana University
• Title: Twisting quantum invariants via Fox calculus
• Date: 10/05/2021
• Time: 4:00 PM - 5:00 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Honghao Gao (gaohongh@msu.edu)

The Reshetikhin-Turaev invariants of a knot are topological invariants built through the representation theory of certain Hopf algebras, such as quantum groups. In the early 2000s, Turaev introduced a G-graded version of this construction that produces invariants of knots equipped with representations of their fundamental group into the group G. This talk will be about a special case of the G-graded construction. We will show that a graded Drinfeld double construction leads to Reshetikhin-Turaev invariants of knots which are “twisted” via the usual Fox calculus. This construction applies to a wide class of Hopf algebras, and in the case of an exterior algebra, it specializes to the twisted Reidemeister torsion of the complement of a knot.

• Speaker: Shiva Chidambaram, MIT
• Title: Abelian varieties with given p-torsion representation
• Date: 10/06/2021
• Time: 4:00 PM - 5:00 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Preston Wake (wakepres@msu.edu)

The Siegel modular variety $\mathcal{A}_2(3)$, which parametrizes abelian surfaces with full level $3$ structure, was recently shown to be rational over $\mathbf{Q}$ by Bruin and Nasserden. What can we say about its twist $\mathcal{A}_2(\rho)$ that parametrizes abelian surfaces $A$ whose $3$-torsion representation is isomorphic to a given representation $\rho$? While it is not rational in general, it is always unirational over $\mathbf{Q}$ showing that $\rho$ arises as the $3$-torsion representation of infinitely many abelian surfaces. We will discuss how we can obtain an explicit description of the universal object over such a unirational cover of $\mathcal{A}_2(\rho)$ using invariant theoretic ideas, thus parametrizing families of abelian surfaces with fixed $3$-torsion representation. Similar ideas work in a few other cases, showing in particular that whenever $(g,p) = (1,2)$, $(1,3)$, $(1,5)$, $(2,2)$, $(2,3)$ and $(3,2)$, the necessary condition of cyclotomic similitude is also sufficient for a mod $p$ Galois representation to arise from the $p$-torsion of a $g$-dimensional abelian variety.

• Speaker: Chris St. Clair, Michigan State University
• Title: Knots and Crosses: An Introduction to Grid Diagrams
• Date: 10/07/2021
• Time: 3:00 PM - 4:00 PM
• Place: C304 Wells Hall
• Contact: Danika Keala Van Niel (vannield@msu.edu)

Grid diagrams are a type of knot diagram which allow us to tackle problems in knot theory combinatorially. After introducing them we will explore some examples of their use in traditional knot invariants and hint at their place in understanding manifolds.

• Speaker: Zheng Xiao, MSU
• Title: CM-algebra and CM-types
• Date: 10/12/2021
• Time: 10:00 AM - 11:00 AM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Zheng Xiao (xiaozhen@msu.edu)

No abstract available.

• Speaker: Ka Ho Wong, Texas A&M University
• Title: Asymptotics of the relative Reshetikhin-Turaev invariants
• Date: 10/12/2021
• Time: 4:00 PM - 5:00 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Honghao Gao (gaohongh@msu.edu)

In a series of joint works with Tian Yang, we made a volume conjecture and an asymptotic expansion conjecture for the relative Reshetikhin-Turaev invariants for a closed oriented 3-manifold with a colored framed link inside it. We propose that their asymptotic behavior is related to the volume, the Chern-Simons invariant and the adjoint twisted Reidemeister torsion associated with the hyperbolic cone metric on the manifold with singular locus the link and cone angles determined by the coloring. In this talk, I will first discuss how our volume conjecture can be understood as an interpolation between the Kashaev-Murakami-Murakami volume conjecture of the colored Jones polynomials and the Chen-Yang volume conjecture of the Reshetikhin-Turaev invariants. Then I will describe how the adjoint twisted Reidemeister torsion shows up in the asymptotic expansion of the invariants. Especially, we find new explicit formulas for the adjoint twisted Reidemeister torsion for the fundamental shadow link complements and for the 3-manifold obtained by doing hyperbolic Dehn-filling on those link complements. Those formulas cover a very large class of hyperbolic 3-manifold and appear naturally in the asymptotic expansion of quantum invariants. Finally, I will summarize the recent progress of the asymptotic expansion conjecture of the fundamental shadow link pairs.

• Speaker: Honghao Gao, MSU
• Title: Rigidity in contact topology
• Date: 10/13/2021
• Time: 4:00 PM - 5:00 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Preston Wake (wakepres@msu.edu)

Legendrian links play a central role in low dimensional contact topology. A rigid theory uses invariants constructed via algebraic tools to distinguish Legendrian links. The most influential and powerful invariant is the Chekanov-Eliashberg differential graded algebra (Chekanov, Inventiones, 2002), which set apart the first non-classical Legendrian pair and stimulated many subsequent developments. The functor of points for the dga is a moduli space which acquires rich algebraic structures and can distinguish exact Lagrangian fillings. Such fillings are difficult to construct and to study, whereas the only known classification is the unique filling for Legendrian unknot (Eliashberg-Polterovich, Annals, 1996). For a long time, a folklore belief is that exact Lagrangian fillings are scarce and a Legendrian link can only have finitely many, based on the observation from limited examples. In this talk, I will report a joint work with Roger Casals, where we applied the techniques from contact topology, microlocal sheaf theory and cluster algebras, and successfully found the first examples of Legendrian links with infinitely many Lagrangian fillings, reversing the general belief.

• Speaker: Joseph Melby, Michigan State University
• Title: Quantum invariants, shadows, and volume
• Date: 10/14/2021
• Time: 3:00 PM - 4:00 PM
• Place: C304 Wells Hall
• Contact: Danika Keala Van Niel (vannield@msu.edu)

I will give some sort of introduction to a cool quantum 3-manifold invariant called the Turaev-Viro invariant and connect it to hyperbolic geometry through the Volume Conjecture. Then we will talk about shadows of 4-manifolds and how they can be used to prove the asymptotic additivity (we made this term up) of the Turaev-Viro invariants for a certain family of link complements.

• Speaker: Yingda Cheng, Michigan State University
• Title: AMS/AWM Joint Lecture: Computational Methods for Kinetic Transport Equations
• Date: 10/19/2021
• Time: 10:00 AM - 11:00 AM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Nicole Hayes (hayesni4@msu.edu)

Kinetic equations are mesoscale description of the transport of particles such as neutrons, photons, electrons, molecules as well as their interaction with a background medium or among themselves, and they have wide applications in many areas of mathematical physics, such as nuclear engineering, fusion device, optical tomography, rarefied gas dynamics, semiconductor device design, traffic network, swarming, etc. Because the equations are posed in the phase space (physical space plus velocity space), any grid-based method will run into computational bottleneck in real applications that are 3D in physical space and 3D in velocity space. This talk will survey three numerical solvers that we developed aiming at efficient computations of kinetic equations: the adaptive sparse grid discontinuous Galerkin method, the reduced basis method and the machine learning moment closure method. They aim at effective reduced order computations of such high dimensional equations. Benchmark numerical examples will be presented. Finally, I will introduce WINASc: Women in Numerical Analysis and Scientific Computing, which is part of the AWM advance network. Meeting Zoom password: awmams

• Speaker: Francis Bonahon, USC
• Title: Quantum invariants of surface diffeomorphisms and 3-dimensional hyperbolic geometry
• Date: 10/19/2021
• Time: 3:00 PM - 4:00 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Honghao Gao (gaohongh@msu.edu)

This talk is motivated by surprising connections between two very different approaches to 3-dimensional topology, namely quantum topology and hyperbolic geometry. The Kashaev-Murakami-Murakami Volume Conjecture connects the growth of colored Jones polynomials of a knot to the hyperbolic volume of its complement. More precisely, for each integer n, one evaluates the n-th Jones polynomial of the knot at the n-root of unity exp(2 pi i/n). The Volume Conjecture predicts that this sequence grows exponentially as n tends to infinity, with exponential growth rate related to the hyperbolic volume of the knot complement. I will discuss a closely related conjecture for diffeomorphisms of surfaces, based on the representation theory of the Kauffman bracket skein algebra of the surface, a quantum topology object closely related to the Jones polynomial of a knot. I will describe the mathematics underlying this conjecture, which involves a certain Frobenius principle in quantum algebra. I will also present experimental evidence for the conjecture, and describe partial results obtained in work in progress with Helen Wong and Tian Yang.

• Speaker: Yizheng Yuan, TU Berlin
• Title: Refined regularity of SLE
• Date: 10/20/2021
• Time: 4:00 PM - 5:00 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Dapeng Zhan (zhan@msu.edu)

SLE (Schramm-Loewner evolution) is a family of random planar curves that have some natural conformal invariance properties. They appear in a variety of planar models that exhibit conformal invariance in the scaling limit. In this talk I will introduce SLE and describe its regularity. Regarding the regularity, the optimal Hoelder and p-variation exponents are known from previous works. I will present a new approach that refines the results to the logarithmic scale. Zoom Passcode: A*****-P**

• Speaker: Bubacarr Bah, African Institute for Mathematical Sciences South Africa
• Title: Cancelled
• Date: 10/21/2021
• Time: 4:30 AM - 5:30 AM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Olga Turanova (turanova@msu.edu)

Cancelled

• Speaker: Jared Bronski, University of Illinois at Urbana–Champaign
• Title: Index Results for the Kuramoto model
• Date: 10/21/2021
• Time: 4:00 PM - 5:00 PM
• Place: C304 Wells Hall (Virtual Meeting Link)
• Contact: Brent Nelson (banelson@msu.edu)

The Kuramoto model is a system of ordinary differential equations modeling the nonlinear interactions of a group phase oscillators. The Kuramoto and related models have been proposed as models for phenomenon like the synchronized flashing of fireflies and the dynamics of circadian rhythms and jet lag. We consider a number of problems in the stability of synchronized solutions to this model. Many of these problems involve some sort of index result, counting the dimension of some unstable manifold. We employ a number of different techniques including geometric, topological, and graph-theoretic ideas. [Zoom passcode distributed upon request.]

• Speaker: Eoin Mackall, University of Maryland
• Title: Chow groups of Severi--Brauer varieties and biquaternion algebras
• Date: 10/27/2021
• Time: 4:00 PM - 5:00 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Igor Rapinchuk (rapinchu@msu.edu)

The Chow groups of Severi--Brauer varieties associated to biquaternion division algebras were originally computed by Karpenko in the mid nineties. The main difficulty in these computations is determining whether or not CH^2, the group of codimension 2 cycles, contains nontrivial torsion; for these varieties this group is torsion-free. Since his original proof, Karpenko has given two other proofs of this result. All of these proofs involve some clever use of K-theory to determine relations between some explicit cycles. In this talk, I'll discuss a new geometric method that one can use to determine these same relations. Passcode: MSUALG

• Speaker: Jared Able, Michigan State University
• Title: Murasugi sums and braids
• Date: 10/28/2021
• Time: 3:00 PM - 4:00 PM
• Place: C304 Wells Hall
• Contact: Danika Keala Van Niel ()

For your favorite knot K, there's a braid diagram for K with n strings, and there are (n-2) ways to split the braid along a string into a pair of braids. What pairs of braids can this splitting yield? To answer this question, we take a detour into the realm of the Murasugi sum, an operation on knots and their Seifert surfaces.

• Speaker: Mike Annunziata, Chuangtian Guan, Nick Rekuski, and Joshua Ruiter, MSU
• Title: Lightning talks
• Date: 10/29/2021
• Time: 3:00 PM - 4:00 PM
• Place:  (Virtual Meeting Link)
• Contact: Joshua Ruiter (ruiterj2@msu.edu)

Each of the four speakers will give a brief (10-12 minute) introduction to their research.

• Speaker: Xin Sun, University of Pennsylvania
• Title: Two types of integrability in Liouville quantum gravity
• Date: 11/03/2021
• Time: 4:00 PM - 5:00 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Dapeng Zhan (zhan@msu.edu)

There are two major resources of integrability in Liouville quantum gravity: conformal field theory and random planar maps decorated with statistical physics models. I will give a few examples of each type and explain how these two types are compatible. Recently, cutting and gluing random surfaces in LQG using SLE curves allows us to blend these two types of integrability to obtain exact results on Liouville conformal field theory, mating of trees, Schramm-Loewner evolution, and conformal loop ensemble. I will present a few results in this direction. Based on joint works with Morris Ang, Nina Holden and Guillaume Remy. Zoom passcode: A*****-P**

• Speaker: Weilin Li, New York University
• Title: TBA
• Date: 11/04/2021
• Time: 2:30 PM - 3:30 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Olga Turanova (turanova@msu.edu)

TBA

• Speaker: Mike Wong, Dartmouth
• Title: TBA
• Date: 11/09/2021
• Time: 4:00 PM - 5:00 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Honghao Gao (gaohongh@msu.edu)

TBA

• Speaker: Sjoerd Dirksen, Utrecht University
• Title: TBA
• Date: 11/11/2021
• Time: 4:30 AM - 5:30 AM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Olga Turanova (turanova@msu.edu)

TBA

• Speaker: Kevin Buzzard, Imperial College London
• Title: TBA
• Date: 11/11/2021
• Time: 4:00 PM - 5:00 PM
• Place: Online (virtual meeting)
• Contact: Francois Greer (greerfra@msu.edu)

No abstract available.

• Speaker: Katrina Honigs, Simon Fraser University
• Title: TBA
• Date: 11/17/2021
• Time: 4:00 PM - 5:00 PM
• Place: Online (virtual meeting)
• Contact: Igor Rapinchuk (rapinchu@msu.edu)

No abstract available.

• Speaker: TBD, Michigan State University
• Title: TBD
• Date: 11/18/2021
• Time: 3:00 PM - 4:00 PM
• Place: C304 Wells Hall
• Contact: Danika Keala Van Niel ()

No abstract available.

• Speaker: Vijay Higgins, MSU
• Title: TBA
• Date: 11/23/2021
• Time: 4:00 PM - 5:00 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Honghao Gao (gaohongh@msu.edu)

TBA

• Speaker: Jack Petok, Dartmouth
• Title: TBA
• Date: 12/01/2021
• Time: 4:00 PM - 5:00 PM
• Place: Online (virtual meeting)
• Contact: Laure Flapan (flapanla@msu.edu)

TBA

• Speaker: Umut Varolgunes, Edinburgh Hodge Institute
• Title: TBA
• Date: 12/07/2021
• Time: 11:00 AM - 11:50 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Honghao Gao (gaohongh@msu.edu)

TBA

• Speaker: Chloe Lewis, Michigan State University
• Title: Isotropy Separation Sequence Part 2
• Date: 12/09/2021
• Time: 3:00 PM - 4:00 PM
• Place: C304 Wells Hall
• Contact: Danika Keala Van Niel ()

No abstract available.