Talk_id  Date  Speaker  Title 
22730

Wednesday 1/8 4:10 PM

François Greer, Stony Brook University

Enumerative geometry and modular forms
 François Greer, Stony Brook University
 Enumerative geometry and modular forms
 01/08/2020
 4:10 PM  5:00 PM
 C304 Wells Hall
GromovWitten invariants are counts of holomorphic curves on a smooth projective variety X. When assembled into a generating series, these invariants often produce special functions. A folklore conjecture predicts that when X admits an elliptic fibration, the GromovWitten generating functions are quasimodular forms. I will discuss recent progress on this conjecture and a program to prove it in general.

22733

Thursday 1/9 4:10 PM

Daxin Xu, California Institute of Technology

Exponential sums, differential equations and geometric Langlands correspondence
 Daxin Xu, California Institute of Technology
 Exponential sums, differential equations and geometric Langlands correspondence
 01/09/2020
 4:10 PM  5:00 PM
 C304 Wells Hall
The understanding of various exponential sums plays a central role in the study of number theory. I will first review the relationship between the Kloosterman sums and the classical Bessel differential equation. Recently, there are two generalizations of this story (corresponding to GL_2case) for arbitrary reductive groups using ideas from the geometric Langlands program, due to FrenkelGross, HeinlothNgôYun. In the end, I will discuss my joint work with Xinwen Zhu where we unify previous two constructions from the padic aspect and identify the exponential sums associated to different groups as conjectured by HeinlothNgôYun.

22732

Friday 1/10 4:10 PM

Tetiana Shcherbyna, Princeton University

Random matrix theory and supersymmetry techniques
 Tetiana Shcherbyna, Princeton University
 Random matrix theory and supersymmetry techniques
 01/10/2020
 4:10 PM  5:00 PM
 C304 Wells Hall
Starting from the works of Erdos, Yau, Schlein with coauthors, the significant
progress in understanding the universal behavior of many random graph and random matrix
models were achieved. However for the random matrices with a spacial structure our
understanding is still very limited. In this talk I am going to overview applications of another
approach to the study of the local eigenvalues statistics in random matrix theory based on
socalled supersymmetry techniques (SUSY) . SUSY approach is based on the representation
of the determinant as an integral over the Grassmann (anticommuting) variables.
Combining this representation with the representation of an inverse determinant as an integral
over the Gaussian complex field, SUSY allows to obtain an integral representation for the main
spectral characteristics of random matrices such as limiting density, correlation functions,
the resolvent's elements, etc. This method is widely (and successfully) used in the physics
literature and is potentially very powerful but the rigorous control of the integral representations,
which can be obtained by this method, is quite
difficult, and it requires powerful analytic and statistical mechanics tools.
In this talk we will discuss some recent progress in application of SUSY to the analysis
of local spectral characteristics of the prominent ensemble of random band matrices,
i.e. random matrices whose entries become negligible if their distance from the main diagonal
exceeds a certain parameter called the band width.

22736

Monday 1/13 4:10 PM

Oliver Pechenik, University of Michigan

$K$theoretic Schubert calculus
 Oliver Pechenik, University of Michigan
 $K$theoretic Schubert calculus
 01/13/2020
 4:10 PM  5:00 PM
 C304 Wells Hall
Schubert calculus studies the algebraic geometry and combinatorics of matrix factorizations. I will discuss recent developments in $K$theoretic Schubert calculus, and their connections to problems in combinatorics and representation theory.

20713

Wednesday 1/15 3:00 PM

Eli Matzri, BarIlan University

The vanishing conjecture for Massey products in Galois cohomology
 Eli Matzri, BarIlan University
 The vanishing conjecture for Massey products in Galois cohomology
 01/15/2020
 3:00 PM  3:50 PM
 C304 Wells Hall
In this talk I will explain what Massey products are and focus on the vanishing conjecture due to Minac and Tan. I will survey the known results and the different methods used to obtain them, focusing on triple Massey products.

22737

Wednesday 1/15 4:10 PM

Nathan Dowlin, Columbia University

Quantum and symplectic invariants in lowdimensional topology.
 Nathan Dowlin, Columbia University
 Quantum and symplectic invariants in lowdimensional topology.
 01/15/2020
 4:10 PM  5:00 PM
 C304 Wells Hall
Khovanov homology and knot Floer homology are two powerful knot invariants developed around two decades ago. Knot Floer homology is defined using symplectic techniques, while Khovanov homology has its roots in the representation theory of quantum groups. Despite these differences, they seem to have many structural similarities. A wellknown conjecture of Rasmussen from 2005 states that for any knot K, there is a spectral sequence from the Khovanov homology of K to the knot Floer homology of K. Using a new family of invariants defined using both quantum and symplectic techniques, I will give a proof of this conjecture and describe some topological applications.

22735

Friday 1/17 4:10 PM

Joseph Waldron, Princeton University

Birational geometry in positive characteristic
 Joseph Waldron, Princeton University
 Birational geometry in positive characteristic
 01/17/2020
 4:10 PM  5:00 PM
 C304 Wells Hall
Birational geometry aims to classify algebraic varieties by breaking them down into elementary building blocks, which may then be studied in more detail. This is conjecturally accomplished via a process called the log minimal model program. The program is now very well developed for varieties over fields of characteristic zero, but many of the most important proof techniques break down outside that situation. In this talk, I will give an overview of the main aims of the log minimal model program, and then focus on recent progress in the classification of varieties defined over fields of positive characteristic.

22744

Tuesday 1/21 4:10 PM

Laure Flapan, Massachusetts Institute of Technology

Modularity and the Hodge/Tate conjectures for some selfproducts
 Laure Flapan, Massachusetts Institute of Technology
 Modularity and the Hodge/Tate conjectures for some selfproducts
 01/21/2020
 4:10 PM  5:00 PM
 C304 Wells Hall
If X is a smooth projective variety over a number field, the Hodge and Tate conjectures describe how information about the subvarieties of X is encoded in the cohomology of X. We explore the role that certain automorphic representations, called algebraic Hecke characters, can play in understanding which cohomology classes of X arise from subvarieties. We use this to deduce the Hodge and Tate conjectures for certain selfproducts of varieties, including some selfproducts of K3 surfaces. This is joint work with J. Lang.

22747

Wednesday 1/22 4:00 PM

Brandon Bavier

An Introduction to Hyperbolic Knot Theory
 Brandon Bavier
 An Introduction to Hyperbolic Knot Theory
 01/22/2020
 4:00 PM  5:00 PM
 C517 Wells Hall
When studying knots, it is common to look at their complement to find invariants of the knot. One way to do this is to put a geometric structure on the complement, and look at common geometric invariants, such as volume. In this introductory level talk, we will cover the basics of hyperbolic geometry, and how we can use its properties to find invariants of hyperbolic knots, knots whose complement is hyperbolic.

22738

Friday 1/24 4:10 PM

PeiKen Hung, Massachusetts Institute of Technology

Einstein's gravity and stability of black holes
 PeiKen Hung, Massachusetts Institute of Technology
 Einstein's gravity and stability of black holes
 01/24/2020
 4:10 PM  5:00 PM
 C304 Wells Hall
Though Einstein's fundamental theory of general relativity has already celebrated its one hundredth birthday, there are still many outstanding unsolved problems. The Kerr stability conjecture is one of the most important open problems, which posits that the Kerr metrics are stable solutions of the vacuum Einstein equation. Over the past decade, there have been huge advances towards this conjecture based on the study of wave equations in black hole spacetimes and structures in the Einstein equation. In this talk, I will discuss the recent progress in the stability problems with special focus on the wave gauge.

22743

Monday 1/27 4:10 PM

Felix Janda, IAS, Princeton University

Enumerative geometry: old and new.
 Felix Janda, IAS, Princeton University
 Enumerative geometry: old and new.
 01/27/2020
 4:10 PM  5:00 PM
 C304 Wells Hall
For as long as people have studied geometry, they have counted geometric objects. For example, Euclid's Elements starts with the postulate that there is exactly one line passing through two distinct points in the plane. Since then, the kinds of counting problems we are able to pose and to answer has grown. Today enumerative geometry is a rich subject with connections to many fields, including combinatorics, physics, representation theory, number theory and integrable systems.
In this talk, I will show how to solve several classical counting questions. I will then move to a more modern problem with roots in string theory which has been the subject of intense study for the last three decades: The computation of the GromovWitten invariants of the quintic threefold, an example of a CalabiYau manifold

21726

Wednesday 1/29 3:00 PM

Tony Feng, MIT

The Spectral Hecke Algebra
 Tony Feng, MIT
 The Spectral Hecke Algebra
 01/29/2020
 3:00 PM  4:00 PM
 C304 Wells Hall
We introduce a derived enhancement of local Galois deformation rings that we call the “spectral Hecke algebra”, in analogy to a construction in the Geometric Langlands program. This is a Hecke algebra that acts on the spectral side of the Langlands correspondence, i.e. on moduli spaces of Galois representations. We verify the simplest form of derived localglobal compatibility between the action of the spectral Hecke algebra on the derived Galois deformation ring of GalatiusVenkatesh, and the action of Venkatesh’s derived Hecke algebra on the cohomology of arithmetic groups.

22755

Wednesday 1/29 4:10 PM

Arman Tavakoli

6 problems in topology and 1 problem in applied geometry with elementary solutions
 Arman Tavakoli
 6 problems in topology and 1 problem in applied geometry with elementary solutions
 01/29/2020
 4:10 PM  5:00 PM
 C517 Wells Hall
I will talk about 6 famous problems in topology and 1 problem from applied geometry that have elementary solutions.
0.Warm up, 1. BorsukUlam, 2. Degree of a map, 3. Hairy ball theorem, 4. Nonorientability of RP2, 5. Maps of arbitrary degree, 6. Alexander's trick, and 7. Reach of a manifold and its estimation.

22748

Thursday 1/30 12:00 PM

Willie Wong, MSU; Andrew Krause, MSU

Deploying ComputerBased Lab Activities in Mainstream Calculus II
 Willie Wong, MSU; Andrew Krause, MSU
 Deploying ComputerBased Lab Activities in Mainstream Calculus II
 01/30/2020
 12:00 PM  1:00 PM
 133F Erick
The course MTH133 is the second semester in our main calculus sequence, and focuses on integral calculus, sequences and series, and the calculus of planar curves. The majority of enrolled students (approximately 2000 per year) have declared interest in engineering and are in their first three semesters at MSU; the remainder are primarily students from the College of Natural Sciences. Over the past 4 years, we developed and piloted the lab activities, with an eye towards deploying them at scale. This year, the labs are in use across all MTH133 sections. We will begin our presentation with a detailed demonstration of one of the labs, mainly to showcase the student experience. We will follow this up with a discussion of our philosophy toward the "place" the labs occupy in calculus instruction, specifically in relation to the extant curriculum. We will also describe ongoing research aimed at understanding students' learning experiences with the labs, as well as some of our findings.

22752

Thursday 1/30 1:00 PM

Misha Shapiro, MSU

Generalized cluster structures in the space of periodic staircase matrices.
 Misha Shapiro, MSU
 Generalized cluster structures in the space of periodic staircase matrices.
 01/30/2020
 1:00 PM  2:00 PM
 C204A Wells Hall
It is well known that cluster relations in $GL_n$ are often modeled on determinantal identities, such as short Plucker relations, DesnanotJacobi identitites and their generalizations. We present a similar construction of determinantal identities in the space of periodic infinite matrices of special (staircase) form and discuss its application to generalized cluster structures in $GL_n$ compatible with a certain subclass of BelavinDrinfeld PoissonLie brackets, in the Drinfeld double of $GL_n$, and in the space of periodic difference operators. This is a joint work with M.Gekhtman and A.Vainshtein.

23769

Wednesday 2/5 3:00 PM

Aklilu Zeleke, MSU

New and Old Combinatorial Identities Part II
 Aklilu Zeleke, MSU
 New and Old Combinatorial Identities Part II
 02/05/2020
 3:00 PM  3:50 PM
 C517 Wells Hall
Using a probabilistic approach, we derive some interesting identities involving beta functions. These results generalize certain wellknown combinatorial identities involving binomial coefficients and gamma functions.

22767

Wednesday 2/5 4:10 PM

Tristan Wellsfilbert

Fast Introduction to Curvature in Topology
 Tristan Wellsfilbert
 Fast Introduction to Curvature in Topology
 02/05/2020
 4:10 PM  5:00 PM
 C517 Wells Hall
I will introduce the basics of Riemannian geometry. First, I will define a Reimannian metric. Then I will define a connection and explain the construction of the LeviCivita connection. Finally, we will define curvature and state some theorems about what the curvature of a manifold says about its topology.

22753

Thursday 2/6 1:00 PM

Matt Mills, MSU

A geometric description of cvectors
 Matt Mills, MSU
 A geometric description of cvectors
 02/06/2020
 1:00 PM  2:00 PM
 C204A Wells Hall
No abstract available.

21728

Thursday 2/6 2:30 PM

Kevin Sackel, Stony Brook

Paint by Numbers... via Contact Geometry
 Kevin Sackel, Stony Brook
 Paint by Numbers... via Contact Geometry
 02/06/2020
 2:30 PM  3:30 PM
 C304 Wells Hall
Consider a trivalent planar graph embedded on the sphere. One can ask how many ways are there to color the faces of such a graph with $k$ colors so that no two adjacent faces are given the same color. Surprisingly, if $k$ is one more than a power of a prime, then one can write down a set of equations and simply count the number of solutions over a finite field to obtain essentially the same answer. This combinatorial correspondence is completely explicit and is a verification of the slogan "augmentations are sheaves" for certain Legendrian surfaces constructed by Treumann and Zaslow in standard contact $\mathbb{R}^5$. In this talk we will describe the contactgeometric framework for this result as well as the explicit combinatorial correspondence. If the speaker is daring enough, we may further speculate about the case of noncommutative augmentations and higher rank sheaves for these Legendrian surfaces, which we expect to go through a higherdimensional generalization of the cross ratio for four elements of the Grassmannian $Gr(n,2n;F)$ for a given field $F$.

20687

Friday 2/7 4:10 PM


The talk this week has been cancelled

 The talk this week has been cancelled
 02/07/2020
 4:10 PM  5:00 PM

No abstract available.

23768

Monday 2/10 4:00 PM

Igor Rapinchuk, MSU

Good reduction in arithmetic geometry and the theory of algebraic groups
 Igor Rapinchuk, MSU
 Good reduction in arithmetic geometry and the theory of algebraic groups
 02/10/2020
 4:00 PM  5:00 PM
 C304 Wells Hall
Techniques involving reduction are commonly used in algebra, number theory, and arithmetic geometry. For example, to show that a polynomial equation with integer coefficients has no integral solutions, one may reduce it modulo p for a suitable prime p and try to argue that the existence of an integral solution would lead to a contradiction. In the first part of the talk, I will give a brief overview of the notion of good reduction in the context of the theory of elliptic curves. In particular, I will indicate how these ideas are connected to some of the most significant results of arithmetic geometry that were obtained in the 20th century. I will then discuss good reduction of linear algebraic groups, a direction that has seen a number of exciting developments over the last few years. To conclude the talk, I will formulate some finiteness conjectures for groups having good reduction that are central to my current research.

22749

Monday 2/10 4:10 PM

Rachael Lund

Administrative load for 101/102/103  walking the line between strictness and flexibility
 Rachael Lund
 Administrative load for 101/102/103  walking the line between strictness and flexibility
 02/10/2020
 4:10 PM  5:00 PM
 C109 Wells Hall
Strategies for dealing with RCPD, emails, missed classes, makeups

22739

Wednesday 2/12 3:00 PM

Yuan Liu, University of Michigan

Heuristics on the distribution of Galois groups of unramified extensions
 Yuan Liu, University of Michigan
 Heuristics on the distribution of Galois groups of unramified extensions
 02/12/2020
 3:00 PM  4:00 PM
 C304 Wells Hall
We will first review several heuristics on the distributions of Galois groups of unramified extensions of global fields, which include the CohenLenstra Heuristics regarding the class groups of quadratic fields and the BostonBushHajir Heuristics regarding the pclass tower groups of quadratic fields. We will then discuss how these heuristics relate to reasonable random group models, and then explain a new conjecture on the distribution of the Galois groups of the maximal unramified extensions of Galois Γ number fields or function fields for a large family of finite groups Γ. Finally, we will give theorems in the function field case to support this new conjecture. This work is joint with Melanie Matchett Wood and David ZureickBrown.

23773

Wednesday 2/12 4:10 PM

ShihFang Yeh

Introduction to Schwarzschild spacetime and black hole
 ShihFang Yeh
 Introduction to Schwarzschild spacetime and black hole
 02/12/2020
 4:10 PM  5:00 PM
 C517 Wells Hall
I would give a brief introduction of Einstein's fields equation and the characteristics of Schwarzschild spacetime first. Then I would investigate the properties of Schwarzschild spacetime by analyzing the extension, the black hole region, and the behavior of geodesics in the extended spacetime. If time permits, I would also introduce the criteria for completeness or incompleteness of spacetime.

22758

Thursday 2/13 1:00 PM

Semen Artamonov, Berkeley

Poisson Geometry of Noncommutative Cluster Algebras
 Semen Artamonov, Berkeley
 Poisson Geometry of Noncommutative Cluster Algebras
 02/13/2020
 1:00 PM  2:00 PM
 C204A Wells Hall
In my talk I will consider noncommutative generalization of cluster algebras, i.e. when cluster charts are free associative algebras. I will show that a family of noncommutative cluster algebras originating from topology can be equipped with a double quasi Poisson bracket compatible with mutations. This includes noncommutative dimer models, examples proposed by A.Berenstein and V.Retakh, and noncommutative pentagram map studied by N.Ovenhouse. Time permits, I will also discuss an ongoing project joint with M.Shapiro and N.Ovenhouse on noncommutative networks.

21724

Thursday 2/13 2:30 PM

Ákos Nagy, Duke University

The Asymptotic Geometry of G_2 monopoles
 Ákos Nagy, Duke University
 The Asymptotic Geometry of G_2 monopoles
 02/13/2020
 2:30 PM  3:30 PM
 C304 Wells Hall
G_2 monopoles are special solutions of the YangMillsHiggs equation on G_2 manifolds, and Donaldson and Segal conjectures that one can construct invariants of noncompact G_2 manifolds by counting G_2 monopoles.
One of the first steps of achieving this goal is understanding the analytic behavior of these monopoles. In this talk, I introduce the proper analytic setup for the problem, and present our results about the asymptotic form of G_2 monopoles on Asymptotically Conical manifolds with structure group being SU(2).
If time permits, I also talk about our further plans in this project, in particular:
1. Generalizations of these results to manifolds with fibered end and higher rank gauge groups.
2. A gluein construction of monopoles with ``large mass''.
This is a join project with Goncalo Oliveira (UFF, Brazil).

22750

Monday 2/17 4:10 PM

Andrew Krause and Tsveta Sendova

MTH 132 large lecture updates / How do we make sure math majors can negate an implication?
 Andrew Krause and Tsveta Sendova
 MTH 132 large lecture updates / How do we make sure math majors can negate an implication?
 02/17/2020
 4:10 PM  5:00 PM
 C109 Wells Hall
No abstract available.

24775

Monday 2/17 4:30 PM

Suo Jun Tan, MSU

Why Study $\ell$adic Galois Representations...?
 Suo Jun Tan, MSU
 Why Study $\ell$adic Galois Representations...?
 02/17/2020
 4:30 PM  5:30 PM
 C517 Wells Hall
To study the absolute Galois group $G_{\mathbb{Q}}$ (or $G_{K}$ for any global field $K$) of the rational numbers $Q$, it’s natural to study its representations. The Krull topology we put on $G_{\mathbb{Q}}$ makes it a "good" topological group (a profinite group) but it’s also incompatible with the usual topology of $GL_n(\mathbb{C})$. In fact, every complex Galois representation of $G_{\mathbb{Q}}$ must have
finite image and thus only captures finite amount of information about the structure of $G_{\mathbb{Q}}$. The main goal of the talk is to introduce $\ell$adic Galois representations $\rho:G_{\mathbb{Q}} → GL_{n}(\mathbb{Q}_{\ell})$ and to explain why they are being studied in number theory. Important examples are $2$
dimensional Galois representations coming from elliptic curves and modular forms. If time permits, we will briefly explain how Fermat’s last theorem was proved using these ideas.

22762

Tuesday 2/18 11:30 AM

Srivatsav Kunnawalkam Elayavalli, Vanderbilt University

A Jungle of $\mathrm{II}_1$ factors
 Srivatsav Kunnawalkam Elayavalli, Vanderbilt University
 A Jungle of $\mathrm{II}_1$ factors
 02/18/2020
 11:30 AM  12:30 PM
 C304 Wells Hall
A remarkable insight of Kenley Jung in 2005 lead to the careful study of the space of embeddings of a tracial von Neumann algebra into the ultraproduct of the hyperfinite $\mathrm{II}_1 $factor, modulo unitary conjugation. While Jung initially proved that this space is a singleton set if and only the domain is amenable, Brown later showed that the space has a convex structure and is very rich in the nonamenable case, in particular is uncountable and not even second countable (a result of Ozawa in an appendix to Brown's paper). In this talk, we shall discuss some recent developments in this subject, by considering arbitrary ultraproduct codomains, weaker relations between embeddings, and finally looking at general automorphisms of ultraproducts. These considerations have interesting connections with model theory of operator algebras, and the Connes' Embedding Problem. Based on joint work with S. Atkinson and I. Goldbring.

24774

Wednesday 2/19 3:00 PM

Anna Weigandt, University of Michigan

Derivatives of Schubert polynomials
 Anna Weigandt, University of Michigan
 Derivatives of Schubert polynomials
 02/19/2020
 3:00 PM  3:50 PM
 C517 Wells Hall
We describe the action of a differential operator when applied to the Schubert basis. We use this to give a short proof of the Macdonald identity. We also discuss an application to the study of the (strong) Sperner property of the weak order on the symmetric group. This property was proven by Gaetz and Gao (2018). Our description of the differential operator leads to a proof of a determinant conjecture of Stanley (2017), which also implies the Sperner property. This is joint work with Zachary Hamaker, Oliver Pechenik and David E Speyer.

24779

Wednesday 2/19 4:10 PM

Seonghyeon Jeong

Underlying geometry of Optimal Transport.
 Seonghyeon Jeong
 Underlying geometry of Optimal Transport.
 02/19/2020
 4:10 PM  5:00 PM
 C517 Wells Hall
Suppose we have manifolds M and N and let $\mu$ and $\nu$ be two probability measures on M and N respectively. And suppose we have a function c, which we call the cost function, from $M \times N$ to real numbers. In Optimal Transport problem, we study a function that transports $\mu$ to $\nu$ and minimize the transport cost. When we study Optimal Transport problem, we face a tensor called MTW. This tensor does important role in regularity theory of optimal maps. If we give an appropriate metric on the product manifold, MTW tensor can be view as a curvature of this manifold. In this talk, we discuss what is the metric on $M \times N$ and compute MTW tensor with this metric.

24777

Thursday 2/20 12:00 PM

Leonardo Abbrescia, MSU

Geometric analysis of 1+1 dimensional quasilinear waves
 Leonardo Abbrescia, MSU
 Geometric analysis of 1+1 dimensional quasilinear waves
 02/20/2020
 12:00 PM  1:00 PM
 C517 Wells Hall
We will present a series of geometric ideas that are useful to study the initial value problem of quasilinear wave equations satisfying the null condition on the (1+1)dimensional Minkowski space. Using a doublenull geometric formulation, we show how the conformal invariance of the equation semilinearizes it into a system that is decoupled from the equations governing the null geometry. This allows us to solve the wave equations independently, which we exploit to show that the null geometry is sufficiently regular to guarantee global existence. If time permits, I will explain how this ties into a global wellposedness result with ``large" initial data.

22759

Thursday 2/20 1:00 PM

Chaya Norton, U of Michigan

Moduli space of vector bundles and the monodromy map
 Chaya Norton, U of Michigan
 Moduli space of vector bundles and the monodromy map
 02/20/2020
 1:00 PM  2:00 PM
 C204A Wells Hall
We develop the notion of a nonabelian Cauchy kernel for a framed vector bundle of rank n and degree ng on a fixed Riemann surface of genus g. This Cauchy kernel can be used to define an affine connection holomorphically varying in the moduli space of vector bundles. Thus we pose and answer the question regarding how the complex symplectic structure on the moduli space of Higgs bundles (or the cotangent bundle to the moduli space of vector bundles) relates to the Goldman symplectic structure. Based on work in progress with Marco Bertola and Giulio Ruzza.

19682

Thursday 2/20 2:30 PM

Spiro Karigiannis, University of Waterloo

BryantSalamon G2 manifolds and coassociative fibrations
 Spiro Karigiannis, University of Waterloo
 BryantSalamon G2 manifolds and coassociative fibrations
 02/20/2020
 2:30 PM  3:30 PM
 C304 Wells Hall
I will discuss joint work with Jason Lotay, which should be on the arXiv before my talk. We show how the three BryantSalamon G2 manifolds can be viewed as coassociative fibrations. In all cases the coassociative fibres are invariant under a 3dimensional group and are thus of cohomogeneity one, In general there are both generic smooth fibres and degenerate singular fibres. The induced Riemannian geometry on the fibres turns out to exhibit asymptotically conical and conically singular behaviour. In some cases we also explicitly determine the induced hypersymplectic structure. In all three cases we show that the "flat limits" of these coassociative fibrations are wellknown calibrated fibrations of Euclidean space. Finally, we establish connections with the multimoment maps of MadsenSwann, the new compact construction of G2 manifolds of JoyceKarigiannis, and recent work of Donaldson involving vanishing cycles and "thimbles".

18590

Thursday 2/20 4:10 PM

Jacob Tsimerman, University of Toronto

ominimal GAGA and applications to Hodge theory
 Jacob Tsimerman, University of Toronto
 ominimal GAGA and applications to Hodge theory
 02/20/2020
 4:10 PM  5:00 PM
 C304 Wells Hall
(joint with B.Bakker Y.Brunebarbe and B.Klingler) One very fruitful way of studying complex algebraic varieties is by forgetting the underlying algebraic structure, and just thinking of them as complex analytic spaces. To this end, it is a natural and fruitful question to ask how much the complex analytic structure remembers. One very prominent result is Chows theorem, stating that any closed analytic subspace of projective space is in fact algebraic. A notable consequence of this result is that a compact complex analytic space admits at most one algebraic structure  a result which is false in the noncompact case. This was generalized and extended by Serre in his famous GAGA paper using the language of cohomology. We explain how we can extend Chow's theorem and in fact all of GAGA to the noncompact case by working with complex analytic structures that are "tame" in the precise sense defined by ominimality. This leads to some very general "algebraization" theorems, which have important applications to Hodge Theory.

19652

Friday 2/21 4:10 PM

Chris Henderson, University of Arizona

Wellposedness, blowup, and smoothing for the Landau equation
 Chris Henderson, University of Arizona
 Wellposedness, blowup, and smoothing for the Landau equation
 02/21/2020
 4:10 PM  5:00 PM
 C304 Wells Hall
The Landau equation is a mesoscopic model in plasma physics that describes the evolution in phasespace of the density of colliding particles. Due to the nonlocal, nonlinear terms in the equation, an understanding of the existence, uniqueness, and qualitative behavior of solutions has remained elusive except in some simplified settings (e.g., homogeneous or perturbative). In this talk, I will report on recent progress in the application of ideas of parabolic regularity theory to this kinetic equation. Using these ideas we can, in contrast to previous results requiring boundedness of fourth derivatives of the initial data, construct solutions with low initial regularity (just $L^\infty$) and show they are smooth and bounded for all time as long as the mass and energy densities remain bounded. This is a joint work with S. Snelson and A. Tarfulea.

20688

Wednesday 2/26 4:10 PM

Katya Krupchyk, University of California, Irvine

Inverse boundary problems for semilinear elliptic PDE
 Katya Krupchyk, University of California, Irvine
 Inverse boundary problems for semilinear elliptic PDE
 02/26/2020
 4:10 PM  5:00 PM
 C304 Wells Hall
In this talk we shall discuss recent progress for partial data inverse boundary problems for semilinear elliptic PDE. It turns out that the presence of a nonlinearity allows one to solve inverse problems in situations where the corresponding linear counterpart is open. In the first part of the talk, we shall also discuss some previous work on partial data inverse boundary problems for linear elliptic PDE, focusing on the case of coefficients of low regularity. This talk is based on joint work with Gunther Uhlmann.

24781

Wednesday 2/26 4:10 PM

Keshav Sutrave

A hot approach to the Hodge Theorem (Heat Equation)
 Keshav Sutrave
 A hot approach to the Hodge Theorem (Heat Equation)
 02/26/2020
 4:10 PM  5:00 PM
 C517 Wells Hall
The Hodge theorem is a result regarding Laplace’s equation for differential forms on a Riemannian manifold (I will introduce the setup for this). Like many celebrated theorems in geometry, it gives a calculable geometric insight on the topology of the space. Normally, the method for solving this PDE is an “elliptic equation” procedure, but I will instead show a heat equation (parabolic) approach to the problem. We will see that the topology emerges in the long time behavior of the heat flow. Further work with this approach leads to results such as the ChernGaussBonnet theorem, and (almost literally) draws a line connecting geometry and topology.

24778

Thursday 2/27 11:30 AM

Kazuhiro Kuwae, Fukuoka University

Stability of estimates for fundamental solutions under FeynmanKac perturbations for symmetric Markov processes
 Kazuhiro Kuwae, Fukuoka University
 Stability of estimates for fundamental solutions under FeynmanKac perturbations for symmetric Markov processes
 02/27/2020
 11:30 AM  12:30 PM
 C304 Wells Hall
This is a joint work with Daehong Kim (Kumamoto) and Panki Kim (Seoul).
We give a necessary and sufficient condition on the stability of global (upper) estimates for fundamental
solution of FeynmanKac semigroup of symmetric Markov processes under the stability of global
heat kernel (upper) estimates by bounded perturbations.
As a corollary, a weak type global (upper) estimate holds for
the fundamental solution of FeynmanKac semigroup with (extended) Kato class conditions for
measures provided the stability of global heat kernel (upper) estimates by bounded perturbations holds.
This generalizes the all known results on the stability of global integral kernel estimates by symmetric FeynmanKac
perturbations with Kato class conditions in the framework of symmetric Markov processes.

22761

Thursday 2/27 1:00 PM

Nick Ovenhouse, U of Minnesota

Laurent Expansion Formulas for Configurations of Flags
 Nick Ovenhouse, U of Minnesota
 Laurent Expansion Formulas for Configurations of Flags
 02/27/2020
 1:00 PM  2:00 PM
 C204A Wells Hall
A cluster algebra can be associated to a polygon, where clusters correspond to triangulations of the polygon. These clusters give coordinates on the Grassmannian Gr(2,n). Schiffler gave explicit expressions for the cluster variables as Laurent polynomials, with the terms indexed by combinatorial objects called "Tpaths". Fock and Goncharov defined a cluster algebra structure for the configuration space of tuples of flags in a 3dimensional vector space, which generalizes the one given by triangulated polygons. In joint work with Andrew Claussen, we describe a suitable generalization of Schiffler's Tpaths to this case, and show that the Laurent expansions of cluster variables are indexed by these generalized Tpaths.

21722

Thursday 2/27 2:30 PM

Aleksander Doan, Columbia University

Nonabelian monopoles and invariants of threemanifolds
 Aleksander Doan, Columbia University
 Nonabelian monopoles and invariants of threemanifolds
 02/27/2020
 2:30 PM  3:30 PM
 C304 Wells Hall
Floer homology groups are invariants of 3dimensional manifolds, defined using partial differential equations of gauge theory. One version of this invariant is associated with the YangMills equations and another with the SeibergWitten equations. While they share many similarities, it is a major open problem to find a general relation between them. I will talk about a joint project with Chris Gerig, whose goal is to relate simpler, numerical invariants obtained by taking the Euler characteristic of certain Floer homology groups. The proof, following ideas of Kronheimer and Mrowka, uses a nonabelian generalization of the SeibergWitten equations.

24780

Thursday 2/27 3:00 PM

Zachary Hamaker, University of Florida

Schubert calculus, involutions and symmetric matrices
 Zachary Hamaker, University of Florida
 Schubert calculus, involutions and symmetric matrices
 02/27/2020
 3:00 PM  3:50 PM
 D227A Wells Hall
In his "Kalkul der abzahlende Geometrie”, Schubert introduced a powerful nonrigorous method for solving enumerative geometry problems known as Schubert calculus. Making this method rigorous motivated a great deal of 20th century algebraic geometry. Since the combinatorics of permutations is central to this theory, combinatorialists have made major contributions to Schubert calculus broadly construed. We will overview some highlights from this field, develop a parallel theory based on the combinatorics of involutions in the symmetric group and conclude by using this work to describe fundamental properties of the geometry of symmetric matrices. This work is joint with Eric Marberg and Brendan Pawlowski.

18591

Thursday 2/27 4:10 PM

Lawrence Craig Evans, UC Berkeley

Riccati Equation Methods for Partial Differential Equations
 Lawrence Craig Evans, UC Berkeley
 Riccati Equation Methods for Partial Differential Equations
 02/27/2020
 4:10 PM  5:00 PM
 C304 Wells Hall
In this expository talk, I will first explain the surprising effectiveness of a log change of variables for elliptic PDE, and connect this with an old ODE trick that leads to Riccati equations. I will then recall some recent progress using PDE methods to study Hamiltonian dynamics (weak KAM theory) and describe some interesting conjectures and formal calculations, again leading to Riccati equations.

23772

Friday 2/28 4:10 PM

Francis Chung, University of Kentucky

Optical Tomography with Local Data
 Francis Chung, University of Kentucky
 Optical Tomography with Local Data
 02/28/2020
 4:10 PM  5:00 PM
 C304 Wells Hall
Optical tomography is the process of obtaining full (3D) reconstructions of the interior optical properties of an object from observations at the boundary. In mathematical terms, this amounts to reconstructing the coefficients of a PDE from measurements of the solutions at the boundary; which PDE is involved depends on which model we use for light propagation. In this talk I'll introduce an optical tomography problem in which we model light propagation by a radiative transport equation, and describe a recent result that allows us to do reconstructions even when our measurements are restricted to a subset of the boundary.

22731

Monday 3/9 2:00 PM

Kevin Hughes, University of Bristol

$L^p$improving for spherical maximal functions
 Kevin Hughes, University of Bristol
 $L^p$improving for spherical maximal functions
 03/09/2020
 2:00 PM  2:50 PM
 C304 Wells Hall
I will discuss recent work on $L^p$improving estimates for spherical maximal functions  continuous and discrete. In the continous setting, this is joint work with Anderson, Roos and Seeger building on important work of SeegerWaingerWright. In the discrete setting, these were independently discovered by myself and by KeslerLace.

24782

Monday 3/9 4:00 PM

Elizabeth Munch, MSU

Drawing TimeVarying Reeb Graphs
 Elizabeth Munch, MSU
 Drawing TimeVarying Reeb Graphs
 03/09/2020
 4:00 PM  5:00 PM
 C517 Wells Hall
Given a realvalued function on a topological space, the Reeb graph encodes the changing component structure of the level sets; this graph also inherits a realvalued function from this setup. The Reeb graph is utilized in a variety of computational topology and topological data analysis applications in order to get a lower dimension representation of a structure which maintains topological properties of the original data. Its applications appear in a wide range of research domains, however, to date these applications are generally limited to the computation of a Reeb graph from a single, stagnant space. We are interested in developing theoretically motivated and robust visualizations for timevarying Reeb graphs. These Reeb "flows" arise in many situations ranging from theory to practice, such as Reeb graphs computed from a space which continuously varies over time. In this talk, we will discuss the initial work on this project and first results. In particular, we will discuss the special case of planarity applied to Reeb graphs, and a class of Reeb graph flows that maintain planarity. These flows arise from a modified version of the Reeb graph interleaving distance.

24789

Tuesday 3/10 3:00 PM

Bridget Tenner, DePaul University

Pinnacle sets: introduction and recent developments
 Bridget Tenner, DePaul University
 Pinnacle sets: introduction and recent developments
 03/10/2020
 3:00 PM  3:50 PM
 C204A Wells Hall
Peak sets of permutations have a long history in the literature. Inspired by work of Billey, Burdzy, and Sagan on those sets, we introduced the pinnacle sets of permutations. Despite natural symmetries, pinnacle sets and peak sets have notably different properties. We will explore some of those differences in this talk, giving characterization and enumerative results about pinnacle sets. Very recently, several papers have added to the literature on pinnacle sets, and we will describe those updates here.
This talk includes joint work with Robert Davis, Sarah Nelson, Kyle Petersen, and Irena Rusu.

24776

Wednesday 3/11 3:00 PM

John Bergdall, Bryn Mawr

Reductions of some 2dimensional Galois representations
 John Bergdall, Bryn Mawr
 Reductions of some 2dimensional Galois representations
 03/11/2020
 3:00 PM  4:00 PM
 C304 Wells Hall
Modular forms are often studied through the lens of Galois representations. As an example, congruences between modular forms can be detected by reducing their Galois representations modulo p. So, in general, there is a great interest in determining reductions of Galois representations associated with modular forms. In our talk, we will explain one such result that improves a result of Berger, Li, and Zhu from 2004. The techniques are in fact completely local, making use of work of Fontaine and Kisin in padic Hodge theory, and we will explain as broadly as possible how the local perspective helps solve problem. This is joint work with Brandon Levin.

24791

Wednesday 3/11 4:10 PM

Rob McConkey

Graph theoretical approach to The Jones Polynomial
 Rob McConkey
 Graph theoretical approach to The Jones Polynomial
 03/11/2020
 4:10 PM  5:00 PM
 C517 Wells Hall
We will begin by introducing the Jones Polynomial, an invariant in knot theory. Then we will talk about state graphs and how they’re related to an object from combinatorics, called combinatorial maps. From here we can define the BollobásRiordanTutte polynomial, which can be used to compute the Jones polynomial. Finally we will explore some of the applications of this construction.

24790

Thursday 3/12 1:00 PM

Linhui Shen, MSU

Drinfeld dual of simple PoissonLie groups and cluster algebras
 Linhui Shen, MSU
 Drinfeld dual of simple PoissonLie groups and cluster algebras
 03/12/2020
 1:00 PM  2:00 PM
 C204A Wells Hall
Let $G$ be a complex connected simple group with the standard PoissonLie structure and let $G^\ast$ be its dual PoissonLie group. The coordinate ring $\mathcal{O}(G^\ast)$ is a Poisson algebra whose deformation quantization gives rise to the quantum group $\mathcal{U}_q(\mathfrak{g})$. We embed $\mathcal{O}(\G^\ast)$ into a larger cluster Poisson algebra together with a Weyl group action. By applying bases theory of cluster algebras, we obtain a natural linear basis $\Theta$ of $\mathcal{O}(\G^\ast)$ with positive integer structure coefficients. We show that the basis $\Theta$, as a set, is invariant under Lusztig's braid group action.

22760

Thursday 3/19 1:00 PM

Mandy Cheung, Harvard University

cancelled
 Mandy Cheung, Harvard University
 cancelled
 03/19/2020
 1:00 PM  2:00 PM
 C204A Wells Hall
process. Partial compactifications of the varieties, studied by Gross, Hacking, Keel, and Kontsevich, generalize the polytope construction of toric varieties. However, the existence of such compactifications is not clear for general setting. Together with Magee and NajeraChavez, we have extended the idea of convex polytope from toric geometry to the cluster setting which we named as broken line convexity. With this description, we can easily write down the compactifications for all the cluster varieties.
If time permits, we can discuss another separated project with Yushen Lin about constructing family Floer mirror for del Pezzo surface of degree 5.

22754

Friday 3/20 3:00 PM

Giulio Tralli

(Cancelled) From Gaussian bounds to Wienertype criteria for parabolic equations
 Giulio Tralli
 (Cancelled) From Gaussian bounds to Wienertype criteria for parabolic equations
 03/20/2020
 3:00 PM  3:50 PM
 C304 Wells Hall
In this talk we discuss the regularity of boundary points for the Dirichlet problem related to a class of linear (possibly degenerate) parabolic equations. We show the validity of Wienertype criteria for hypoelliptic operators with a fundamental solution satisfying twosided Gaussian bounds with respect to some reference distance. The Wiener condition is expressed, in analogy with a result by Landis for the heat equation, in terms of a series of balayages. As an application, we present sharp sufficient conditions of regularity for
a model class of Hormander operators enjoying suitable homogeneity properties. This is a joint work with F. Uguzzoni.

21725

Friday 3/20 4:10 PM


Cancelled

 Cancelled
 03/20/2020
 4:10 PM  5:00 PM
 C304 Wells Hall
No abstract available.

24788

Wednesday 3/25 4:10 PM

Perry Kleinhenz, Northwestern

(Cancelled) Sharp stabilization rates for the damped wave equation on the torus
 Perry Kleinhenz, Northwestern
 (Cancelled) Sharp stabilization rates for the damped wave equation on the torus
 03/25/2020
 4:10 PM  5:00 PM
 C304 Wells Hall
We study the decay rate of energy of solutions to the damped wave equation on the 2torus when the geometric control condition is violated. In particular we assume the damping is invariant in one direction and consider two cases: the damping is zero on a strip and vanishes like $x^{\beta}$ or the damping is $C^{26}$. When the damping vanishes like a polynomial we show the semigroup is stable exactly at rate $1/t^{(\beta+2)/(\beta+3)}$. When the damping is sufficiently regular we show the semigroup is stable at least at rate $1/t^{3/4}$.

23774

Thursday 3/26 2:30 PM

Mark Pengitore, Ohio State University

TBD
 Mark Pengitore, Ohio State University
 TBD
 03/26/2020
 2:30 PM  3:30 PM
 C304 Wells Hall
No abstract available.

19627

Friday 3/27 4:10 PM


The talk this week has been cancelled.

 The talk this week has been cancelled.
 03/27/2020
 4:10 PM  5:00 PM
 C304 Wells Hall
No abstract available.

22745

Wednesday 4/1 4:10 PM

Yilin Wang, MIT

(Cancelled)
 Yilin Wang, MIT
 (Cancelled)
 04/01/2020
 4:10 PM  5:00 PM
 C304 Wells Hall
No abstract available.

22746

Friday 4/3 4:10 PM


Cancelled

 Cancelled
 04/03/2020
 4:10 PM  5:00 PM
 C304 Wells Hall
No abstract available.

24784

Thursday 4/9 9:30 AM

Vladimir Fock, Strassbourgh

Higher measured laminations and tropical curves. Zoom: https://msu.zoom.us/j/451121888
 Vladimir Fock, Strassbourgh
 Higher measured laminations and tropical curves. Zoom: https://msu.zoom.us/j/451121888
 04/09/2020
 9:30 AM  10:30 AM
 C204A Wells Hall
We shall define a notion of a higher lamination  a graph
embedded into a Riemann surface with edges coloured by generators of an
affine Weyl group. This notion generalises the notion of the ordinary
integral measured lamination and on the other hand of a tropical curve
and can be constructed out of a integral Lagrangian submanifold of the
cotangent bundle.

18594

Thursday 4/9 4:10 PM

Adrian Ioana, UC San Diego

TBD
 Adrian Ioana, UC San Diego
 TBD
 04/09/2020
 4:10 PM  5:00 PM
 C304 Wells Hall
No abstract available.

22768

Friday 4/10 4:10 PM


Cancelled

 Cancelled
 04/10/2020
 4:10 PM  5:00 PM
 C304 Wells Hall
No abstract available.

24786

Wednesday 4/15 4:10 PM

Annalaura Stingo, UC Davis

(Cancelled) Almost globalwell posedness for quasilinear strongly coupled waveKleinGordon systems in two space dimension
 Annalaura Stingo, UC Davis
 (Cancelled) Almost globalwell posedness for quasilinear strongly coupled waveKleinGordon systems in two space dimension
 04/15/2020
 4:10 PM  5:00 PM
 C304 Wells Hall
In this talk we will prove the almost global existence of small solutions of stronglycoupled waveKleinGordon systems in 2+1 spacetime dimension. We consider quadratic quasilinear null form type nonlinearities, and consider initial data that are only mildly decaying at infinity and have minimal regularity. The proof relies on a systematical analysis of the nonlinearities, and combines energy estimates localized to dyadic spacetime regions and pointwise interpolation estimates within the same regions. This is a joint work with M. Ifrim.

24783

Thursday 4/16 9:30 AM

Alexander Varchenko

Positive populations. Zoom: https://msu.zoom.us/j/451121888
 Alexander Varchenko
 Positive populations. Zoom: https://msu.zoom.us/j/451121888
 04/16/2020
 9:30 AM  10:30 AM
 C204A Wells Hall
I will discuss a positive structure on the varieties of critical points of
master functions for the KZ differential equations. The structure is
introduced in my recent preprint with V. Schechtman. The positive
structure comes as a combination of the ideas from classical works
by G. Lusztig and my previous work with E. Mukhin on the relations
between these varieties of critical points and the flag varieties.

24785

Thursday 4/16 4:10 PM

Alexander Varchenko, University of North Carolina at Chapel Hill

TBD
 Alexander Varchenko, University of North Carolina at Chapel Hill
 TBD
 04/16/2020
 4:10 PM  5:00 PM
 C304 Wells Hall
No abstract available.

23771

Friday 4/17 4:10 PM


Cancelled

 Cancelled
 04/17/2020
 4:10 PM  5:00 PM
 C304 Wells Hall
TBD

18599

Thursday 4/23 4:10 PM

Rafe Mazzeo, Stanford University

TBD
 Rafe Mazzeo, Stanford University
 TBD
 04/23/2020
 4:10 PM  5:00 PM
 C304 Wells Hall
No abstract available.

21730

Monday 4/27 3:00 PM

J. Maurice Rojas, Texas A&M University and NSF

TBA
 J. Maurice Rojas, Texas A&M University and NSF
 TBA
 04/27/2020
 3:00 PM  4:00 PM
 C517 Wells Hall
No abstract available.
