Talk_id  Date  Speaker  Title 
8242

Monday 1/8 4:10 PM

David Hansen, Columbia University

Elliptic curves and padic Lfunctions
 Elliptic curves and padic Lfunctions
 01/08/2018
 4:10 PM  5:00 PM
 C304 Wells Hall
 David Hansen, Columbia University
I'll explain the notion of a padic Lfunction, try to
motivate why one might care about such a gadget, and give some history of their construction and applications. At the end of the talk I'll discuss a recent joint work with John Bergdall in which (among other things) we construct canonical padic Lfunctions associated with modular elliptic curves over totally real number fields.

8231

Tuesday 1/9 4:10 PM

Yoonsang Lee, Lawrence Berkeley National Laboratory

Uncertainty Quantification of Physicsconstrained Problems – Data Assimilation and Parameter Estimation
 Uncertainty Quantification of Physicsconstrained Problems – Data Assimilation and Parameter Estimation
 01/09/2018
 4:10 PM  5:00 PM
 C304 Wells Hall
 Yoonsang Lee, Lawrence Berkeley National Laboratory
Observation data along with mathematical models play a crucial role in improving prediction skills in science and engineering. In this talk we focus on the recent development of uncertainty quantification methods, data assimilation and parameter estimation, for Physicsconstrained problems that are often described by partial differential equations. We discuss the similarities shared by the two methods and their differences in mathematical and computational points of view and future research topics. As applications, numerical weather prediction for geophysical flows and parameter estimation of kinetic reaction rates in the hydrogenoxygen combustion are provided.

8230

Wednesday 1/10 4:10 PM

Preston Wake, UCLA

Quantifying congruences between Eisenstein series and cusp forms
 Quantifying congruences between Eisenstein series and cusp forms
 01/10/2018
 4:10 PM  5:00 PM
 C304 Wells Hall
 Preston Wake, UCLA
Consider the following two problems in algebraic number theory:
1. For which prime numbers p can we easily show that the Fermat equation x^p + y^p =z^p has no nontrivial integer solutions?
2. Given an elliptic curve E over the rational numbers, what can be said about the group of rational points of finite order on E?
These seem like very different problems, but, surprisingly, they share a common theme: they are both related to the existence of congruences between two types of modular forms, Eisenstein series and cusp forms. We will explain these examples, and discuss a new technique for giving quantitative information about these congruences (for example, counting the number of cusp forms congruent to an Eisenstein series). We will explain how this can give finer arithmetic information than simply knowing the existence of a congruence. This is joint work with Carl WangErickson.

8232

Friday 1/12 4:10 PM

John Calabrese, Rice University

From Hilbert's Nullstellensatz to quotient categories
 From Hilbert's Nullstellensatz to quotient categories
 01/12/2018
 4:10 PM  5:00 PM
 C304 Wells Hall
 John Calabrese, Rice University
A common theme in algebraic geometry is the interplay between algebra and geometry. In this talk I will discuss a few "reconstruction theorems", in which the algebra determines the geometry.

9248

Wednesday 1/17 4:10 PM

Tristan Collins, Harvard University

SasakiEinstein metrics and Kstability
 SasakiEinstein metrics and Kstability
 01/17/2018
 4:10 PM  5:00 PM
 C304 Wells Hall
 Tristan Collins, Harvard University
I will discuss the connection between SasakiEinstein metrics and algebraic geometry in the guise of Kstability. In particular, I will give a differential geometric perspective on Kstability which arises from the Sasakian view point, and use Kstability to find infinitely many nonisometric SasakiEinstein metrics on the 5sphere. This is joint work with G. Szekelyhidi.

9251

Wednesday 1/17 4:10 PM

Hitesh Gakhar, MSU

Dualities in Persistent (co)Homology
 Dualities in Persistent (co)Homology
 01/17/2018
 4:10 PM  5:00 PM
 C204A Wells Hall
 Hitesh Gakhar, MSU
For a filtered topological space, its persistent homology is a multiset of half open real intervals known as barcode. Each bar represents the lifespan of a homology class. A fundamental principle is that the length of such a bar determines the significance of the corresponding class. In 2011, V. de Silva et al studied the relationships between (persistent) absolute homology, absolute cohomology, relative homology and relative cohomology. This talk will be a theoretical overview of that study.

9253

Monday 1/22 4:10 PM

Joshua Ruiter, MSU

Infinite Galois Extensions
 Infinite Galois Extensions
 01/22/2018
 4:10 PM  5:00 PM
 C517 Wells Hall
 Joshua Ruiter, MSU
No abstract available.

7200

Monday 1/22 4:10 PM

Dr. Robert Caldwell

Academic Integrity
 Academic Integrity
 01/22/2018
 4:10 PM  5:00 PM
 C109 Wells Hall
 Dr. Robert Caldwell
Dr. Robert Caldwell, MSU's Ombudsperson, will attend this meeting. This will be an opportunity to ask him questions regarding challenging scenarios many of us have encountered during exam proctoring, grading of tests and projects.

8235

Tuesday 1/23 1:15 PM

Elise Lockwood, Oregon State University

Investigating Subtleties of the Multiplication Principle
 Investigating Subtleties of the Multiplication Principle
 01/23/2018
 1:15 PM  2:45 PM
 252 EH
 Elise Lockwood, Oregon State University
Central to introductory probability, and a primary feature of most discrete mathematics courses, the Multiplication Principle is fundamental to combinatorics, underpinning many standard formulas and providing justification for counting strategies. Given its importance, the ways it is presented in textbooks are surprisingly varied. In this talk, I identify key elements of the principle and present a categorization of statement types that emerged from a textbook analysis. I also incorporate excerpts from a reinvention study that sheds light on how students reason through key elements of the principle. Findings from both the textbook analysis and the reinvention study reveal surprisingly subtle aspects of the multiplication principle that can be made concrete for students through carefully chosen examples. I conclude with a number of potential mathematical and pedagogical implications of the categorization.

9249

Tuesday 1/23 4:10 PM

Bruce Sagan, MSU

An Introduction to Stanley's Theory of PPartitions. I
 An Introduction to Stanley's Theory of PPartitions. I
 01/23/2018
 4:10 PM  5:00 PM
 C304 Wells Hall
 Bruce Sagan, MSU
Richard Stanley developed a powerful generalization of the theory of integer partitions where the parts of the partition are arranged on any labeled poset P. In this first lecture we will develop some intuition by computing the generating functions for various families of ordinary integer partitions. This will motivate Stanley's generalization which will be discussed in the second lecture. No background will be assumed.

9255

Wednesday 1/24 4:10 PM

Hitesh Gakhar, MSU

Dualities in Persistent (co)HomologyPart II
 Dualities in Persistent (co)HomologyPart II
 01/24/2018
 4:10 PM  5:00 PM
 C517 Wells Hall
 Hitesh Gakhar, MSU
For a filtered topological space, its persistent homology is a multiset of half open real intervals known as barcode. Each bar represents the lifespan of a homology class. A fundamental principle is that the length of such a bar determines the significance of the corresponding class. In 2011, V. de Silva et al studied the relationships between (persistent) absolute homology, absolute cohomology, relative homology and relative cohomology. This talk will be a theoretical overview of that study.

7231

Thursday 1/25 11:00 AM

Jonas Lührmann

Probabilistic scattering for the 4D energycritical defocusing nonlinear wave equation
 Probabilistic scattering for the 4D energycritical defocusing nonlinear wave equation
 01/25/2018
 11:00 AM  12:00 PM
 C304 Wells Hall
 Jonas Lührmann
We consider the Cauchy problem for the energycritical defocusing
nonlinear wave equation in four space dimensions. It is known that for
initial data at energy regularity, the solutions exist globally in time
and scatter to free waves. However, the problem is illposed for initial
data at supercritical regularity, i.e. for regularities below the
energy regularity.
In this talk we study the supercritical data regime for this Cauchy
problem from a probabilistic point of view, using a randomization
procedure that is based on a unitscale decomposition of frequency
space. We will present an almost sure global existence and scattering
result for randomized radially symmetric initial data of supercritical
regularity. This is the first almost sure scattering result for an
energycritical dispersive or hyperbolic equation for scaling
supercritical initial data.
The main novelties of our proof are the introduction of an approximate
Morawetz estimate to the random data setting and new large deviation
estimates for the free wave evolution of randomized radially symmetric data.
This is joint work with Ben Dodson and Dana Mendelson.

6187

Thursday 1/25 2:00 PM

Siqi He, Caltech

The Extended Bogomolny Equations and Teichmuller space
 The Extended Bogomolny Equations and Teichmuller space
 01/25/2018
 2:00 PM  3:00 PM
 C304 Wells Hall
 Siqi He, Caltech
We will discuss Witten’s gauge theory approach to Jones polynomial and Khovanov homology by counting solutions to some gauge theory equations with singular boundary conditions. When we reduce these equations to 3dimensional, we call them the extended Bogomolny equations. We will discuss a DonaldsonUlenbeckYau type correspondence of the moduli space of the singular solutions to the Extended Bogomolny equations and Teichmuller space. If time permits, we will also discuss the relationship of the singular solutions moduli space with higher Teichmuller theory. This is joint work with Rafe Mazzeo.

9256

Thursday 1/25 3:00 PM

Xiaochuan Yang, MSU

An invitation to large scale sojourn properties of Brownian motion
 An invitation to large scale sojourn properties of Brownian motion
 01/25/2018
 3:00 PM  3:50 PM
 C405 Wells Hall
 Xiaochuan Yang, MSU
For a one dimensional Brownian motion, we consider the sets of times where Brownian motion stays inside some moving boundaries. The boundaries considered are power functions with the power in [0, 1/2]. Since the usual scaling for Brownian motion at time t is square root of t, the sojourn sets we considered describe the recurrence of a Brownian motion around zero. We give large scale geometric properties of these sets using macroscopic dimensions introduced by Barlow and Taylor in the late 80's. The audience of 881/882 might find this talk interesting.

9258

Monday 1/29 4:10 PM

Nick Ovenhouse, MSU

Noncommutative Poisson Structures
 Noncommutative Poisson Structures
 01/29/2018
 4:10 PM  5:00 PM
 C517 Wells Hall
 Nick Ovenhouse, MSU
No abstract available.

7201

Monday 1/29 4:30 PM

Bronlyn Wassink, Mathematics, MSU

QL Updates
 QL Updates
 01/29/2018
 4:30 PM  5:20 PM
 C109 Wells Hall
 Bronlyn Wassink, Mathematics, MSU
No abstract available.

9259

Tuesday 1/30 10:20 AM

Rostyslav Kravchenko, Northwestern University

Invariant and characteristic random subgroups and their applications
 Invariant and characteristic random subgroups and their applications
 01/30/2018
 10:20 AM  11:10 AM
 C304 Wells Hall
 Rostyslav Kravchenko, Northwestern University
The invariant random subgroups (IRS) were implicitly used by Stuck and Zimmer in 1994 and defined explicitly by Abert, Glasner and Virag in 2012. We recall the definition of IRS and discuss their properties. We also define the notion of characteristic random subgroups (CRS) which are a natural analog of IRSs for the case of the group of all automorphisms. We determine CRS for free abelian groups and for free groups of finite rank. Using our results on CRS of free groups we show that for some groups of geometrical nature there are infinitely many continuous ergodic IRS.

9261

Tuesday 1/30 4:10 PM

Kate Juschenko, Northwestern University

Amenability of discrete groups and their actions
 Amenability of discrete groups and their actions
 01/30/2018
 4:10 PM  5:00 PM
 C304 Wells Hall
 Kate Juschenko, Northwestern University
The subject of amenability essentially begins in 1900's with Lebesgue. He asked whether the properties of his integral are really fundamental and follow from more familiar integral axioms. This led to the study of positive, finitely additive and translation invariant measure on reals as well as on other spaces. In particular the study of isometryinvariant measure led to the BanachTarski decomposition theorem in 1924. The class of amenable groups was introduced by von Neumann in 1929, who explained why the paradox appeared only in dimensions greater or equal to three, and does not happen when we would like to decompose the twodimensional ball. In 1940's, M. Day formally defined a class of elementary amenable groups as the largest class of groups amenability of which was known to von Naumann. He asked whether there are other groups then that. Currently there are many groups that answer von NeumannDay's question. However, in each particular case it is algebraically difficult to show that the group is not elementary amenable, and analytically difficult to show that it is amenable. The talk is aimed to discuss recent developments and approaches in the field. In particular, it will be shown how to prove amenability of all known nonelementary amenable groups using only one single approach. We will also discuss techniques coming from random walks of groups.

9250

Tuesday 1/30 4:10 PM

Bruce Sagan, MSU

An Introduction to Stanley's Theory of PPartitions, II
 An Introduction to Stanley's Theory of PPartitions, II
 01/30/2018
 4:10 PM  5:00 PM
 C517 Wells Hall
 Bruce Sagan, MSU
In this second lecture we will describe how Stanley associated to any labelled poset P a set of partitions having a rational generating function. Its denominator only depends on the number of elements of P and the numerator can be computed using an associated set of permutations and the major index statistic. If one bounds the size of the parts, then the major index is replaced by the number of descents.

7229

Wednesday 1/31 3:00 PM

Arie Israel, University of Texas at Austin

A new proof of the finiteness principle
 A new proof of the finiteness principle
 01/31/2018
 3:00 PM  3:50 PM
 C304 Wells Hall
 Arie Israel, University of Texas at Austin
The BrudnyiShvartsman finiteness principle is a foundational result in the study of Whitneytype extension problems. This result provides an answer to the following question: How can we tell whether there exists a Höldersmooth function that takes prescribed values on a given (arbitrary) subset of Euclidean space? In this talk I will describe new machinery for answering this question based on the notion of the “local complexity” of a set at a given position and scale. To complete the main induction argument we must prove that the complexity of an arbitrary set is bounded uniformly by an absolute constant. This is accomplished through an elementary lemma on the stabilization of the dynamics of a 1parameter family of nonisotropic dilations acting on the space of positivedefinite matrices. We conjecture an improvement to the constants in the stabilization lemma which would result in an improvement to the bestknown constants in the finiteness principle. This is joint work with A. FreiPearson and B. Klartag.

9257

Wednesday 1/31 4:10 PM

Olga Turanova, UCLA

Reactiondiffusion equations in biology
 Reactiondiffusion equations in biology
 01/31/2018
 4:10 PM  5:00 PM
 C304 Wells Hall
 Olga Turanova, UCLA
Reactiondiffusion equations describe a variety of physical and biological phenomena. In this talk, I begin by presenting the classical FisherKPP equation and its significance to ecology. I then describe recent results on other PDEs of reactiondiffusion type, including nonlocal equations arising in evolutionary ecology, as well as ones that model tumor growth (joint with Inwon Kim). I will highlight the mathematical challenges and techniques that arise in the analysis of these PDEs.

9247

Thursday 2/1 2:00 PM

Guillem Cazassus, Indiana University

Towards extended Floer field theories
 Towards extended Floer field theories
 02/01/2018
 2:00 PM  2:50 PM
 C304 Wells Hall
 Guillem Cazassus, Indiana University
Donaldson polynomials are powerful invariants associated to smooth fourmanifolds. The introduction by Floer of Instanton homology groups, associated to some 3manifolds, allowed to define analogs of such polynomials for (some) fourmanifolds with boundary, that have a structure similar with a TQFT.
Wehrheim and Woodward developed a framework called "Floer field theory" which, according to the AtiyahFloer conjecture, should permit to recover Donaldson invariants from a 2functor from the 2category Cob_{2+1+1} to a 2category Symp they defined, which is an enrichment of Weinstein's symplectic category.
I will describe a framework that should permit to extend such a 2functor to lower dimensions. This framework should permit to define new invariants in Manolescu and Woodward's symplectic instanton homology (sutured theory, equivariant version). This is work in progress.

9263

Thursday 2/1 4:10 PM

Daniel Thompson, Ohio State University

Geodesic flow in nonpositive curvature: An inspiration for new techniques in ergodic theory
 Geodesic flow in nonpositive curvature: An inspiration for new techniques in ergodic theory
 02/01/2018
 4:10 PM  5:00 PM
 C304 Wells Hall
 Daniel Thompson, Ohio State University
We discuss some recent progress in the smooth ergodic theory of geodesic flows. This talk will be suitable for a general mathematical audience, and will start with an intuitive overview of the classic results developed by luminaries such as Anosov, Bowen and Ruelle in the well understood setting of surfaces with variable negative curvature. Efforts to understand the much more difficult case of nonpositive curvature were initiated by Pesin in the 1970’s. However, despite substantial successes, the picture has remained far from complete. There has been a great deal of recent progress in this area, which has required, and motivated, the development of new machinery in the abstract theory. I will give an overview of some recent developments, including:
1) General machinery developed by Vaughn Climenhaga and myself, which gives “nonuniform" dynamical criteria for uniqueness of equilibrium measures;
2) Joint work with Keith Burns, Vaughn Climenhaga and Todd Fisher, where we apply this machinery to geodesic flow on nonpositive curvature manifolds;
3) If time permits, I will also mention related joint work with JeanFrancois Lafont and Dave Constantine, where we develop the theory of equilibrium measures for geodesic flow on locally CAT(1) spaces; these are geodesic metric spaces which generalize negative curvature Riemannian manifolds by having the “thin triangle” property.

9265

Monday 2/5 4:10 PM

Anton M. Zeitlin, Louisiana State University

Quantum Integrable Systems and Enumerative Geometry
 Quantum Integrable Systems and Enumerative Geometry
 02/05/2018
 4:10 PM  5:00 PM
 C304 Wells Hall
 Anton M. Zeitlin, Louisiana State University
The correspondence between integrable systems and enumerative geometry
started roughly 25 years ago in the works of Givental and his collaborators,
studying quantum cohomology and quantum Ktheory. Around 10 years ago,
physicists Nekrasov and Shatashvili proposed an unexpected relation between
quantum Ktheory and quantum integrable systems based on quantum groups
within their studies of 3dimensional gauge theories. Their bold proposal
led to a lot of interesting developments in mathematics, bringing a new life
to older ideas of Givental, and enriching it with flavors of geometric
representation theory via the results of Braverman, Maulik, Nakajima, Okounkov
and many others. In this talk I will focus on recent breakthroughs in the
subject, leading to the proper mathematical understanding of NekrasovShatashvili
original papers as well as some other subsequent conjectures made by physicists.
Our main illustration of such a relation is an interplay between equivariant quantum Ktheory of the cotangent bundles to Grassmanians and the Heisenberg XXZ spin chain. We will also
discuss relation of equivariant quantum Ktheory of flag varieties and
manybody integrable systems of RuijsenaarsSchneider and Toda.

9268

Monday 2/5 4:10 PM

Charlotte Ure, MSU

Introduction to Descent Theory
 Introduction to Descent Theory
 02/05/2018
 4:10 PM  5:00 PM
 C517 Wells Hall
 Charlotte Ure, MSU
No abstract available.

13291

Tuesday 2/6 11:00 AM

Seonghyeon Jeong, MSU

Hölder regularity for solutions of the MongeAmpère equation
 Hölder regularity for solutions of the MongeAmpère equation
 02/06/2018
 11:00 AM  1:00 PM
 C517 Wells Hall
 Seonghyeon Jeong, MSU
No abstract available.

8243

Tuesday 2/6 2:00 PM

Boyu Zhang, Harvard University

Rectifiability and Minkowski bounds for the singular sets of multiplevalued harmonic spinors
 Rectifiability and Minkowski bounds for the singular sets of multiplevalued harmonic spinors
 02/06/2018
 2:00 PM  3:00 PM
 C304 Wells Hall
 Boyu Zhang, Harvard University
We prove that the singular set of a multiplevalued harmonic spinor on a 4manifold is 2rectifiable and has finite Minkowski content. This result improves a regularity result of Taubes in 2014. It implies more precise descriptions for the limit behavior of nonconvergent sequences of solutions to many important gaugetheoretic equations, such as the KapustinWitten equations, the VafaWitten equations, and the SeibergWitten equations with multiple spinors.

9254

Wednesday 2/7 4:10 PM

Vladimir Peller, Michigan State University

Absolute continuity of spectral shift
 Absolute continuity of spectral shift
 02/07/2018
 4:10 PM  5:00 PM
 C517 Wells Hall
 Vladimir Peller, Michigan State University
No abstract available.

9269

Wednesday 2/7 4:10 PM

Eylem Zeliha YILDIZ, MSU

Invertible Knot Concordances
 Invertible Knot Concordances
 02/07/2018
 4:10 PM  5:00 PM
 C204A Wells Hall
 Eylem Zeliha YILDIZ, MSU
In this talk I will give a constructive proof to " Let k be a knot in S1 ×S2 freely homotopic to S1 ×pt then S1 × pt bounds an invertible concordance and k splits (S1 × pt) × [0, 1]."

9267

Thursday 2/8 3:00 PM


Dynamical System Seminar Almost sure invariance principle for hyperbolic systems with singularities.
 Dynamical System Seminar Almost sure invariance principle for hyperbolic systems with singularities.
 02/08/2018
 3:00 PM  4:00 PM
 C517 Wells Hall

Speaker: Jianyu Chen, University of Massachusetts Amherst
Title: Almost sure invariance principle for hyperbolic systems with singularities.
Abstract: We investigate a wide class of twodimensional hyperbolic systems with singularities, and prove the almost sure invariance principle (ASIP) for the random process generated by sequences of dynamically H\"older observables. The observables could be unbounded, and the process may be nonstationary
and need not have linearly growing variances.
Our results apply to Sinai dispersing billiards and their conservative perturbations, as well as the induced systems of Bunimovich billiards. The random processes are not restricted to the ergodic sum, but applicable to entropy fluctuation, shrinking target problems, etc.

9266

Friday 2/9 4:10 PM

Anna Mazzucato, Pennsylvania State University

Optimal mixing and irregular transport by incompressible flows
 Optimal mixing and irregular transport by incompressible flows
 02/09/2018
 4:10 PM  5:00 PM
 C304 Wells Hall
 Anna Mazzucato, Pennsylvania State University
I will discuss transport of passive scalars by incompressible flows (such as a die in a fluid) and measures of optimal mixing and stirring under physical constraint on the flow. In particular, I will present recent results concerning examples of flows that achieve the optimal theoretical rate in the case of flows with a prescribed bound on certain Sobolev norms of the associated velocity, such as under an energy or an enstrophy budget. These examples are related to examples of (instantaneous) loss of Sobolev regularity for solutions to linear transport equation with nonLipschitz velocity.

9270

Monday 2/12 4:10 PM

Dennis Kriventsov, NYU Courant

Spectral Optimization and Free Boundary Problems
 Spectral Optimization and Free Boundary Problems
 02/12/2018
 4:10 PM  5:00 PM
 C304 Wells Hall
 Dennis Kriventsov, NYU Courant
A classic subject in analysis is the relationship between the spectrum of the Laplacian on a domain and that domain's geometry. One approach to understanding this relationship is to study domains which extremize some function of their spectrum under geometric constraints. I will explain how to attack these problems using tools from the calculus of variations to find solutions. A key difficulty with this method is showing that the optimizers (which are a priori very weak) are actually smooth domains, and I address this issue in some recent work with Fanghua Lin. Our results are based on relating spectral optimization problems to certain vectorvalued free boundary problems of Bernoulli type.

9275

Monday 2/12 5:00 PM


New directions in the MLC
 New directions in the MLC
 02/12/2018
 5:00 PM  6:00 PM
 C109 Wells Hall

We're hoping to share our experiences from different projects related to supporting student learning outside of the classroom to generate ideas about how the MLC can shift to facilitate more productive learning for our students.

9272

Tuesday 2/13 4:10 PM

Nick Ovenhouse, MSU

Cluster Expansions Using Snake Graphs
 Cluster Expansions Using Snake Graphs
 02/13/2018
 4:10 PM  5:00 PM
 C517 Wells Hall
 Nick Ovenhouse, MSU
We will begin by outlining the construction of a cluster algebra associated to any surface with boundary (and marked points). Then we will discuss a formula, due to Schiffler, which explicitly gives an arbitrary cluster variable as a Laurent monomial in the initial variables, using the perfect matchings of an associated graph, called a "snake graph".

10275

Wednesday 2/14 4:10 PM

Kumar, Sanjay Lakshman, MSU

Skein Theory and TuraevViro Invariant
 Skein Theory and TuraevViro Invariant
 02/14/2018
 4:10 PM  5:00 PM
 C204A Wells Hall
 Kumar, Sanjay Lakshman, MSU
This talk will be a brief introduction to the TuraevViro Invariant. The TuraevViro Invariant is a 3manifold invariant defined on a triangulation of a manifold. Using skeintheoretic methods, I will demonstrate a proof of its invariance with a technique known as chainmail. This technique illustrates a close relationship between the TuraevViro Invariant and the surgerypresentation invariants originally defined by Reshetikhin and Turaev.

10276

Thursday 2/15 11:00 AM

Martin Fraas, Virginia Tech

Quantization of conductance in gapped interacting systems
 Quantization of conductance in gapped interacting systems
 02/15/2018
 11:00 AM  12:00 PM
 C304 Wells Hall
 Martin Fraas, Virginia Tech
I will present two closely connected results. The first is the linear response theory in gapped interacting systems, and a proof of the associated Kubo formula. The second is a short proof of the quantization of the Hall conductance for gapped interacting quantum lattice systems on the twodimensional torus.

9271

Friday 2/16 4:10 PM

Brent Nelson, UC Berkeley

Nontracial free transport
 Nontracial free transport
 02/16/2018
 4:10 PM  5:00 PM
 C304 Wells Hall
 Brent Nelson, UC Berkeley
Von Neumann algebras are certain *subalgebras of bounded operators acting on a Hilbert space. They are generally thought of as noncommutative measure spaces and offer connections to many fields of mathematics (e.g. group theory, lowdimensional topology, logic, ergodic theory, and random matrix theory to name a few). In some instances an analogy with probability spaces is more appropriate, and indeed this is precisely what informs the field of free probability, wherein one uses noncommutative analogs of probabilistic notions to study the structure of von Neumann algebras. One particular example of this is free transport. In probability theory, transport refers to a measurable map between probability spaces that pushes one measure onto the other. Following work of Brenier in 1991, transportation theory has known great success. Free transport, the noncommutative analog that was introduced by Guionnet and Shlyakhtenko in 2014, offers methods for proving isomorphisms between von Neumann algebras. In this talk, I will discuss these ideas as well my work, which used free transport to prove isomorphisms between certain socalled "nontracial" von Neumann algebras.

7214

Friday 2/16 4:10 PM

Ekaterina Rapinchuk, MSU

Auction Dynamics for SemiSupervised Data Classification
 Auction Dynamics for SemiSupervised Data Classification
 02/16/2018
 4:10 PM  5:00 PM
 B117 Wells Hall
 Ekaterina Rapinchuk, MSU
We reinterpret the semisupervised data classification problem using an auction dynamics framework (inspired by real life auctions) in which elements of the data set make bids to the class of their choice. This leads to a novel forward and reverse auction method for data classification that readily incorporates volume/classsize constraints into an accurate and efficient algorithm requiring remarkably little training/labeled data. We prove that the algorithm is unconditionally stable, and state its average and worst case time complexity.

9274

Monday 2/19 4:10 PM

Steve Plemmons, MSU

Teaching Technology Updates
 Teaching Technology Updates
 02/19/2018
 4:10 PM  5:00 PM
 C109 Wells Hall
 Steve Plemmons, MSU
No abstract available.

12277

Tuesday 2/20 4:10 PM

Alexander Wilson, MSU

Determining the Regularity of Formal Languages
 Determining the Regularity of Formal Languages
 02/20/2018
 4:10 PM  5:00 PM
 C517 Wells Hall
 Alexander Wilson, MSU
The concept of a regular language is very useful for computers parsing data and generally in theoretical computer science. We will define a formal language, what makes a formal language regular, and methods to decide whether a language is regular.

12283

Wednesday 2/21 4:10 PM

Brandon Bavier, MSU

An Introduction to Hyperbolic Knots
 An Introduction to Hyperbolic Knots
 02/21/2018
 4:10 PM  5:00 PM
 C204A Wells Hall
 Brandon Bavier, MSU
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. This talk is an introduction to hyperbolic knots, knots whose complement admits a hyperbolic structure. This will include a couple of diagramatic conditions to detect hyperbolicity, as well as using the structure to calculate bounds on the volume of the complement.

9252

Wednesday 2/21 4:10 PM

Alexander Volberg, MSU

Fractional Laplacians on Hamming cube and its Poincar\'e inequalities
 Fractional Laplacians on Hamming cube and its Poincar\'e inequalities
 02/21/2018
 4:10 PM  5:00 PM
 C517 Wells Hall
 Alexander Volberg, MSU
No abstract available.

12281

Thursday 2/22 3:00 PM


Dynamical System Seminar:
 Dynamical System Seminar:
 02/22/2018
 3:00 PM  4:00 PM
 C517 Wells Hall

Speaker: Huyi Hu, MSU
Title: Infimum of the Metric Entropy of Anosov Systems
Abstract: We show that any Anosov diffeomorphism can be deformed continuously within the space of all Anosov diffeomorphisms in a way that the metric entropy with respect to the SRB measure can be arbitrarily close to $0$. That is, there is a path $\{f_t: t\in (0,1]\}$ such that $f_1=f$, and for each $t$, $f_t$ is an Anosov diffeomorphism, and $\lim_{t\to 0} h_{\mu_t}(f_t)=0$, where $\mu_t$ is an SRB measure of $f_t$ and $h_{\mu_t}(f_t)$ denote the metric entropy.
Similar results can be obtained within the space of volume preserving Anosov diffeomorphisms.

10277

Thursday 2/22 3:00 PM

Mohammad Jahangoshahi, University of Chicago

Smoothness of the partition function for multiple SchrammLoewner evolutions in simply connected domains
 Smoothness of the partition function for multiple SchrammLoewner evolutions in simply connected domains
 02/22/2018
 3:00 PM  3:50 PM
 C405 Wells Hall
 Mohammad Jahangoshahi, University of Chicago
We consider the measure on multiple chordal SchrammLoewner evolution curves. We establish a derivative estimate using properties of the Poisson kernel and use it to give a direct proof that the partition function is C^2 if \kappa<4.

9264

Friday 2/23 4:10 PM

Mike O'Neil, Courant Institute, NYU

Fast highorder CADindependent Nystrom methods for frequencydomain electromagnetics
 Fast highorder CADindependent Nystrom methods for frequencydomain electromagnetics
 02/23/2018
 4:10 PM  5:00 PM
 C304 Wells Hall
 Mike O'Neil, Courant Institute, NYU
Over the past three decades, there has been a myriad of advances in fast algorithms, singular quadrature, and integral equation theory relevant to the computational solution of partial diﬀerential equations, namely Maxwell’s equations, which govern the propagation of electromagnetic radiation. These advances have culminated in the ability to perform largescale computations, but highorder accurate applications to solving integral equations has mostly been restricted to trivial geometries deﬁned by analytic formulas or large analytically deﬁned patches. These geometric descriptions are very limiting, given the advances that have been made in threedimensional modeling software and fabrication. In this talk, I will describe recent advances in the numerical discretization of boundary integral equations along surfaces in three dimensions, new techniques for computing the resulting singular integrals, and the coupling of these techniques to fast algorithms, such as the fast multipole method.

12280

Monday 2/26 12:00 PM

Lynmarie Posey and Kristen Bieda, MSU

Mathematical Knowledge for Teaching Chemistry
 Mathematical Knowledge for Teaching Chemistry
 02/26/2018
 12:00 PM  1:00 PM
 252 EH
 Lynmarie Posey and Kristen Bieda, MSU
Progress toward STEM degree depends not only on completing required mathematics courses but also being able to successfully use mathematics to support learning in science courses. Introductory college chemistry courses are often the first place where inadequate preparation in mathematics impedes students’ learning in science. In this talk, Drs. Posey and Bieda will share their efforts to strategically incorporate mathematics support for students in Introductory Chemistry. Our findings suggest important implications for developing students’ conceptual understanding in mathematics courses. We will also share what we have learned about forging and sustaining an interdisciplinary research project.

13286

Monday 2/26 4:10 PM

Chuangtian Guan, MSU

Structure of finitely generated Lambdamodules
 Structure of finitely generated Lambdamodules
 02/26/2018
 4:10 PM  5:00 PM
 C517 Wells Hall
 Chuangtian Guan, MSU
No abstract available.

12278

Tuesday 2/27 4:10 PM

Oliver Pechenik, University of Michigan

Taking the long way home: Orbits of plane partitions
 Taking the long way home: Orbits of plane partitions
 02/27/2018
 4:10 PM  5:00 PM
 C304 Wells Hall
 Oliver Pechenik, University of Michigan
Plane partitions are piles of cubes stacked in the corner of a room. P. Cameron and D. FonderFlaass (1995) studied a simple action on such piles, whose dynamics are nonetheless quite mysterious. In particular, repeating this action will always eventually return the original pile, but sometimes the voyage is much longer than expected. Motivated by some deep problems in algebraic geometry, H. Thomas and A. Yong (2009) introduced a suite of combinatorial algorithms on certain grids of numbers. In particular, there is a beautiful Ktheoretic promotion operator, which again has some mysteriously large orbits, despite its simple combinatorial definition. We'll see how these two mysteries are in fact the same mystery, and use this relation to explain special cases of both actions. (Based on joint work with Kevin Dilks and Jessica Striker)

8236

Wednesday 2/28 1:45 PM

Jennifer LangerOsuna, Stanford University

Fostering productive and inclusive collaborative mathematics classrooms
 Fostering productive and inclusive collaborative mathematics classrooms
 02/28/2018
 1:45 PM  3:15 PM
 252 EH
 Jennifer LangerOsuna, Stanford University
Studentled group work is an increasingly common activity in K12 mathematics classrooms. Students are expected to debate ideas, justify conjectures, and come to consensus on reasonable approaches to solving problems. Yet several studies have shown that some students become unduly influential, while others' contributions are routinely marginalized. This talk pursues the question, how can collaborative mathematics classrooms foster both equity and productivity? To do so, this talk begins with an exploration of the role of authority relations during collaborative math activity, followed by new design research, in partnership with local schools, based on the results of earlier, exploratory work. The talk closes by contextualizing these projects in a broader body of work focused on examining classrooms designed to equitably engage students from diverse backgrounds in intellectually productive mathematical activity.

8237

Thursday 3/1 2:00 PM

Matthias Nagel, McMaster University, Canada

Triple linking numbers and surface systems
 Triple linking numbers and surface systems
 03/01/2018
 2:00 PM  3:00 PM
 C304 Wells Hall
 Matthias Nagel, McMaster University, Canada
We relate fillability of two link exteriors,
and the question when two links admit homeomorphic
surface systems to (a refinement of) Milnor’s triple
linking numbers. This extends a theorem of DavisRoth
to include also links with nonvanishing linking numbers.
This is joint work with C. Davis, P. Orson, and M. Powell.

12285

Thursday 3/1 3:00 PM


Optimal Large Deviation Theory for analytic quasiperiodic Schr\"odinger cocycle and H\"older regularity of the Lyapunov exponent
 Optimal Large Deviation Theory for analytic quasiperiodic Schr\"odinger cocycle and H\"older regularity of the Lyapunov exponent
 03/01/2018
 3:00 PM  4:00 PM
 C517 Wells Hall

Abstract:
We consider 1d discrete quasiperiodic Schr\"odinger equations and the associated Schr\"odinger cocycles. Suppose the potential is real analytic function with bounded extension, assume positive Lyapunov exponents. We prove some refined Large Deviation Theory (LDT) for any irrational frequency in an exponential regime with respect to the Lyapunov exponent. The large deviation estimates imply some optimal H\"older continuity results of the Lyapunov exponents and the integrated density of states. For small Lyapunov exponent regime, we show that the local H\"older exponent is independent of energy E for Liouville frequency. In the large coupling regime, we show that the local H\"older exponent is independent of the coupling constant. Previously, such coupling independency is only known in the case where the potential is a trigonometric polynomial with (Strong) Diophantine frequency.

13285

Thursday 3/1 3:10 PM

John Machacek, MSU

Upper cluster algebras and choice of ground ring
 Upper cluster algebras and choice of ground ring
 03/01/2018
 3:10 PM  4:00 PM
 C329 Wells Hall
 John Machacek, MSU
Cluster algebra structures often appear naturally in coordinate rings of algebraic varieties. In many cases the coordinate ring ends up being isomorphic to the corresponding upper cluster algebra. The choice of ground ring the cluster algebra is generated over determines if the cluster algebra consists of regular functions on the algebraic variety. We will discuss how to the choice of ground effects wether or not the cluster algebra coincides with its upper cluster algebra.

11277

Thursday 3/1 4:10 PM

Selim Esedoglu, University of Michigan

Algorithms for mean curvature motion of networks
 Algorithms for mean curvature motion of networks
 03/01/2018
 4:10 PM  5:00 PM
 C304 Wells Hall
 Selim Esedoglu, University of Michigan
Motion by mean curvature for networks of surfaces arises in a variety of
applications, such as the dynamics of foam and the evolution of
microstructure in polycrystalline materials. It is steepest descent
(gradient flow) for an energy: the sum of the areas of the surfaces
constituting the network.
During the evolution, surfaces may collide and junctions (where three or
more surfaces meet) may merge and split off in myriad ways as the
network coarsens in the process of decreasing its energy. The first idea
that comes to mind for simulating this evolution  parametrizing the
surfaces and explicitly specifying rules for cutting and pasting when
collisions occur  gets hopelessly complicated. Instead, one looks for
algorithms that generate the correct motion, including all the necessary
topological changes, indirectly but automatically via just a couple of
simple operations.
An almost miraculously elegant such algorithm, known as threshold
dynamics, was proposed by Merriman, Bence, and Osher in 1992. Extending
this algorithm, while preserving its simplicity, to more general
energies where each surface in the network is measured by a different,
possibly anisotropic, notion of area requires new mathematical
understanding of the original version, which then elucidates a
systematic path to new algorithms.

9245

Thursday 3/8 2:00 PM

No seminar

Spring Break
 Spring Break
 03/08/2018
 2:00 PM  3:00 PM
 C304 Wells Hall
 No seminar
No abstract available.

9273

Monday 3/12 4:10 PM

Valentina Maddalena, MSU

New Approaches to MTH 126: Survey of Calculus II
 New Approaches to MTH 126: Survey of Calculus II
 03/12/2018
 4:10 PM  5:00 PM
 C109 Wells Hall
 Valentina Maddalena, MSU
No abstract available.

13298

Monday 3/12 4:10 PM

Nick Rekuski, MSU

Schubert Calculus and Cohomology of Grassmannians
 Schubert Calculus and Cohomology of Grassmannians
 03/12/2018
 4:10 PM  5:00 PM
 C517 Wells Hall
 Nick Rekuski, MSU
In this first lecture, we shall begin by constructing a CWstructure for the complex Grassmannian. We will then begin our exploitation of this CWstructure with the goal of answering questions in enumerative geometry. These questions include “How many lines lie on the intersection of two quadric hypersurfaces in P^4?” and “Given four smooth curves in P^3, how many lines will intersect all four curves?”

13293

Monday 3/12 5:30 PM

Alex Lubotzky, Hebrew University

Real applications of nonreal numbers: Ramanujan graphs (First Phillips Lecture)
 Real applications of nonreal numbers: Ramanujan graphs (First Phillips Lecture)
 03/12/2018
 5:30 PM  6:30 PM

 Alex Lubotzky, Hebrew University
The real numbers form a completion of the field of rational numbers. We will describe the fields of padic numbers which are different completions of the rationals. Once they are defined, one can study analysis and geometry over them. While being very abstract, the main motivation for studying them came from number theory. Developments in the last 23 decades shows various applications to the real world: communication networks, etc. This is done via expander graphs and Ramanujna grpahs which are "Riemann surfaces over these padic fields". All notions will be explained.

13300

Tuesday 3/13 11:00 AM

Leonardo Abbrescia, MSU

Local and Global existence of L2 solutions to the KdV equation
 Local and Global existence of L2 solutions to the KdV equation
 03/13/2018
 11:00 AM  1:00 PM
 C517 Wells Hall
 Leonardo Abbrescia, MSU
No abstract available.

13295

Tuesday 3/13 4:00 PM

Alex Lubotzky, Hebrew University

High dimensional expanders: From Ramanujan graphs to Ramanujan complexes (Second Phillips Lecture)
 High dimensional expanders: From Ramanujan graphs to Ramanujan complexes (Second Phillips Lecture)
 03/13/2018
 4:00 PM  5:00 PM
 115 International Center
 Alex Lubotzky, Hebrew University
Expander graphs in general, and Ramanujan graphs, in particular, have played a major role in combinatorics and computer science in the last 4 decades and more recently also in pure math. Approximately 10 years ago, a theory of Ramanujan complexes was developed by Li, LubotzkySamuelsVishne and others. In recent years a high dimensional theory of expanders is emerging. The notions of geometric and topological expanders were defined by Gromov in 2010 who proved that the complete d dimensional simplicial complexes are such. He raised the basic question of existence of such bounded degree complexes of dimension d greater than 1. Ramanujan complexes were shown to be geometric expanders by FoxGromovLafforgueNaorPach in 2013, but it was left open if they are also topological expanders. By developing new isoperimetric methods for “locally minimal small” F_2cochains, it was shown recently by Kaufman Kazdhan Lubotzky for small dimensions and EvraKaufman for all dimensions that the dskeletons of (d+1)dimensional Ramanujan complexes provide bounded degree topological expanders. This answers Gromov’s original problem, but still leaves open whether the Ramanujan complexes themselves are topological expanders. We will describe these developments and the general area of high dimensional expanders and some of its open problems.

13296

Wednesday 3/14 10:00 AM

Alex Lubotzky, Hebrew University

Groups' approximation, stability and high dimensional expanders (Third Phillips Lecture)
 Groups' approximation, stability and high dimensional expanders (Third Phillips Lecture)
 03/14/2018
 10:00 AM  11:00 AM
 C304 Wells Hall
 Alex Lubotzky, Hebrew University
Several wellknown open questions (such as: are all groups sofic or hyperlinear?) have a common form: can all groups be approximated by asymptotic homomorphisms into the symmetric groups Sym(n) (in the sofic case) or the unitary groups U(n) (in the hyperlinear case)?
In the case of U(n), the question can be asked with respect to different metrics and norms. We answer, for the first time, one of these versions, showing that there exist fintely presented groups which are not approximated by U(n) with respect to the Frobenius (=L_2)norm.
The strategy is via the notion of “stability”: some higher dimensional cohomology vanishing phenomena is proven to imply stability and using higher dimensional expanders, it is shown that some nonresidually finite groups (central extensions of some lattices in padic Lie groups) are Frobenious stable and hence cannot be Frobenius approximated.
All notions will be explained. Joint work with M. De Chiffre, L. Glebsky and A. Thom.

13302

Wednesday 3/14 3:00 PM

Prof. Chris Marx , Oberlin College

Hiring Cycle and Expectations for Faculty at Liberal Arts Schools
 Hiring Cycle and Expectations for Faculty at Liberal Arts Schools
 03/14/2018
 3:00 PM  4:00 PM
 C304 Wells Hall
 Prof. Chris Marx , Oberlin College
This seminar is aimed at postdocs and graduate students who will be on the job market soon, but all are welcome.
The seminar will start with a short (20 minute) presentation on Chris Marx about the hiring cycle and expectations for faculty at liberal arts schools. Afterwards, there will be a discussion/question and answer period.

13299

Wednesday 3/14 4:10 PM

Wenzhao Chen, MSU

Correction term, diagonalization theorem and the sliceness of 2bridge knots
 Correction term, diagonalization theorem and the sliceness of 2bridge knots
 03/14/2018
 4:10 PM  5:00 PM
 C204A Wells Hall
 Wenzhao Chen, MSU
About a decade ago, Lisca classified which 2bridge knots are smoothly slice using an obstruction derived from Donaldson's diagonaliztion theorem. It is known that the diagonalization theorem can be proved using the Heegaard Floer correction term. Moreover, this correction term can also be used to construct a slicing obstruction for knots. In this expository talk, I will explain Josh Greene's proof that these two slicing obstructions actually coincide for 2bridge knots.

13294

Thursday 3/15 11:00 AM

Chris Marx, Oberlin College

Dependence of the density of states on the probability distribution for discrete random Schrödinger operators
 Dependence of the density of states on the probability distribution for discrete random Schrödinger operators
 03/15/2018
 11:00 AM  12:00 PM
 C304 Wells Hall
 Chris Marx, Oberlin College
We prove the Höldercontinuity of the density of states measure (DOSm) and the integrated density of states (IDS) with respect to the probability distribution for discrete random Schrödinger operators with a finiterange potential. In particular, our result implies that the DOSm and the IDS for smooth approximations of the Bernoulli distribution converge to the corresponding quantities for the BernoulliAnderson model. Other applications of the techniques are given to the dependency of the DOSm and IDS on the disorder, and the continuity of the Lyapunov exponent in the weakdisorder regime. The talk is based on recent joint work with Peter Hislop (Univ. of Kentucky).

12282

Thursday 3/15 2:00 PM

Kristen Hendricks, MSU

Connected Heegaard Floer homology and homology cobordism
 Connected Heegaard Floer homology and homology cobordism
 03/15/2018
 2:00 PM  3:00 PM
 C304 Wells Hall
 Kristen Hendricks, MSU
We study applications of Heegaard Floer homology to homology cobordism. In particular, to a homology sphere Y, we define a module HF_conn(Y), called the connected Heegaard Floer homology of Y, and show that this module is invariant under homology cobordism and isomorphic to a summand of HF_red(Y). The definition of this invariant relies on involutive Heegaard Floer homology. We use this to define a new filtration on the homology cobordism group, and to give a reproof of Furuta's theorem. This is joint work with Jen Hom and Tye Lidman.

13301

Thursday 3/15 3:00 PM


Unstable entropy and pressure for partially hyperbolic systems
 Unstable entropy and pressure for partially hyperbolic systems
 03/15/2018
 3:00 PM  4:00 PM
 C517 Wells Hall

We study ergodic properties caused by the unstable part of partially hyperbolic systems. We define unstable metric entropy, topological entropy and pressures, and prove the corresponding variational principles. For unstable metric entropy we obtain affineness, upper semicontinuity and a version of ShannonMcMillanBreiman theorem. We also obtain existence of Gibbs ustates, differentiability properties of unstable pressure, such as tangent functionals, Gateaux differentiability and Frechet differentiability.

13308

Monday 3/19 4:10 PM

Nick Rekuski, MSU

Schubert Calculus and Cohomology of Grassmannains
 Schubert Calculus and Cohomology of Grassmannains
 03/19/2018
 4:10 PM  5:00 PM
 C517 Wells Hall
 Nick Rekuski, MSU
In this second talk, we will present formulas for the multiplicative structure of the Grassmannian’s cohomology. Using these formulas, we shall answer the problems raised last time and more. These problems will include “Fix four lines in P^3. How many lines will intersect all four of these lines?” and “Fix four curves in P^3. How many lines will intersect all four of these curves?”

13304

Tuesday 3/20 4:10 PM

Guowei Wei; Vladimir Peller; Mark Iwen

Faculty Research Presentations
 Faculty Research Presentations
 03/20/2018
 4:10 PM  5:10 PM
 C304 Wells Hall
 Guowei Wei; Vladimir Peller; Mark Iwen
These talks are aimed at first and second year students. Faculty will give an overview of problems that a student could work on. At the 3/20 seminar, we will have 1) Guowei Wei, Is it time for a great chemistry between mathematics and biology?; 2) Vladimir Peller, Contemporary problems of operator theory; and 3) Mark Iwen, Computational Nonlinear Approximation in Signal Processing and Inverse Problems.

13303

Wednesday 3/21 4:10 PM

Tyler Bongers, MSU

Holder regularity of quasiconformal maps
 Holder regularity of quasiconformal maps
 03/21/2018
 4:10 PM  5:00 PM
 C517 Wells Hall
 Tyler Bongers, MSU
Quasiconformal maps in the complex plane are homeomorphisms that satisfy certain geometric distortion inequalities; infinitesimally, they map circles to ellipses with bounded eccentricity. The local distortion properties of these maps give rise to a certain degree of global regularity and Holder continuity. In this talk, we will discuss improved lower bounds for the Holder continuity of these maps; the analysis is based on combining the isoperimetric inequality with a study of the length of quasicircles. Furthermore, the extremizers for Holder continuity can be characterized, and we will also give some applications to solutions to elliptic partial differential equations.

7202

Thursday 3/22 2:00 PM

Adam Lowrance, Vassar College

Almost alternating, Turaev genus one, and semiadequate links
 Almost alternating, Turaev genus one, and semiadequate links
 03/22/2018
 2:00 PM  3:00 PM
 C304 Wells Hall
 Adam Lowrance, Vassar College
A link is almost alternating if it is nonalternating and has a diagram such that one crossing change transforms it into an alternating diagram. Turaev genus one links are a certain generalization of nonalternating Montesinos links. A link is semiadequate if it has a diagram where at least one of the allA or allB Kauffman state graphs is loopless. In this talk, we discuss the Jones polynomial and Khovanov homology of links in these three classes, and we discuss open problems about the relationships between the three classes.

13305

Thursday 3/22 4:10 PM

Rajesh Kulkarni; Matt Hirn; Di Liu

Faculty Research Presentations
 Faculty Research Presentations
 03/22/2018
 4:10 PM  5:10 PM
 C304 Wells Hall
 Rajesh Kulkarni; Matt Hirn; Di Liu
These talks are aimed at first and second year students. Faculty will give an overview of problems that a student could work on. At the 3/22 seminar, we will have 1) Rajesh Kulkarni; 2) Matt Hirn, Understanding high dimensional data analysis and machine learning via harmonic analysis; 3) Di Liu

13306

Friday 3/23 4:10 PM

Shitao Liu, Clemson University

Observability of the viscoelastic wave equation
 Observability of the viscoelastic wave equation
 03/23/2018
 4:10 PM  5:00 PM
 C100 Wells Hall
 Shitao Liu, Clemson University
In this talk we give a proof of the Neumann boundary observability inequality for the viscoelastic wave equation in an arbitrary space dimension. To do this, we first give a new proof of the boundary observability for the classical wave equation that extends the harmonic analysis perspective of D.L.Russell to higher space dimensions. We then argue by perturbation to show the Riesz sequence property of the corresponding harmonic system for the viscoelastic wave equation.

7215

Friday 3/23 4:10 PM

Kristen Hendricks, Mathematics, MSU

Avoiding Collisions and Braiding String: Configuration Spaces and the Braid Group
 Avoiding Collisions and Braiding String: Configuration Spaces and the Braid Group
 03/23/2018
 4:10 PM  5:00 PM
 C304 Wells Hall
 Kristen Hendricks, Mathematics, MSU
There are many realworld problems that amount to studying the possible paths of n objects through a space X such that those objects never collide. (Examples include flight traffic patterns around an airport, or automated carts moving around a factory floor.) We think about such problems by studying paths in configuration spaces, spaces consisting of ordered sets of distinct points in X. In one of the simplest cases, these spaces turn out to be closely linked to a seemingly different mathematical object, the nstranded braid group. We introduce configuration spaces and the braid group and learn about their relationship.

13311

Tuesday 3/27 4:10 PM

John Machacek, MSU

A hypergraphic combinatorial Hopf algebra
 A hypergraphic combinatorial Hopf algebra
 03/27/2018
 4:10 PM  5:00 PM
 C304 Wells Hall
 John Machacek, MSU
We will give a brief introduction to combinatorial Hopf algebras using a Hopf algebra structure on hypergraphs as the main example. Combinatorial reciprocity results that can be obtain by combining AguiarBergeronSottile character theory and antipode formulas will be emphasized. In particular, we will see a generalization of Stanley's theorem on acyclic orientations.

8234

Wednesday 3/28 4:10 PM

Robin Neumayer, Northwestern University

On minimizers and critical points for anisotropic isoperimetric problems
 On minimizers and critical points for anisotropic isoperimetric problems
 03/28/2018
 4:10 PM  5:00 PM
 C517 Wells Hall
 Robin Neumayer, Northwestern University
Anisotropic surface energies are a natural generalization of the perimeter that arise in models for equilibrium shapes of crystals. We discuss some recent results for anisotropic isoperimetric problems concerning the strong quantitative stability of minimizers, bubbling phenomena for critical points, and a weak Alexandrov theorem for nonsmooth anisotropies. Part of this talk is based on joint work with Delgadino, Maggi, and Mihaila.

9243

Thursday 3/29 2:00 PM

Ramanujan Santharoubane, University of Virginia

Asymptotic of quantum representations of surface groups
 Asymptotic of quantum representations of surface groups
 03/29/2018
 2:00 PM  3:00 PM
 C304 Wells Hall
 Ramanujan Santharoubane, University of Virginia
In a previous work with Thomas Koberda we defined actions of surface groups on the vector spaces coming from the WittenReshetikhinTuraev TQFT. For l a given loop in a surface we can define the trace of the associated operator. Actually, this is a sequence of invariant depending on a sequence of roots of unity. For any z on the unit circle, we study the asymptotic of this sequence of invariant when the sequence of roots of unity converges to z. The main theorem says that this asymptotic is determined by the evaluation at z of a Laurent polynomial depending only on l. This polynomial can be viewed as a Jones polynomial for surface groups. The main corollary concerns the socalled AMU conjecture which relates TQFT representations of mapping class groups to the NielsenThurston classification.
This talk represent a joint work with Julien Marché.

13309

Thursday 3/29 4:10 PM

Parimala Raman, Emory University

Quadratic forms and Clifford algebras
 Quadratic forms and Clifford algebras
 03/29/2018
 4:10 PM  5:00 PM
 C304 Wells Hall
 Parimala Raman, Emory University
Clifford algebras play an important role in the classification of quadratic forms over number fields. Surprisingly, the also play a critical role in studying the isotropy (existence of nontrivial zeros) of quadratic forms over function fields of curves over totally imaginary number fields. We shall explain some open questions concerning isotropy of quadratic forms over function fields of curves over number fields and their connection to Clifford algebras.

13312

Tuesday 4/3 4:10 PM

John Machacek, MSU

Hypergraphic polytopes
 Hypergraphic polytopes
 04/03/2018
 4:10 PM  5:00 PM
 C304 Wells Hall
 John Machacek, MSU
We will define and study hypergraphic polytopes. These polytopes make up a proper subset of all generalized permutahedra and include all graphic zonotopes. We will show how the normal fan of hypergraphic polytopes can be understood in terms of acyclic orientations of hypergraphs. This will provide additional understanding of the antipode of the hypergraphic Hopf algebra from last week.

13287

Wednesday 4/4 3:00 PM

Evangelia Gazaki, University of Michigan

Kummer Theory on products of elliptic curves over a padic field
 Kummer Theory on products of elliptic curves over a padic field
 04/04/2018
 3:00 PM  4:00 PM
 C304 Wells Hall
 Evangelia Gazaki, University of Michigan
In this talk I will present some very recent work, joint with I. Leal about zerocycles on a product X=E_1 X E_2 of two elliptic curves over a padic field. In this work we prove that the cycle map to etale cohomology is injective for a large variety of cases, using a method introduced by Raskind and Spiess, namely using an analogue of the Milnor Kgroup of a field, defined by Kato and Somekawa. As an application, we obtain some new results about zerocycles over local and global fields.
Throughout the talk I will only assume some basic familiarity with elliptic curves. Everything else will be selfcontained and explained in the talk.

12279

Wednesday 4/4 4:10 PM

Armin Schikorra, University of Pittsburgh

TBA
 TBA
 04/04/2018
 4:10 PM  5:00 PM
 C517 Wells Hall
 Armin Schikorra, University of Pittsburgh
No abstract available.

9246

Thursday 4/5 2:00 PM

Juanita PinzonCalcedo, North Carolina State

TBA
 TBA
 04/05/2018
 2:00 PM  3:00 PM
 C304 Wells Hall
 Juanita PinzonCalcedo, North Carolina State
No abstract available.

13288

Thursday 4/5 4:10 PM

Gopal Prasad, University of Michigan

Number theory in geometry
 Number theory in geometry
 04/05/2018
 4:10 PM  5:00 PM
 C304 Wells Hall
 Gopal Prasad, University of Michigan
Historically, it is geometry which led to important developments in several areas of mathematics including number theory. But recently there have been several instances of number theory being applied to settle important questions in geometry. I will talk about two problems in whose solution number theory has been used in a crucial way.
The first one, settled in collaboration with SaiKee Yeung, is classification of fake projective planes and their higher dimensional analogs. (I recall that fake projective planes are smooth projective complex surfaces with same Betti numbers as the complex projective plane, but which are not isomorphic to the complex projective plane. The first such surface was constructed by David Mumford.)
The second problem concerns compact Riemannian manifolds and it has the following very interesting formulation due to Mark Kac: “Can one hear the shape of a drum?”. In precise mathematical terms, the question asks whether two compact Riemannian manifolds with same spectrum (i.e., the set of eigenvalues counted with multiplicities) are isometric. The answer is in general “no”. However, Andrei Rapinchuk and I investigated Kac’s question, using number theoretic results and tools, for a particularly nice class of manifolds, namely locally symmetric spaces. The answer turned out to be very interesting and has led to several other developments which, if time permits, I will mention.

13310

Friday 4/6 4:10 PM

Moon Duchin, Tufts University

Random walks and gerrymandering
 Random walks and gerrymandering
 04/06/2018
 4:10 PM  5:00 PM
 B117 Wells Hall
 Moon Duchin, Tufts University
A familiar idea in math and computing has recently made a big splash in redistricting lawsuits: if you want to understand a large, complicated space with mysterious structure, you should just drop yourself down in the space and walk around randomly for a long time. What you see when you explore may produce a good representative sample of the space, even if your exploration is way shorter than the time it would take to see everything. This idea is gaining traction in trying to understand whether a congressional redistricting plan is reasonable or not, by comparing it to a huge ensemble of other possibilities found by random walk in the space of plans. I'll overview some of these ideas and tell you how they've played out in Wisconsin, North Carolina, and Pennsylvania.

13297

Monday 4/9 2:00 PM

Aleksander Doan, Stony Brook University

TBA
 TBA
 04/09/2018
 2:00 PM  3:00 PM
 C304 Wells Hall
 Aleksander Doan, Stony Brook University
No abstract available.

9244

Thursday 4/12 2:00 PM

Adam Saltz, University of Georgia

TBA
 TBA
 04/12/2018
 2:00 PM  3:00 PM
 C304 Wells Hall
 Adam Saltz, University of Georgia
No abstract available.

13289

Thursday 4/12 4:10 PM

Maria Gualdani, George Washington University

TBA
 TBA
 04/12/2018
 4:10 PM  5:00 PM
 C304 Wells Hall
 Maria Gualdani, George Washington University
No abstract available.

7204

Monday 4/16 4:10 PM

Rita Gitik

A New Algorithm in Group Theory
 A New Algorithm in Group Theory
 04/16/2018
 4:10 PM  5:30 PM
 C304 Wells Hall
 Rita Gitik
We describe a new algorithm which determines if the intersection of a quasiconvex subgroup of a negatively curved group with any of its conjugates is infinite. The algorithm is based on the concepts of a coset graph and a weakly Nielsen generating set of a subgroup. We also give a new proof of decidability of a membership problem for quasiconvex subgroups of negatively curved groups.

13313

Wednesday 4/18 3:30 PM

Elizabeth de Freitas, Manchester Metropolitan University

What is a Mathematical Concept?
 What is a Mathematical Concept?
 04/18/2018
 3:30 PM  5:00 PM
 252 EH
 Elizabeth de Freitas, Manchester Metropolitan University
This presentation explores alternative approaches to the question: What is a mathematical concept? Philosophical and historical insights about the nature of mathematical concepts are discussed, with special attention to how concepts emerge and are established through particular mathematical practices. Such work shifts our attention to the material labour and onto generative nature of mathematical activity. New mathematical concepts emerge and old ones are creatively deformed when embodied practices redistribute what is considered sensible and perceptible. I discuss the pedagogical implications of this approach, and the important way such theoretical framing shifts our thinking about mathematics dis/ability. My aim is to rescue mathematical concepts from the staid curricular lists which entomb them, and to consider examples of how we might reanimate concepts in classroom activity.

9262

Thursday 4/19 2:00 PM

Calvin Woo, Indiana University

TBA
 TBA
 04/19/2018
 2:00 PM  3:00 PM
 C304 Wells Hall
 Calvin Woo, Indiana University
No abstract available.

13290

Thursday 4/19 4:10 PM

Zinovy Reichstein, University of British Columbia

TBA
 TBA
 04/19/2018
 4:10 PM  5:00 PM
 C304 Wells Hall
 Zinovy Reichstein, University of British Columbia
No abstract available.

13307

Friday 4/20 4:10 PM

HauTieng Wu, Duke University

Sensor fusion via two types of diffusion — with sleep dynamics and fetal health as examples.
 Sensor fusion via two types of diffusion — with sleep dynamics and fetal health as examples.
 04/20/2018
 4:10 PM  5:00 PM
 C304 Wells Hall
 HauTieng Wu, Duke University
Quantifying the intrinsic structure from a given massive dataset, which is often nonlinear and complex, is a common challenge shared in almost all scientific fields, including data science. The problem is becoming more challenging when the data are from multiple sensors with heterogenous data types. The diffusion geometry is a flexible framework for this challenge that has led to several convincing results with solid theoretical backup. We will discuss how to apply the diffusion geometry, particularly the alternating diffusion and commutator, to deal with the sensor fusion problem. Its application to the sleep dynamics analysis and fetal electrocardiogram analysis will be discussed.

13314

Thursday 4/26 4:10 PM

Ben McReynolds, Purdue Univeresity

TBA
 TBA
 04/26/2018
 4:10 PM  5:00 PM
 C304 Wells Hall
 Ben McReynolds, Purdue Univeresity
No abstract available.
