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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

13322

Tuesday 4/3 10:20 AM

Sukanya Basu, University of Michigan

TBA
 TBA
 04/03/2018
 10:20 AM  11:10 AM
 C304 Wells Hall
 Sukanya Basu, University of Michigan
TBA

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.

13323

Tuesday 4/10 10:20 AM

Andrew Krause, MSU

TBA
 TBA
 04/10/2018
 10:20 AM  11:10 AM
 C304 Wells Hall
 Andrew Krause, MSU
TBA

13324

Wednesday 4/11 10:20 AM

David Tannor

TBA
 TBA
 04/11/2018
 10:20 AM  11:10 AM
 C304 Wells Hall
 David Tannor
TBA

13289

Thursday 4/12 4:10 PM

Maria Gualdani, George Washington University

The Landau equation: old and new
 The Landau equation: old and new
 04/12/2018
 4:10 PM  5:00 PM
 C304 Wells Hall
 Maria Gualdani, George Washington University
Kinetic equations are used to describe evolution of interacting particles. The most famous kinetic equation is the Boltzmann equation: formulated by Ludwig Boltzmann in 1872, this equation describes motion of a large class of gases. Later, in 1936 Lev Landau derived from the Boltzmann equation a new mathematical model for motion of plasma. This latter equation was named the Landau equation. One of the main features of the Landau and Boltzmann equations is nonlocality, meaning that particles interact at large, noninfinitesimal length scales. The Boltzmann and Landau equations present integrodifferential operators that are highly nonlinear, singular and with degenerating coefficients. Despite the fact that many mathematicians and physicists have been working on these equations, many important questions are still unanswered due to their mathematical complexity. In this talk we concentrate on the mathematical results of the Landau equation. We will first review existing results and open problems and in the second part of the talk we will focus on recent developments of wellposedness and regularity theory.

13336

Tuesday 4/17 4:10 PM

Ekaterina Rapinchuk, Michigan State University

An Auction Dynamics Approach to SemiSupervised Data Classification
 An Auction Dynamics Approach to SemiSupervised Data Classification
 04/17/2018
 4:10 PM  5:00 PM
 C304 Wells Hall
 Ekaterina Rapinchuk, Michigan State University
We reinterpret the semisupervised data classification problem using an auction dynamics framework inspired by real life auctions. This novel forward and reverse auction procedure for data classification requires remarkably little training/labeled data and readily incorporates volume/class size constraints. We prove that the algorithm always terminates with the right properties for any choice of parameters and derive its computational complexity. Experimental results on benchmark machine learning datasets show that our approach exceeds the performance of current stateoftheart methods, while requiring a fraction of the computational time. This is joint work with Matt Jacobs and Selim Esedoglu.

13290

Thursday 4/19 4:10 PM

Zinovy Reichstein, University of British Columbia

Simplifying polynomials by Tschirnhaus transformations: old and new
 Simplifying polynomials by Tschirnhaus transformations: old and new
 04/19/2018
 4:10 PM  5:00 PM
 C304 Wells Hall
 Zinovy Reichstein, University of British Columbia
I will revisit classical problems of simplifying polynomials in one variable by Tschirnhaus transformations. Surprisingly, many of the old questions are still open. I will restate them in geometric terms and discuss recent work in this area.

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.
