Colloquium Archives for Academic Year 2018


Math Department Welcome

When: Wed, September 13, 2017 - 3:15pm
Where: Kirwan Hall 3206
Speaker: () -


Approximation Algorithms: Some ancient, some new - the good, the bad and the ugly

When: Wed, September 20, 2017 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Samir Khuller (University of Maryland Computer Science ) - https://www.cs.umd.edu/users/samir/
Abstract: NP-complete problems abound in every aspect of our daily lives. One approach is to simply deploy heuristics, but for many of these we do not have any idea as to when the heuristic is effective and when it is not. Approximation algorithms have played a major role in the last three decades in developing a foundation for a better understanding of optimization techniques - greedy algorithms, algorithms based on LinearProgramming (LP) relaxations have paved the way for the design of (in some cases) optimal heuristics. Are these the best ones to use in “typical” instances? Maybe, maybe not.


In this talk we will focus on two specific areas - one is in the use of greedy algorithms for a basic graph problem called connected dominating set, and the other is in the development of LP based algorithms for a basic scheduling problem in the context of data center scheduling.

Faculty Meeting with CMNS Interim Dean, Jerry Wilkinson

When: Wed, September 27, 2017 - 3:15pm
Where: Kirwan Hall 3206
Speaker: (CMNS Dean's Office) -


Binet-Legendre metric and applications of Riemannian results in Finsler geometry

When: Wed, October 4, 2017 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Vladimir Matveev (Friedrich-Schiller-Universität Jena ) - http://users.minet.uni-jena.de/~matveev/
Abstract: We introduce a construction that associates a Riemannian metric $g_F$ (called the
Binet-Legendre metric) to a
given Finsler metric $F$ on a smooth manifold $M$. The transformation
$F \mapsto g_F$ is $C^0$-stable and has good
smoothness properties, in contrast to previously considered
constructions. The Riemannian metric $g_F$ also behaves nicely under
conformal or isometric transformations of the Finsler metric $F$ that
makes it a powerful tool in Finsler geometry. We illustrate that by
solving a number of named problems in Finsler geometry. In particular
we extend a classical result of Wang to all dimensions. We answer a
question of Matsumoto about local conformal mapping between two
Berwaldian spaces and use it to investigation of essentially conformally Berwaldian manifolds.
We describe all possible conformal self maps and all self similarities
on a Finsler manifold, generasing the famous result of Obata to Finslerian manifolds. We also classify all compact conformally flat
Finsler manifolds. We solve a conjecture of Deng and Hou on locally
symmetric Finsler spaces. We prove smoothness of isometries of Holder-continuous Finsler metrics. We construct new ``easy to calculate''
conformal and metric invariants of finsler manifolds.
The results are based on the papers arXiv:1104.1647, arXiv:1409.5611,
arXiv:1408.6401, arXiv:1506.08935,
arXiv:1406.2924
partially joint with M. Troyanov (EPF Lausanne) and Yu. Nikolayevsky (Melbourne).

(No colloquium)

When: Wed, October 11, 2017 - 3:15pm
Where: Kirwan Hall 3206
Speaker: General Departmental Meeting () -


No colloquium

When: Wed, October 18, 2017 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Departmental Meeting () -


No colloquium

When: Wed, October 25, 2017 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Departmental Meeting () -


Some results on affine Deligne-Lusztig varieties

When: Wed, November 1, 2017 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Xuhua He (UMD) - http://www.math.umd.edu/~xuhuahe/
Abstract: In Linear Algebra 101, we encounter two important features of the group of invertible matrices: Gauss elimination method, or the LU decomposition of almost all matrices, which is an important special case of the Bruhat decomposition; the Jordan normal form, which gives a classification of the conjugacy classes of invertible matrices.

The study of the interaction between the Bruhat decomposition and the conjugation action is an important and very active area. In this talk, we focus on the affine Deligne-Lusztig variety, which describes the interaction between the Bruhat decomposition and the Frobenius-twisted conjugation action of loop groups. The affine Deligne-Lusztig variety was introduced by Rapoport around 20 years ago and it has found many applications in arithmetic geometry and number theory.

In this talk, we will discuss some recent progress on the study of affine Deligne-Lusztig varieties, and some applications to Shimura varieties.

Quantitative estimates of propagation of chaos for large systems of interacting particles

When: Wed, November 8, 2017 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Pierre-Emmanuel Jabin (UMD) - http://www2.cscamm.umd.edu/~jabin/
Abstract: We present a new method to derive quantitative estimates proving the propagation of chaos for large stochastic or deterministic systems of interacting particles. Our approach requires to prove large deviations estimates for non-continuous potentials modified by the limiting law. But it leads to explicit bounds on the relative entropy between the joint law of the particles and the tensorized law at the limit; and it can be applied to very singular kernels that are only in negative Sobolev spaces and include the Biot-Savart law for 2d Navier-Stokes

Scale, pattern and biodiversity

When: Wed, November 15, 2017 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Simon Levin (Princeton ) -
Abstract: One of the deepest problems in ecology is in understanding how so many species coexist, competing for a limited number of resources. This motivated much of Darwin’s thinking, and has remained a theme explored by such key thinkers as Hutchinson (“The paradox of the plankton”), MacArthur, May and others. A key to coexistence, is in the development of spatial and spatio-temporal patterns, and in the coevolution of life-history patterns that both generate and exploit spatio-temporal heterogeneity. Here, general theories of pattern formation, which have been prevalent not only in ecology but also throughout science, play a fundamental role in generating understanding. The interaction between diffusive instabilities, multiple stable basins of attraction, critical transitions, stochasticity and far-from-equilibrium phenomena creates a broad panoply of mechanisms that can contribute to coexistence, as well as a rich set of mathematical questions and phenomena. This lecture will cover as much of this as time allows.

Math Teaching Forum

When: Fri, November 17, 2017 - 3:00pm
Where: Kirwan Hall 3206
Speaker: () -
Abstract: Our lecturers Hilaf Hasson, Kendall Williams and Allan Yashinski will be hosting the panel on the realities of teaching. The target audience first includes Math TAs but we are hoping to attract many in the department. Light refreshments to follow in room 3201.

Ergodic properties of parabolic systems.

When: Wed, November 29, 2017 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Adam Kanigowski
http://www.adkanigowski.cba.pl/en.php
Abstract: Parabolic dynamical systems are systems of intermediate (polynomial) orbit growth. Most important classes of parabolic systems are: unipotent flows on homogeneous spaces and their smooth time changes, smooth flows on compact surfaces, translation flows and IET's (interval exchange transformations). Since the entropy of parabolic systems is zero, other properties describing chaoticity are crucial: mixing, higher order mixing, decay of correlations.
One of the most important tools in parabolic dynamics is the Ratner property (on parabolic divergence), introduced by M. Ratner in the class of horocycle flows. This property was crucial in proving famous Ratner's rigidity theorems in the above class.

We will introduce generalisations of Ratner's property for other parabolic systems and discuss it's consequences for chaotic properties. In particular this allows to approach the Rokhlin problem in the class of smooth flows on surfaces and in the class of smooth time changes of Heisenberg nilflows.

Mobius disjointness for some dynamical systems of controlled complexity

When: Wed, December 6, 2017 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Zhiren Wang
http://www.personal.psu.edu/zxw14/
Abstract: Sarnak's Mobius disjointness conjecture speculates that the Mobius sequence is disjoint to all topological dynamical systems of zero topological entropy. We will survey the recent developments in this area, and discuss several special classes of dynamical systems of controlled complexity that satisfy this conjecture. Part of the talk is based on joint works with Wen Huang, Xiangdong Ye, and Guohua Zhang. No background knowledge in either dynamical systems or number theory will be assumed.


Dimension gaps in self-affine sponges

When: Thu, December 7, 2017 - 2:00pm
Where: Kirwan Hall 3206
Speaker: David Simmons (University of York) -
Abstract: Abstract: In this talk, I will discuss a long-standing open problem in the dimension theory of dynamical systems, namely whether every expanding repeller has an ergodic invariant measure of full Hausdorff dimension, as well as my recent result showing that the answer is negative. The counterexample is a self-affine sponge in $\mathbb R^3$ coming from an affine iterated function system whose coordinate subspace projections satisfy the strong separation condition. Its dynamical dimension, i.e. the supremum of the Hausdorff dimensions of its invariant measures, is strictly less than its Hausdorff dimension. More generally we compute the Hausdorff and dynamical dimensions of a large class of self-affine sponges, a problem that previous techniques could only solve in two dimensions. The Hausdorff and dynamical dimensions depend continuously on the iterated function system defining the sponge, which implies that sponges with a dimension gap represent a nonempty open subset of the parameter space. This work is joint with Tushar Das (Wisconsin -- La Crosse).

TBA (Douglas Lecture)

When: Fri, December 8, 2017 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Daniel Tataru (UC Berkeley) - https://math.berkeley.edu/~tataru/


Taking Mathematics to Heart

When: Fri, February 2, 2018 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Alfio Quarteroni (Politecnico di Milano, Milan, Italy and EPFL, Lausanne, Switzerland ) - https://cmcs.epfl.ch/people/quarteroni
Abstract: Abstract : In this presentation I will highlight the great potential offered by the interplay between data science and computational science to efficiently solve real life large scale problems . The leading application that I will address is the numerical simulation of the heart function.

The motivation behind this interest is that cardiovascular diseases unfortunately represent one of the leading causes of death in Western Countries.

Mathematical models based on first principles allow the description of the blood motion in the human circulatory system, as well as the interaction between electrical, mechanical and fluid-dynamical processes occurring in the heart. This is a classical environment where multi-physics processes have to be addressed.


Appropriate numerical strategies can be devised to allow for an effective description of the fluid in large and medium size arteries, the analysis of physiological and pathological conditions, and the simulation, control and shape optimization of assisted devices or surgical prostheses.

This presentation will address some of these issues and a few representative applications of clinical interest.

Defects in periodic homogenization problems : Toward a complete theory [Appl Math Colloquium]

When: Tue, February 6, 2018 - 3:30pm
Where: Kirwan Hall 3206
Speaker: Claude Le Bris (Ecole des Ponts and Inria) - https://cermics.enpc.fr/~lebris/
Abstract: We will present some recent mathematical contributions related to nonperiodic homogenization problems. The difficulty stems from the fact that the medium is not assumed periodic, but has a structure with a set of embedded localized defects, or more generally a structure that, although not periodic, enjoys nice geometrical features. The purpose is then to construct a theoretical setting providing an efficient and accurate approximation of the solution. The questions raised ranged from the theory of elliptic PDEs, homogenization theory to harmonic analysis and singular operators.

Aziz Lecture

When: Wed, February 7, 2018 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Claude Le Bris () -


Spectral analysis on singular spaces

When: Fri, February 9, 2018 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Alexander Teplyaev (University of Connecticut) - http://teplyaev.math.uconn.edu
Abstract: The talk will outline recent achievements and challenges in spectral and stochastic analysis on non-smooth spaces that are very singular, but can be approximated by graphs or manifolds. In particular, the talk will present two of most interesting examples that are currently
under investigation. One example deals with the spectral analysis of the Laplacian on the famous basilica Julia set, the Julia set of the polynomial z^2-1. This is a joint work with Luke Rogers and several students at UConn. The other example deals with spectral, stochastic, functional analysis for the canonical diffusion on the pattern spaces of an aperiodic Delone set. This is a joint work with Patricia Alonso-Ruiz, Michael Hinz and Rodrigo Trevino.

Stability for symmetric groups and Hecke algebras

When: Wed, February 14, 2018 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Weiqiang Wang (University of Virginia)
Abstract: We will describe a certain stability for the centers of the group algebras of the symmetric groups S_n for varying n, and its geometric counterpart. (To experts: this is not about Schubert calculus). We shall then explain the generalization of this stability phenomenon for wreath products and for Hecke algebras. This talk should be accessible to graduate students.

Alpha invariants and birational geometry.

When: Wed, February 21, 2018 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Ivan Cheltsov (University of Edinburgh, UK) - http://www.maths.ed.ac.uk/cheltsov/

Abstract: Tian introduced alpha invariants to study the existence of
Kahler-Einstein metrics on Fano manifolds.
In this talk we describe (explicit and implicit) appearance of alpha
invariants in (global and local) birational geometry.

Nonlinear fluid-structure interaction with fiber-reinforced soft composites: a unified mathematical framework for mathematical analysis, computation and applications

When: Fri, February 23, 2018 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Suncica Canic (University of Houston) - https://www.math.uh.edu/~canic/
Abstract: Fiber-reinforced structures arise in many engineering and biological applications. Examples include space inflatable habitats, vascular stents supporting compliant vascular walls, and aortic valve leaflets. In all these examples a metallic mesh, or a collection of fibers, is used to support an elastic structure, and the resulting composite structure has novel mechanical characteristics preferred over the characteristics of each individual component. These structures interact with the surrounding deformable medium, e.g., blood flow or air flow, or another elastic structure, constituting a fluid-structure interaction (FSI) problem. Modeling and computer simulation of this class of FSI problems is important for manufacturing and design of novel materials, space habitats, and novel medical constructs.
Mathematically, these problems give rise to a class of highly nonlinear, moving- boundary problems for systems of partial differential equations of mixed type. To date, there is no general existence theory for solutions of this class of problems, and numerical methodology relies mostly on monolithic/implicit schemes, which suffer from bad condition numbers associated with the fluid and structure sub- problems. In this talk we present a unified mathematical framework to study existence of weak solutions to FSI problems involving incompressible, viscous fluids and elastic structures. The mathematical framework provides a constructive existence proof, and a partitioned, loosely coupled scheme for the numerical solution of this class of FSI problems. The constructive existence proof is based on time-discretization via operator splitting, and on our recent extension of the Aubin-Lions-Simon compactness lemma to problems on moving domains. The resulting numerical scheme has been applied to problems in cardiovascular medicine, showing excellent performance, and providing medically beneficial information. Examples of applications in coronary angioplasty and micro- swimmer biorobot design will be shown.

Recent Work in Mixture Models and Clustering

When: Tue, February 27, 2018 - 3:30pm
Where:

Kirwan Hall 3206
Speaker: Paul McNicholasAbstract: The application of mixture models for clustering has burgeoned into an important subfield of multivariate statistics and, in particular, classification. The framework for mixture model-based clustering is established and some historical context is provided. Then, some previous work is reviewed before some recent advances are presented. Previous work is discussed with some focus on technical detail. However, recent advances are presented with more focus on illustration via real data problems. The recent work discussed will include an approach for clustering Airbnb reviews as well as applications of mixtures of matrix variate distributions.

Five points on the sphere

When: Wed, March 14, 2018 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Richard Schwartz (Brown University) - http://www.math.brown.edu/~res/
Abstract: In my talk I will discuss the problem of putting 5
points on the sphere in such a way as to minimize their total
potential energy with respect to a power law. General questions
about the energy of point configurations go under the heading of
Thomson's problem and have been studied for about 100 years.
I'll sketch my rigorous computer-assisted proof that the
triangular bi-pyramid is the global minimizer with respect to
a power law of exponent s if and only if s<s*, where s* is
a "phase transition constant" discovered experimentally by
Melnyk-Knop-Smity in 1977.

Distinguished Lecture in Geometry - Richard Schoen (Stanford, UC Irvine)

When: Thu, March 15, 2018 - 4:30pm
Where: Kirwan Hall 3206
Speaker: Richard Schoen (Stanford, UC Irvine)
Abstract: This talk will be a survey of some of the geometric problems and ideas which either arose from general relativity or have direct bearing on the Einstein equations.
It is intended for a general mathematical audience with minimal physics background.
Topics will include an introduction to the Cauchy problem for the Einstein equations, problems related to gravitational mass which are closely related to the Riemannian geometry of positive scalar curvature, and trapped surfaces which are related to the mean curvature and minimal surfaces.
https://www-math.umd.edu/geometry-week.html

Distinguished Lecture Geometry - Richard Schoen (Stanford, UC Irvine)

When: Fri, March 16, 2018 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Richard Schoen (Stanford, UC Irvine)
Abstract: Positive Mass Theorem Revisited - We will introduce the positive mass theorem which is a problem originating in general relativity, and which turns out to be connected to important mathematical questions including the study of metrics of constant scalar curvature and the stability of minimal hypersurface singularities. We will then give a general description of our recent work with S. T. Yau on resolving the theorem on high dimensional non-spin manifolds.
https://www-math.umd.edu/research/conferences/geometry-week-march-12-16-2018/distinguished-lectures-in-geometric-analysis.html

Overview of the N-body Problem

When: Wed, March 28, 2018 - 3:15pm
Where: Kirwan Hall 3206

Speaker: Richard Montgomery (UCSC) - https://people.ucsc.edu/~rmont/

Abstract: How can a cat, falling from upside-down with zero angular momentum, right herself? Viewing the cat’s problem from the perspective of symplectic reduction and gauge theory led me into the N-bodyproblem. The cat suggested the primacy of shape space: configuration space modulo symmetries. Deletingcollisions from the planar three body problem yields a shape space homotopic to a pair of pants: a thrice-punctured sphere. Is every free homotopy class of loops on this punctured sphere realized by some periodicsolution to the planar three-body problem? I aim to describe four results inspired by this last question.1. The figure eight orbit -its rediscovery, and existence proof. 2. That every negative energy zero angularmomentum solution (with a single exception) suffers collinear instants . 3. If I ‘cheat’ by changing thepotential from 1/r to 1/r2, and take the masses equal. then modulo symmetries, the bounded zero angularmomentum flow is conjugate to geodesic flow for a complete noncompact negatively curved metric on thepair of pants. 4. The answer to the homotopy question is ‘yes’ provided we accept small but nonzero angularmomentum and the masses are equal or nearly equal. (Result 1 is joint with Alain Chenciner, and result 4with Rick Moeckel. )

A Structure Theorem for Stationary Group Actions

When: Wed, April 4, 2018 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Hillel Furstenberg () -
Abstract: Structure theorems play an important role in dynamics with Veech's structure theorem as an outstanding example. We will describe a structure theorem in a measure-theoretic context: namely for "stationary" group actions. These are actions where a measure on a group space is invariant "on the average" relative to a probability measure on the group. One application is to "multiple recurrence" for non-amenable group actions, and associated Ramsey type theorems.

Spring Teaching forum

When: Wed, April 11, 2018 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Teaching forum () -

Eigenvalue problem for reductive groups

When: Wed, April 18, 2018 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Shrawan Kumar (UNC at Chapel Hill) - http://www.unc.edu/math/Faculty/kumar/
Abstract: See PDF.

TBA

When: Wed, April 25, 2018 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Alexander Vladimirsky (Cornell University) - http://www.math.cornell.edu/~vlad/


Counting points, counting fields, and new heights

When: Fri, April 27, 2018 - 11:00am
Where: Kirwan Hall 3206

Speaker: Jordan Ellenberg http://www.math.wisc.edu/~ellenber/
Abstract: The basic objects of algebraic number theory are number fields, and the basic invariant of a number field is its discriminant, which in some sense measures its arithmetic complexity. A basic finiteness result, proved by Hermite at the end of the 19th century, is that there are only finitely many degree-d number fields of discriminant at most X. It thus makes sense to put all the number fields in order of their discriminant, and ask if we can say how many you’ve encountered by the time you get to discriminant X.

This is an old problem, governed by a conjecture of Narkiewicz. Interest in this area was revitalized by the work of Bhargava; the first step in his program was to count number fields of degree 4 and 5. (Degree 6 remains completely out of reach!) I’ll talk about the long history of this problem and its variants, and discuss two recent results:

1) (joint with TriThang Tran and Craig Westerland) We prove that the upper bound conjectured by Narkiewicz is true “up to epsilon" when Q is replaced by a rational function field F_q(t) — this is much more than is known in the number field case, and relies on a new upper bound for the cohomology of Hurwitz spaces coming from quantum shuffle algebras: https://arxiv.org/abs/1701.04541

2) (joint with Matt Satriano and David Zureick-Brown) Another much-studied counting problem in number theory is the Batyrev-Manin conjecture, which asks about the number of rational points on a variety of bounded height, or, in more concrete terms, questions like:
“How many solutions does an equation like x^3 + y^3 + z^3 + w^3 = 0 have in integers of absolute value at most X?”

It turns out there’s a way to synthesize the Narkiewicz conjecture and the Batyrev-Manin conjecture into a unified heuristic which includes both of those conjectures as special cases, and which says much more in general. This involves defining “the height of a rational point on an algebraic stack” and I will say as much about what this means as there’s time to!

The Geometry of Redistricting - Jordan Ellenberg

When: Fri, April 27, 2018 - 3:30pm
Where: 3206 Kirwan Hall


On a conjecture for p-torsion in class groups of number fields

When: Wed, May 2, 2018 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Lillian Pierce (Duke University/IAS) - https://services.math.duke.edu/~pierce/
Abstract: This talk will survey ideas surrounding a conjecture in number theory about the structure of class groups of number fields. Each number field has associated to it a finite abelian group, the class group, and as long ago as Gauss, deep questions arose about the distribution of class groups as the field varies over a family. Many of these questions remain unanswered. We will introduce one particular conjecture about p-torsion in class groups, and indicate how it is closely related to several other deep conjectures in number theory. Then we will present several contrasting ways we have recently made progress toward the p-torsion conjecture.

TBA (Aziz)

When: Fri, May 4, 2018 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Arnaud Debussche (ENS, Rennes, France) - http://w3.ens-rennes.fr/math/people/arnaud.debussche/