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 ) -
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 ) -
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,
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) -
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) -
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
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
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) -

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 ) -
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.

Aziz Lecture

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


When: Wed, February 14, 2018 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Weiqiang Wang (University of Virginia) -


When: Wed, February 21, 2018 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Ivan Cheltsov (University of Edinburgh, UK) -


When: Wed, March 14, 2018 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Richard Schwartz (Brown University) -


When: Wed, March 28, 2018 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Richard Montgomery (UCSC) -


When: Wed, April 18, 2018 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Shrawan Kumar (UNC at Chapel Hill) -
Abstract: TBA


When: Wed, April 25, 2018 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Alexander Vladimirsky (Cornell University) -


When: Fri, April 27, 2018 - 3:15pm
Where: Kirwan Hall 3206
Speaker: TBA Kirwan Lecture () -


When: Wed, May 2, 2018 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Lillian Pierce (Duke University/IAS) -

TBA (Aziz)

When: Fri, May 4, 2018 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Arnaud Debussche (ENS, Rennes, France) -