## Seminars and Colloquia by Series

Thursday, October 5, 2017 - 11:00 , Location: Skiles 006 , , Hebrew University of Jerusalem , Organizer: Mayya Zhilova
The study of nonconventional sums $S_{N}=\sum_{n=1}^{N}F(X(n),X(2n),\dots,X(\ell n))$, where $X(n)=g \circ T^n$ for a measure preserving transformation $T$, has a 40 years history after Furstenberg showed that they are related to the ergodic theory proof of Szemeredi's theorem about arithmetic progressions in the sets of integers of positive density. Recently, it turned out that various limit theorems of probabilty theory can be successfully studied for sums $S_{N}$ when $X(n), n=1,2,\dots$ are weakly dependent random variables. I will talk about a more general situation of nonconventional arrays of the form $S_{N}=\sum_{n=1}^{N}F(X(p_{1}n+q_{1}N),X(p_{2}n+q_{2}N),\dots,X(p_{\ell}n+q_{\ell}N))$ and how this is related to an extended version of Szemeredi's theorem. I'll discuss also ergodic and limit theorems for such and more general nonconventional arrays.
Tuesday, September 19, 2017 - 11:05 , Location: Skiles 006 , , UCLA Math , Organizer: Sung Ha Kang
Simulation of hyperelastic materials is widely adopted in the computer graphics community for applications that include virtual clothing, skin, muscle, fat, etc. Elastoplastic materials with a hyperelastic constitutive model combined with a notion of stress constraint (or feasible stress region) are also gaining increasing applicability in the field. In these models, the elastic potential energy only increases with the elastic partof the deformation decomposition. The evolution of the plastic part is designed to satisfy the stress constraint. Perhaps the most common example of this phenomenon is denting of an elastic shell. However, other very powerful examples include frictional contact material interactions. I will discuss some of the mathematical aspects of these models and present some recent results and examples in computer graphics applications.
Thursday, September 7, 2017 - 11:05 , Location: Skiles 006 , , Imperial College London , Organizer: Mayya Zhilova
I will present a survey of the main results about first and second order models of swarming where repulsion and attraction are modeled through pairwise potentials. We will mainly focus on the stability of the fascinating patterns that you get by random particle simulations, flocks and mills, and their qualitative behavior. Qualitative properties of local minimizers of the interaction energies are crucial in order to understand these complex behaviors. Compactly supported global minimizers determine the flock patterns whose existence is related to the classical H-stability in statistical mechanics and the classical obstacle problem for differential operators.
Thursday, March 30, 2017 - 11:05 , Location: Skiles 006 , Larry Goldstein , University of Southern California , Organizer: Christian Houdre
Charles Stein brought the method that now bears his name to life in a 1972 Berkeley symposium paper that presented a new way to obtain information on the quality of the normal approximation, justified by the Central Limit Theorem asymptotic, by operating directly on random variables. At the heart of the method is the seemingly harmless characterization that a random variable $W$ has the standard normal ${\cal N}(0,1)$ distribution if and only if E[Wf(W)]=E[f'(W)] for all functions $f$ for which these expressions exist. From its inception, it was clear that Stein's approach had the power to provide non-asymptotic bounds, and to handle various dependency structures. In the near half century since the appearance of this work for the normal, the `characterizing equation' approach driving Stein's method has been applied to roughly thirty additional distributions using variations of the basic techniques, coupling and distributional transformations among them. Further offshoots are connections to Malliavin calculus and the concentration of measure phenomenon, and applications to random graphs and permutations, statistics, stochastic integrals, molecular biology and physics.
Thursday, March 16, 2017 - 16:05 , Location: Skiles 006 , Erich Kaltofen , North Carolina State University , Organizer: Anton Leykin
We present algorithms for performing sparse univariate polynomial interpolation with errors in the evaluations of the polynomial. Our interpolation algorithms use as a substep an algorithm that originally is by R. Prony from the French Revolution (Year III, 1795) for interpolating exponential sums and which is rediscovered to decode digital error correcting BCH codes over finite fields (1960). Since Prony's algorithm is quite simple, we will give a complete description, as an alternative for Lagrange/Newton interpolation for sparse polynomials. When very few errors in the evaluations are permitted, multiple sparse interpolants are possible over finite fields or the complex numbers, but not over the real numbers. The problem is then a simple example of list-decoding in the sense of Guruswami-Sudan. Finally, we present a connection to the Erdoes-Turan Conjecture (Szemeredi's Theorem). This is joint work with Clement Pernet, Univ. Grenoble.
Thursday, March 2, 2017 - 11:05 , Location: Skiles 006 , , Yale University , Organizer: Anton Leykin
The piecewise linear objects appearing in tropical geometry are shadows, or skeletons, of nonarchimedean analytic spaces, in the sense of Berkovich, and often capture enough essential information about those spaces to resolve interesting questions about classical algebraic varieties.  I will give an overview of tropical geometry as it relates to the study of algebraic curves, touching on applications to moduli spaces.
Tuesday, February 28, 2017 - 11:05 , Location: Skiles 006 , , Adam Mickiewicz University , , Organizer: Lutz Warnke
The talk is meant to be a gentle introduction to a part of combinatorial topology which studies randomly generated objects. It is a rapidly developing field which combines elements of topology, geometry, and probability with plethora of interesting ideas, results and problems which have their roots in combinatorics and linear algebra.
Thursday, January 26, 2017 - 11:05 , Location: Skiles 006 , Bill Massey , Princeton , Organizer: Shahaf Nitzan
The multi-server queue with non-homogeneous Poisson arrivals and customer abandonment is a fundamental dynamic rate queueing model for large scale service systems such as call centers and hospitals. Scaling the arrival rates and number of servers gives us fluid and diffusion limits. The diffusion limit suggests a Gaussian approximation to the stochastic behavior. The fluid mean and diffusion variance can form a two-dimensional dynamical system that approximates the actual transient mean and variance for the queueing process. Recent work showed that a better approximation for mean and variance can be computed from a related two-dimensional dynamical system. In this spirit, we introduce a new three-dimensional dynamical system that estimates the mean, variance, and third cumulant moment. This surpasses the previous two approaches by fitting the number in the queue to a quadratic function of a Gaussian random variable. This is based on a paper published in QUESTA and is joint work with Jamol Pender of Cornell University.
Thursday, January 19, 2017 - 11:05 , Location: Skiles 006 , , Univ. of Barcelona , , Organizer: Yao Yao
The long term behavior of dynamical systems can be understood by studying invariant manifolds that act as  landmarks that anchor the orbits. It is important to understand which invariant manifolds persist under modifications of the system. A deep mathematical theory, developed in the 70's shows that invariant manifolds which persist under changes are those that have sharp expansion (in the future or in the past) in the the normal directions. A deep question is what happens in the boundary of these theorems of persistence. This question requires to understand the interplay between the geometric properties and the functional analysis of the functional equations involved.In this talk we present several mechanisms in which properties of normal hyperbolicity degenerate, so leading to the breakdown of the invariant manifold. Numerical studies lead to surprising conjectures relating the breakdown to phenomena in phase transitions. The results have been obtained combining numerical exploration and rigorous reasoning.
Tuesday, January 3, 2017 - 11:05 , Location: Skiles 006 , Barry Simon , California Institute of Technology , Organizer: Shahaf Nitzan
This is not a mathematics talk but it is a talk for mathematicians. Too often, we think of historical mathematicians as only names assigned to theorems. With vignettes and anecdotes, I'll convince you they were also human beings and that, as the Chinese say, "May you live in interesting times" really is a curse.  More tales following up on the talk I gave at GaTech in Nov., 2013.  It is not assumed listeners heard that earlier talk.