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Colloquia for the Fall 2015 Semester

Juhi Jang
Monday, August 31 KAP 414 3:30 PM - 4:30 PM
On the kinetic Fokker-Planck equation with absorbing barrier

We discuss the well-posedness theory of classical solutions to the Kolmogorov equation, a simplest kinetic Fokker-Planck equation in bounded domains with absorbing boundary conditions. We show that the solutions are smooth up to the boundary away from the singular set and they are Holder continuous up to the singular set. This is joint work with H.J. Hwang, J. Jung and J.L. Velazquez.

Igor Kukavica
Monday, September 14 KAP 414 3:30 PM - 4:30 PM
To be Announced

Monday, September 21 KAP 414 3:30 PM - 4:30 PM
Career Panel

Mason Porter
Wednesday, September 30 KAP 414 3:30 PM - 4:30 PM
Special Time
Joint with the Colloquium: TBA

Geordie Richards
University of Rochester
Monday, October 5 KAP 414 3:30 PM - 4:30 PM
To be Announced

Stanley Osher
Monday, October 12 KAP 414 3:30 PM - 4:30 PM
CAMS Distinguished Lecturer
To be Announced

Richard Schoen
Stanford University
Monday, October 19 KAP 414 3:30 PM - 4:30 PM
To be Announced

Vlad Vicol
Monday, November 2 KAP 414 3:30 PM - 4:30 PM
To be Announced

Natasa Pavlovic
University of Texas
Monday, November 16 KAP 414 3:30 PM - 4:30 PM
To be Announced

Colloquia for the Spring 2015 Semester

Sylvester Gates
University of Maryland
Monday, January 26 KAP 414 3:30 PM - 4:30 PM
CAMS Distinguished Lecturer
How Attempting To Answer A Physics Question Led Me to Graph Theory, Error-Correcting Codes, Coxeter Algebras, and Algebraic Geometry

We discuss how a still unsolved problem in the representation theory of Superstring/M-Theory has led to the discovery of previously unsuspected connections between diverse topics in mathematics.

Wilfrid Gangbo
Georgia Tech
Monday, February 2 KAP 414 3:30 PM - 4:30 PM
Existence of a solution to an equation arising from Mean Field Games

We construct a small time strong solution to a nonlocal Hamilton–Jacobi equation introduced by Lions, the so-called master equation, originating from the theory of Mean Field Games. We discover a link between metric viscosity solutions to local Hamilton–Jacobi equations studied independently by Ambrosio–Feng and G–Swiech, and the master equation. As a consequence we recover the existence of solutions to the First Order Mean Field Games equations, first proved by Lions. We make a more rigorous connection between the master equation and the Mean Field Games equations. (This talk is based on a joint work with A. Swiech).

Jerome Goldstein
University of Memphis
Monday, February 9 KAP 414 3:30 PM - 4:30 PM
Energy asymptotics for dissipative waves

Topics include sharp results on equipartition of energy, overdamping, and asymptotic parabolicity. These are for linear waves, and these problems have a long history, the newest being asymptotic parabolicity, which was born in G I Taylor's 1922 paper. This is joint work with G. Reyes-Souto.

Mickael Chekroun
Monday, March 9 KAP 414 3:30 PM - 4:30 PM
Non-Markovian Reduced Equations for Stochastic PDEs

In this talk, a novel approach to deal with the parameterization problem of the “small" spatial scales by the “large" ones for stochastic partial differential equations (SPDEs) will be discussed. This approach relies on stochastic parameterizing manifolds (PMs) which are random manifolds aiming to provide — in a mean square sense — approximate parameterizations of the small scales by the large ones. Backward-forward systems will be introduced to give access to such PMs as pullback limits depending — through the nonlinear terms — on (approximations of) the time-history of the dynamics on the low modes. These auxiliary systems will be used for the effective derivation of non-Markovian reduced stochastic differential equations from Markovian SPDEs. The non-Markovian effects are here exogenous in the sense that they result from the interactions between the external driving noise and the nonlinear terms, given a projection of the dynamics onto the modes with low wavenumbers. It will be shown that these non-Markovian terms allow in certain circumstances to restore in a striking way the missing information due to the low-mode projection, namely to parameterize what is not observed. Noise-induced large excursions or noise-induced transitions will serve as illustrations.

Geoffrey Spedding
Monday, March 23 KAP 414 3:30 PM - 4:30 PM
Wake Signature Detection

The various regimes of strongly stratified flows have been studied extensively in theory, laboratory and numerical experiment. In the case of stratified, initially-turbulent wakes, the particular applications have drawn the research into high Froude and Reynolds number regimes (an internal Froude number is a ratio between timescales of turbulent motions vs. the restoring buoyancy forces, and a Reynolds number can be viewed as a ratio of timescales of advection vs. diffusion), that quite surprisingly have turned out to have rather general application. If, as seems likely, the conditions for making persistent flows with robust pattern are widespread, then we may consider the generation of, and search for, geometric pattern as being a phenomenon that is almost ubiquitous. Here we consider cases that range from island wakes that persist for more than 10,000 km to copepod tracks that have initial scales on the order of mm. Similarities and analogies will be noted in a somewhat qualitative fashion, in the hopes of inspiring future work.

Reception: Emmanuel Candes

Monday, April 13 Gerontology Courtyard 3:15 PM - 4:00 PM
CAMS Distinguished Lecturer
You are cordially invited to attend

Emmanuel Candes
Stanford University, Joint with the Marshall School of Business
Monday, April 13 Gerontology Auditorium 4:00 PM - 5:00 PM
CAMS Distinguished Lecturer
Around the Reproducibility of Scientific Research: A Knockoff Filter for Controlling the False Discovery Rate

The big data era has created a new scientific paradigm: collect data first, ask questions later. When the universe of scientific hypotheses that are being examined simultaneously is not taken account, inferences are likely to be false. The consequence is that follow up studies are likely not to be able to reproduce earlier reported findings or discoveries. This reproducibility failure bears a substantial cost and this talk is about new statistical tools to address this issue. Imagine that we observe a response variable together with a large number of potential explanatory variables, and would like to be able to discover which variables are truly associated with the response. At the same time, we need to know that the false discovery rate (FDR)---the expected fraction of false discoveries among all discoveries---is not too high, in order to assure the scientist that most of the discoveries are indeed true and replicable. We introduce the knockoff filter, a new variable selection procedure controlling the FDR in the statistical linear model whenever there are at least as many observations as variables. This method achieves exact FDR control in finite sample settings no matter the design or covariates, the number of variables in the model, and the amplitudes of the unknown regression coefficients, and does not require any knowledge of the noise level. This work is joint with Rina Foygel Barber.

Yuri Tschinkel
Director of the MPS Division of the Simons Foundation and Professor at the Courant Institute
Wednesday, April 15 KAP 414 4:45 PM - 5:30 PM
Special Time
Simons Foundation Discussion

The Simons Foundation Division for Mathematics and the Physical Sciences (MPS) seeks to extend the frontiers of basic research. The Division’s primary focus is on mathematics, theoretical physics and theoretical computer science. The division awards grants primarily through competitive, open, application-based procedures.

Yuri Tschinkel
Director of the MPS Division of the Simons Foundation and Professor at the Courant Institute
Wednesday, April 15 KAP 414 3:30 PM - 4:30 PM
Special Time
Geometry of Numbers

I will discuss Minkowski's geometric ideas and their modern incarnations.

Anthony Suen
Hong Kong Institute of Education
Monday, April 27 KAP 414 3:30 PM - 4:30 PM
Existence of intermediate weak solution to the equations of multi-dimensional chemotaxis systems

We prove the global-in-time existence of intermediate weak solutions of the equations of chemotaxis system in a bounded domain of $\mathbb{R}^2$ or $\mathbb{R}^3$ with initial chemical concentration small in $H^1$. No smallness assumption is imposed on the initial cell density which is in $L^2$. We first show that when the initial chemical concentration $c_0$ is small only in $H^1$ and $(n_0-n_\infty,c_0)$ is smooth, the classical solution exists for all time. Then we construct weak solutions as limits of smooth solutions corresponding to mollified initial data. Finally we determine the asymptotic behavior of the global solutions.

Grace Wahba
University of Wisconsin
Monday, May 4 KAP 414 3:30 PM - 4:30 PM
CAMS Distinguished Lecturer
Learning Genetic Risk Models Using Distance Covariance

We extend an approach suggested by Li, Zhong and Zhu (2012) to use distance covariance (DCOV) as a variable selection method by providing the DCOV Variable Selection Theorem, which gives a principled stopping rule for a greedy variable selection algorithm. We apply the resulting DCOV Variable Selection Method in two genetic based classification problems with small sample size and large vectors of gene expression data.

The first problem involves the well known SBRCT (Small Blue Round Cell Tumor) childhood Leukemia data, which involves gene expression data from four different types of Leukemia, and it is well known that these data are easy to classify.

The second involves Ovarian Cancer data from The Cancer Genome Atlas, and involves Ovarian Cancer patients that are either sensitive or resistant to a platinum based cancer chemotherapy. The Ovarian Cancer data presents a difficult classification problem.