Colloquia for the Fall 2015 Semester


Juhi Jang
USC
Monday, August 31
KAP 414
3:30 PM  4:30 PM

On the kinetic FokkerPlanck equation with absorbing barrier
We discuss the wellposedness theory of classical solutions to the Kolmogorov equation, a simplest kinetic FokkerPlanck 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
USC
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
Oxford
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
UCLA
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
Princeton
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, ErrorCorrecting Codes, Coxeter Algebras, and Algebraic Geometry
We discuss how a still unsolved problem in the representation theory of Superstring/MTheory 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 socalled 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. ReyesSouto.



Mickael Chekroun
UCLA
Monday, March 9
KAP 414
3:30 PM  4:30 PM

NonMarkovian 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. Backwardforward systems will be introduced to give access to such PMs as pullback limits depending — through the nonlinear terms — on (approximations of) the timehistory of the dynamics on the low modes. These auxiliary systems will be used for the effective derivation of nonMarkovian reduced stochastic differential equations from Markovian SPDEs. The nonMarkovian 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 nonMarkovian terms allow in certain circumstances to restore in a striking way the missing information due to the lowmode projection, namely to parameterize what is not observed. Noiseinduced large excursions or noiseinduced transitions will serve as illustrations.



Geoffrey Spedding
USC A&ME
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, initiallyturbulent 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 discoveriesis 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, applicationbased 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 multidimensional chemotaxis systems
We prove the globalintime 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 $(n_0n_\infty,c_0)$ 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.

