Week of April 5, 2020

Mon Apr 6, 2020
4:00pm to 5:00pm - Join Zoom Meeting https://uci.zoom.us/j/186261599 - Applied and Computational Mathematics
Matthew Jacobs - (UCLA)
A fast approach to optimal transport: the back-and-forth method

Given two probability measures and a transportation cost, the optimal transport problem asks to find the most cost efficient way to transport one measure to the other.  Since its introduction in 1781 by Gaspard Monge, the optimal transport problem has found applications in logistics, economics, physics, PDEs, and more recently data science.  However, despite sustained attention from the numerics community, solving optimal transport problems has been a notoriously difficult task.  

In this talk I will introduce the back-and-forth method, a new algorithm to efficiently solve the optimal transportation problem for a general class of strictly convex transportation costs.  Given two probability measures supported on a discrete grid with n points, the method computes the optimal map in O(n log(n)) operations using O(n) storage space.   As a result, the method can compute highly accurate solutions to optimal transportation problems on spatial grids as large as 4096 x 4096 and 384 x 384 x 384 in a matter of minutes.  If time permits, I will demonstrate an extension of the algorithm to the simulation of a class of gradient flows.

This talk is joint work with Flavien Leger.

Tue Apr 7, 2020
2:00pm to 2:50pm - Zoom - Working Group in Information Theory
Kat Dover - (UCI)
Extremization of mutual information for memoryless sources and channels

This week, we will discuss Section 5.1 of the lecture notes of Wu and Polyanski: 
http://people.lids.mit.edu/yp/homepage/papers.html

Working Group in Information Theory is a self-educational project in the department. Techniques based on information theory have become essential in high-dimensional probability, theoretical computer science and statistical learning theory. On the other hand, information theory is not taught systematically. The goal of this group is to close this gap.

Fri Apr 10, 2020
3:00am - RH 340P - Harmonic Analysis
Oscar Dominguez [CANCELED] - (Universidad Complutense de Madrid, Spain )
CANCELED

Maximal functions play a central role in the study of differentiation,
singular integrals and almost everywhere convergence. With Sergey Tikhonov
(ICREA, Barcelona) we recently proved some pointwise estimates for maximal
functions in terms of smoothness and rearrangements. I plan to discuss the recent
progress on these topics and some applications. In particular, I will discuss the
Fefferman-Stein inequality for the sharp maximal function for r.i. spaces which
are close to L∞.

2:00pm to 2:50pm - TBA - Inverse Problems
Hanming Zhou - (UC Santa Barbara)
Cancelled: TBA

TBA

4:00pm to 5:00pm - https://zoom.us/j/8473088589 - Graduate Seminar
Hamid Hezari - (UC Irvine)
TBA