
Daniel O'Connor
Fri Jan 19, 2018
3:00 pm
Proximal algorithms offer state of the art performance for many large scale optimization problems. In recent years, the proximal algorithms landscape has simplified, making the subject quite accessible to undergraduate students. Students are empowered to achieve impressive results in areas such as image and signal processing, medical imaging, and...

Konstantin Tikhomirov
Thu Jan 18, 2018
4:00 pm
Convexgeometric methods, involving random projection operators and coverings, have been successfully used in the study of the largest and smallest singular values, delocalization of eigenvectors, and, among further applications, in establishing the limiting spectral distribution for certain random matrix models. Conversely, random linear...

Daniel Litt
Wed Jan 17, 2018
4:00 pm
Let X be an algebraic variety  that is, the solution set to a system of polynomial equations. Then the fundamental group of X has several incarnations, reflecting the geometry, topology, and arithmetic of X. This talk will discuss some of these incarnations and the subtle relationships between them, and will describe an...

Connor Mooney
Tue Jan 9, 2018
4:00 pm
Hilbert's 19th problem asks if minimizers of "natural" variational integrals are smooth. For the past century, this problem inspired fundamental regularity results for elliptic and parabolic PDEs. It also led to the construction of several beautiful counterexamples to regularity. The dichotomy of regularity vs. singularity...

Steven Sam
Mon Jan 8, 2018
3:00 pm
Representation stability is an exciting new area that combines ideas from commutative algebra and representation theory. The metaidea is to combine a sequence of objects together using some newly defined algebraic structure, and then to translate abstract properties about this structure to concrete properties about the original object of study....

Jeffrey Kuan
Fri Dec 8, 2017
3:00 pm
Markov duality in spin chains and exclusion processes has found a wide variety of applications throughout probability theory. We review the duality of the asymmetric simple exclusion process (ASEP) and its underlying algebraic symmetry. We then explain how the algebraic structure leads to a wide generalization of models with...

Jennifer Wilson
Mon Nov 20, 2017
4:00 pm
This talk will illustrate some topological properties of the space F_k(M) of ordered ktuples of distinct points in a manifold M. For a fixed manifold M, as k increases, we might expect the topology of the configuration spaces F_k(M) to become increasingly complicated. Church and others showed, however, that when M is connected and open, there is...