Seminars and Colloquia by Series

TBA

Series
PDE Seminar
Time
Tuesday, January 21, 2020 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Prof. Xiaomin WangSouthern University of Science and Technology

TBA

Probabilistic approach to Bourgain's hyperplane conjecture

Series
Stochastics Seminar
Time
Thursday, January 16, 2020 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Arnaud MarsigliettiUniversity of Florida

The hyperplane conjecture, raised by Bourgain in 1986, is a major unsolved problem in high-dimensional geometry. It states that every convex set of volume 1 in the Euclidean space has a section that is lower bounded away from 0 uniformly over the dimension. We will present a probabilistic approach to the conjecture. 

Random matrix theory and supersymmetry techniques

Series
Job Candidate Talk
Time
Monday, January 6, 2020 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Tatyana ShcherbynaPrinceton University
Starting from the works of Erdos, Yau, Schlein with coauthors, significant progress in understanding universal behavior of many random graph and random matrix models were achieved. However for random matrices with a spatial structure, our understanding is still very limited.  In this talk I am going to overview applications of another approach to the study of the local eigenvalue statistics in random matrix theory based on so-called supersymmetry techniques (SUSY). The SUSY approach is based on the representation of the determinant as an integral over the Grassmann (anticommuting) variables. Combining this representation with the representation of an inverse determinant as an integral over the Gaussian complex field, SUSY allows to obtain an integral representation for the main spectral characteristics of random matrices such as limiting density, correlation functions, the resolvent's elements, etc. This method is widely (and successfully) used in the physics literature and is potentially very powerful but the rigorous control of the integral representations, which can be obtained by this method, is quite difficult, and it requires powerful analytic and statistical mechanics tools. In this talk we will discuss some recent progress in application of SUSY  to the analysis of local spectral characteristics of the prominent ensemble of random band matrices, i.e. random matrices whose entries become negligible if their distance from the main diagonal exceeds a certain parameter called the band width. 
 

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