Special Colloquium
Galyna Livshyts
Georgia Institute of Technology
On various questions (and answers) in High-dimensional probability
Abstract: In this talk, several topics from High-dimensional probability shall be discussed.
This fascinating area is rich on beautiful problems, and several easy-to-state questions will be outlined.
Further, some connections between them will be explained throughout the talk.
I shall discuss several directions of my research. One direction is invertibility properties of inhomogeneous
random matrices: I will present sharp estimates on the small ball behavior of the smallest singular value of a very general ensemble of random matrices, and will briefly explain the new tools I developed in order to obtain these estimates.
Another direction is isoperimetric-type inequalities in high-dimensional probability. Such inequalities are intimately tied with concentration properties of probability measures. Among other results, I will present a refinement of the concavity properties of the standard gaussian measure in an n-dimensional euclidean space, under certain structural assumptions, such as symmetry. This result constitutes the best known to date estimate in the direction of the conjecture of Gardner and Zvavitch from 2007.
Tuesday December 3, 2019 at 3:00 PM in 636 SEO