### TBA by Prasad Tetali

- Series
- High Dimensional Seminar
- Time
- Wednesday, April 15, 2020 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Prasad Tetali – GaTech

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- Series
- High Dimensional Seminar
- Time
- Wednesday, April 15, 2020 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Prasad Tetali – GaTech

- Series
- High Dimensional Seminar
- Time
- Wednesday, April 8, 2020 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Vlad Yaskin – University of Alberta

Tba

- Series
- High Dimensional Seminar
- Time
- Wednesday, April 1, 2020 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Speaker
- Alexei Novikov – Penn State – novikov@psu.edu

TBA

- Series
- High Dimensional Seminar
- Time
- Wednesday, March 25, 2020 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Samantha Petti – Georgia Tech

TBA

- Series
- High Dimensional Seminar
- Time
- Wednesday, March 11, 2020 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Speaker
- Santosh Vempala – Georgia Tech

TBA

- Series
- High Dimensional Seminar
- Time
- Wednesday, March 4, 2020 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Speaker
- Vladimir Oliker – Emory University

In his book Convex Polyhedra, ch. 7 (end of subsection 2) A.D. Aleksandrov raised a general question of finding variational statements and proofs of existence of convex polytopes with given geometric data. As an example of a geometric problem in which variational approach was successfully applied, Aleksandrov quotes the Minkowski problem. He also mentions the Weyl problem of isometric embedding for which a variational approach was proposed (but not fully developed and not completed) by W. Blashke and G. Herglotz. The first goal of this talk is to give a variational formulation and solution to the problem of existence and uniqueness of a closed convex hypersurface in Euclidean space with prescribed integral Gaussian curvature (also posed by Aleksandrov who solved it using topological methods). The second goal of this talk is to show that in variational form the Aleksandrov problem is closely connected to the theory of optimal mass transport on a sphere with cost function and constraints arising naturally from geometric considerations.

- Series
- High Dimensional Seminar
- Time
- Wednesday, February 26, 2020 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Petros Valettas – University of Missouri, Columbia

- Series
- High Dimensional Seminar
- Time
- Wednesday, February 19, 2020 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Michail Sarantis – GeorgiaTech

Let $N_n$ be an $n\times n$ matrix whose entries are i.i.d. copies of a random variable $\zeta=\xi+i\xi'$, where $\xi,\xi'$ are i.i.d., mean zero, variance one, subgaussian random variables. We will present a result of Luh, according to which the probability that $N_n$ has a real eigenvalue is exponentially small in $n$. An interesting part of the proof is a small ball probability estimate for the smallest singular value of a complex perturbation $M_n=M+N_n$ of the original matrix.

- Series
- High Dimensional Seminar
- Time
- Wednesday, January 29, 2020 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Speaker
- Han Huang – Georgia Tech

Let $K$ be a n dimensional convex body with of volume $1$. and barycenter of $K$ is the origin. It is known that $|K \cap -K|>2^{-n}$. Via thin shell estimate by Lee-Vempala (earlier versions were done by Guedon-Milman, Fleury, Klartag), we improve the bound by a sub-exponential factor. Furthermore, we can improve the Hadwiger’s Conjecture in the non-symmetric case by a sub-exponential factor. This is a joint work with Boaz A. Slomka, Tomasz Tkocz, and Beatrice-Helen Vritsiou.

- Series
- High Dimensional Seminar
- Time
- Wednesday, January 22, 2020 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Galyna Livshyts – Georgia Tech

The first part of this pair of talks will be given at the Analysis seminar right before; attending it is not necessary, as all the background will be given in this lecture as well, and the talks will be sufficiently independent of each other.

I will discuss the L_p-Brunn-Minkowski inequality for log-concave measures, explain ‘’Bochner’s method’’ approach to this problem and state and prove several new results. This falls into a general framework of isoperimetric type inequalities in high-dimensional euclidean spaces. Joint with Hosle and Kolesnikov.

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