## Seminar on Geometry, Probability, and Computing

by Alperen Ergür @ UTSA, Grigorios Paouris @ TAMU, and Petros Valettas @ Mizzou.

Discrete and convex geometry, computational algebraic geometry, computational phase transitions, high dimensional probability, convex optimization, computational topology, and complexity theory.

We don't record the talks. This is meant to be a working seminar to facilitate discussions.

The format: First 30 mins will be an introduction that is accessible to students and faculty from math, CS, and engineering. Then we have 5 mins break. After the break we have a 45 mins seminar talk.

In Spring 2021, the seminar takes place on Thursdays between 10:00 am to 11:30 am CST.

Feb 4, Alexander Barvinok, University of Michigan, Ann Arbor, Title: Testing systems of real quadratic equations for (approximate) solutions
Slides

Feb 11, Alperen Ergur, UTSA, Title: Semidefinite Representations of Derivative Relaxations of Spectrahedra (after Parrilo and Saunderson)

Feb 25, Nikhil Srivastava, University of California, Berkeley, Title: The Quantitative Lax Conjecture Notes

March 4, Gennadiy Averkov, Technical University of Brandenburg, Title: Are semidefinite relaxations a silver bullet for polynomial optimization?
Slides

March 11, Grigorios Paouris, TAMU, Title: Matching Polytope has exponential extension complexity (after Rothvoβ)
Slides

March 18, Jonathan Leake, Technical University of Berlin and LFIAS, Title: Flow polytope volume bounds via polynomial capacity
Slides

March 25, Greg Blekherman, Georgia Institute of Technology, Title: Tropicalization in Convex Geometry and Combinatorics
Slides

April 8, Rekha Thomas, University of Washington at Seattle, Title: Lifts of Convex Sets Slides

April 15, Jesús Rebollo Beuno, University of Missouri at Columbia, Title: Complexity of Unconditional Convex Bodies (after Rudelson) Notes

April 22, Georgy Scholten, North Carolina State University, Title: Sparse Moments of Univariate Step Functions

April 29, David Papp, North Carolina State University, Title: Sum of Squares Without Semidefinite Programming