## 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, randomized numerical analysis, 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 a 5 mins break. After the break we have a 45 mins seminar talk.

In fall 2022, the seminar takes place on Fridays between 10:00 am to 11:30 am CST.

Nov 11, Alex Wein, UC Davis, Computational Phases Transitions in Tensor Decomposition Slides

Nov 18, Alexander Barninok, U Michigan Ann Arbor, When a system of quadratic equations has a real solution Slides

Dec 2, Thomas Rothvoβ, U Washington Seattle, The Vector Balancing Constant for Zonotpes Slides

Dec 9, Daniel Dadush, CWI Amsterdam, From approximate to exact integer programming, Slides

The list of speakers on Spring 2022 and related documents are below.

March 17, Kevin Shu, Georgia Tech, Locally PSD Matrices and Hyperbolic Polynomials Slides

March 24, Jun-Ting (Tim) Hsieh, CMU, Algorithmic Thresholds for Refuting Random Polynomials Slides

March 31, Marcus Michelen, Univ. of Illinois at Chicago, Anti-concentration of random variables from zero-free regions Slides

April 7, Charilaos Efthymiou, Warwick, Sampling from Gibbs measures on graphs and hypergraphs Notes and Slides

April 14, Jonathan Leake, TU Berlin, Approximate counting via Lorentzian polynomials and entropy optimization Slides

April 21, Levent Dogan, TU Berlin, Polynomial time algorithms in invariant theory for torus actions Slides

April 28, Elias Tsigaridas, Inria-Paris, Sampling from feasible regions of semi-definite programs Slides

May 5, Josue Tonelli Cueto, Inria-Paris, On the complexity of sampling from parametric curves Notes

May 12, Boris Hanin, Princeton, Universality in Random Neural Networks Notes

The list of speakers on Spring 2021 and related documents are below.

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