# Computer Science/Discrete Mathematics Seminar I

**Topic: **Strongly log concave polynomials, high dimensional simplicial complexes, and an FPRAS for counting Bases of Matroids

**Speaker: **Shayan Oveis Gharan

**Affiliation: **University of Washington

**Date & Time: **Monday February 25th, 2019, 11:00am - 12:00pm

**Location: **Simonyi Hall 101

**Video:** https://video.ias.edu/csdm/2019/0225-ShayanOveisGharan

A matroid is an abstract combinatorial object which generalizes the notions of spanning trees, and linearly independent sets of vectors. I will talk about an efficient algorithm based on the Markov Chain Monte Carlo technique to approximately count the number of bases of any given matroid. The proof is based on a new connections between high dimensional simplicial complexes, and a new class of multivariate polynomials called completely log-concave polynomials. In particular, we exploit a fundamental fact from our previous work that the bases generating polynomial of any given matroid is a log-concave function over the positive orthant. Based on joint works with Nima Anari, Kuikui Liu, and Cynthia Vinzant.