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The Geometry of Polynomials for Log-Concavity and ExpansionLog concavity is an important feature of many functions and discrete sequences appearing across mathematics, including combinatorics, algebraic geometry, convex analysis, and optimization. In this talk I will survey recent developments in our understanding of functional log concavity with a focus on applications to combinatorial inequalities and algorithms for approximate counting and sampling. At the heart of this story are rich classes of multivariate generating polynomials that give rise to discrete probability distributions that can be approximately sampled efficiently using Markov chains. The basis-generating polynomial of a matroid is a fundamental example. We will explore applications to matroids and extensions to other combinatorial structures.Uploaded 06-10-26 Learn more about your ad choices. Visit megaphone.fm/adchoices
