Colloquium - Liam Solus

Date: December 11, 2018

Time: 4:00PM - 5:00PM

Location: BLOC 220

Speaker: Liam Solus, KTH Royal Institute of Technology

Description: Title: Combinatorics in the Analysis of Distributions
Abstract: A fundamental problem in mathematics is to determine the shape, structure, or characteristic features of a given probability distribution. This question arises in a variety of forms across research areas including algebra, geometry, statistics, physics, and computer science. Oftentimes, combinatorics can help us describe the desired features of the distribution in question. In this talk, we will discuss two instances of this problem and how combinatorics helps give the answer: the first arising in artificial intelligence and the second in algebra and geometry. In the first instance, we will see how combinatorics and its connections to discrete geometry can help us model cause-effect relationships amongst jointly distributed random variables. In the second, we will examine how the zeros of univariate palindromic polynomials with nonnegative coefficients can be used to answer recent questions and conjectures on the shape of discrete distributions associated to certain lattice polytopes or subdivisions of Cohen-Macaulay complexes.