URA Seminar - Stephen Melczer

Title: Adventures in Enumeration

Abstract: We make the argument that by combining pure mathematical tools with computational insights and applications from a vast array of disciplines, combinatorics is the perfect area to see all the wonders of math on display. Applications discussed include the analysis of classical algorithms, restricted permutations, models predicting the shape of biomembranes, queuing theory, random walks, ratchet models for gene expression, maximum likelihood degree in algebraic statistics, transcendence of zeta values, sampling algorithms for perfect matchings in bipartite graphs, and parallel synthesis for DNA storage.