PCMI Summer Session — Probabilistic and Extremal Combinatorics

Extremal graph theory and Ramsey theory are two of the central branches of modern extremal combinatorics, which seeks to understand the size and structure of discrete objects under certain natural constraints. In this course we will explore these topics, seeing both some of the beautiful techniques developed to study such problems, as well as many innocent-looking problems that seem completely out of reach of the currently-known techniques. We will also see some of the many connections these questions have to other areas of mathematics, including geometry, number theory, probability, and theoretical computer science.

Topics: Research Theme: Extremal and Probabilistic Combinatorics