Algebraic Methods in Combinatorics

Combinatorics using some algebraic constructions. We use dimension arguments to get bounds on interesting combinatorial numbers. We study the eigenvalues of adjacency matrices on graphs to get information about graphs at hand. This has great applications in the so called extremal combinatorics.

In combinatorial geometry we will be studying combinatorial identities and inequalities that relate to point sets and polytopes. For instance, how many points in R^d can you find such that the distance between any two of them is one of two given real numbers? We will find bounds for these quantities using linear algebra.

Finally, we will be studying spectral theory on graphs. This has some interesting combinatorial consequences on graph properties.

Date and time info
Wednesday, 9am - 11am

Keywords
graph theory, convex geometry, extremal combinatorics, ham sandwich theorem

Prerequisites
Abstract algebra, linear algebra

Language
English