## Spectral Turán problems

- March 26, 2021
- 2:30 p.m.

## Abstract

In this talk we will discuss what subgraphs can be guaranteed if a graph has a large eigenvalue. This is the spectral analog of the Turán problem and was first raised by Brualdi and Solheid and Nikiforov. We will give an overview of how to prove theorems in this area and will discuss some intuition for how to guess what the extremal graph(s) should be. This is joint work with Sebi Cioaba, Dheer Desai, Lihua Feng, Josh Tobin, and Xiao-Dong Zhang.