Affiliation: University of Delaware, USA

**Title: Spectral Turan Problems on trees and even cycles**

**Abstract**: In this talk, we discuss some recent progress with the spectral analogue of a few Tur\’an problems: Instead of maximizing the number of edges, our objective is to maximize the spectral radius of the adjacency matrices of graphs not containing some subgraphs.

You can watch the talk here, and the slides are available here.

*This talk was given on July 4th, 2022*

**Title: The spectral radius of graphs with no odd wheels**

**Abstract**: The odd wheel $W_{2k+1}$ is the graph formed by joining a vertex to a cycle of length $2k$. In this talk, we will investigate the largest value of the spectral radius of the adjacency matrix of an $n$-vertex graph that does not contain $W_{2k+1}$. We determine the structure of the spectral extremal graphs for all $k \geq 2$, k not equal to 4 and 5. When $k=2$, we show that these spectral extremal graphs are among the Tur\’an-extremal graphs on $n$ vertices that do not contain $W_{2k+1}$ and have the maximum number of edges, but when $k \geq 9$, we show that the family of spectral extremal graphs and the family of Turán-extremal graphs are disjoint.

You can watch the talk here, and the slides are available here.

*This talk was given on June 7th, 2021*