We will have a research visitor, and we would like to schedule the following seminar:

Date and time: Thursday October 6, 2022 10:00am-11:00am

Speaker: Dheer Desai, University of Wyoming

Title: Spectral Turan Problems on trees and even cycles

Abstract: In this talk, we discuss some recent progress for 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 forbidden subgraph(s). We will overview some known results and compare extremal graphs for both kinds of problems. A celebrated theorem of Erd\H{o}s, Stone and Simonovits gives the asymptotics of the Tur\'an numbers when the forbidden graphs have chromatic number more than 2. A similar result also holds for the spectral Tur\'an numbers. In contrast, the asymptotics are not known for several basic bipartite graphs. We will discuss a recursive method that was initially used to obtain spectral Tur\'an results when the forbidden graphs had chromatic number more than two, and has recently been used to find spectral extremal graphs for even cycles and trees.

The speaker will be presenting in person in StuCo 4113. All are welcome to join in person or on zoom.

Please contact MathStats-staff@ucdenver.edu for Zoom url