Title: Quantum independence number
|Affiliation:||University of Waterloo|
|Zoom:||Contact Soffia Arnadottir|
From this talk you will be able to learn what quantum independence number is and how it is different from the classical independence number. I will provide both known individual and infinite families of the graphs where classical and quantum independent numbers are different, as well as some of our generalisations of these examples.
Title: Interlacing methods in Extremal Combinatorics
|Zoom:||Contact Emma Watson|
Extremal Combinatorics studies how large or how small a collection of finite objects could be, if it must satisfy certain restrictions. In this talk, we will discuss applications of spectral graph theory, more specifically eigenvalue interlacing, to prove various interesting results in Extremal Combinatorics. We will discuss the Erdos-Ko-Rado Theorem and its degree version, an isodiametric inequality for discrete cubes, and the resolution of a thirty-year-old open problem in Theoretical Computer Science, the Sensitivity Conjecture of Nisan and Szegedy. Several open problems will also be mentioned during this talk.