PostDoc, University of Warwick

Sparse robust expander

One of the most exciting developments in combinatorics in the past four decades is that of expanders. It was first introduced to construct networks (represented by graphs) that are economical (sparse) and robust (highly connected). Depending on the perspective, expanders can be defined in various different ways. From the algebraic point of view, expanders are the graphs with large spectral gap; from the probabilistic point of view, random walks on expanders are rapidly mixing; and from the graph theoretic point of view, an expander is a graph whose vertex subsets have `large' boundaries. Due to this nature, expanders have found applications in other areas of mathematics and theoretical computer science. In this talk, I will present an embedding strategy using a notion of sublinear expander first introduced by Komlos and Szemeredi. As applications, it settles a conjecture of Mader in $1999$ on large clique-subdivisions in dense graphs without $4$-cycles. Joint work with Jozsef Balogh and Hong Liu.

I am a postdoctoral researcher at the Mathematics Institute of the University of Warwick with Oleg Pikhurko. I completed my PhD at the University of Illinois at Urbana-Champaign in August 2016 advised by J\'ozsef Balogh.

Watch video from here.