University Seminar (CCAS): Computability, Complexity, and Algebraic Structure

Time: Wednesday, February 28, 2:20pm – 3:35pm

Place: Tompkins Hall (725 23rd Street NW), Room 205

Speaker:  Max Alekseyev, GWU

Title:  Combinatorial exploration of breakpoint graphs at the intersection of quantum and bio-informatics

Abstract:  Breakpoint graphs were first introduced for the analysis of genome evolution almost three decades ago, and since then they have been actively studied and used in a variety of bioinformatics applications. In the simplest form, breakpoint graphs represent edge-colored (multi)graphs formed by 3 perfect matchings of different colors. Every pair of colors in a breakpoint graph defines a collection of cycles, in which the colors of edges alternate. Breakpoint graphs have rich combinatorial properties and connection to other combinatorial objects such as Bell polynomials.
Recently it was discovered that some special breakpoint graphs also appear in quantum informatics, while evaluating sums arising in the Weingarten calculus in the asymptotic limit of the number of degrees of freedom. This enabled us to employ techniques and results originally developed in bioinformatics to gain fine-grained understanding of the entanglement properties of a set of quantum states. In this talk I will present the mathematical side of the story, with just a bit of bio- and quantum informatics. 

This is a joint work with Adam Ehrenberg, Joseph Iosue, and Alexey Gorshkov from the University of Maryland.