##### Department of Mathematics,

University of California San Diego

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### Math 243 - Functional Analysis Seminar

## Priyanga Ganesan

#### Texas A \& M University

## Spectral bounds for chromatic number of quantum graphs

##### Abstract:

Quantum graphs are an operator space generalization of classical graphs that have appeared in different branches of mathematics including operator systems theory, non-commutative topology and quantum information theory. In this talk, I will review the different perspectives to quantum graphs and introduce a chromatic number for quantum graphs using a non-local game with quantum inputs and classical outputs. I will then show that many spectral lower bounds for chromatic numbers in the classical case (such as Hoffmanâ€™s bound) also hold in the setting of quantum graphs. This is achieved using an algebraic formulation of quantum graph coloring and tools from linear algebra.

Host: David Jekel

### November 16, 2021

### 10:00 AM

### Please email djekel@ucsd.edu for Zoom details.

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