Exponentially Many Graphs Are Determined by Their Spectrum

Explore the fascinating world of spectral graph theory in this 49-minute seminar talk from the Spectral Geometry in the clouds series. Delve into Matthew Kwan's research on graphs determined by their spectrum, a discrete analogue of Kac's famous question about "hearing the shape of a drum." Discover how this topic relates to practical graph isomorphism testing and gain insights into which graphs can be uniquely identified by their adjacency matrix spectrum. Learn about Kwan's recent collaborative work with Ilya Koval, which demonstrates that exponentially many graphs are determined by their spectrum. Enhance your understanding of this intriguing area of mathematics and its potential applications in graph theory and beyond.