Can We Hear the Shape of a Graph? -
Can we hear the shape of a drum? This question has prompted a fundamental area of research in modern mathematics. One of the main characters in this story is the Laplace operator (aka the Laplacian), that can be defined using basic tools of calculus.

In this talk we will explore the graph Laplacian, a discrete version of the Laplace operator, which has broad applications in graph theory, combinatorics and mathematical physics. We will also explore how some of the properties of a graph (connectivity, cycles/trees and walks) can be extracted from the graph Laplacian. We will talk about recent work with undergraduate students on connections between the graph Laplacian and quantum mechanics.