Geometric Analysis from Drums to Dynamics
Time and place
1 PM on Monday, February 11th, 2013; Artino lab (NAC 1/511)
Julie Rowlett (University of Goettingen)
Abstract
Have you ever wondered why, when a rock guitarist plays high notes in a solo, he grips the strings down low on the guitar? Geometry affects physical properties, like sound, which can be described using analysis in general, and spectral theory in particular. We will begin with motivating examples and proceed to investigate M. Kac's question, "Can one hear the shape of a drum?" Spectral theory can be used not only to describe sound travel but also to describe the energy states of quantum particles. We will next explore relationships between the spectrum and Hamiltonian dynamics on some complete, negatively curved manifolds. In conclusion, I will discuss further directions and applications of geometric analysis.