Instructor: Prof. Masoud Khalkhali
Email: masoud@uwo.ca
Application Deadline: January 18th, 2021
Lecture Times: Mondays and Wednesdays | 2:00 pm - 3:30 pm 
Course Dates: January 11th - April 14th, 2021

Course Overview
One of the central questions of spectral geometry is to know how much of the geometry and topology of a Riemannian manifold can be recovered from its Laplace spectrum. For example, is it true that isospectral manifolds are isometric? The essence of this question was captured in the title of a famous article by Marc Kac "Can one hear the shape of a drum?". Topics to be covered: spectral decomposition of L²(M), direct and inverse spectral  problems, Minakshisundaram-Pleijel asymptotic expansion of the heat kernel, Weyl's asymptotic law, lattice theta functions and Milnor's counterexample, Counterexamples of Gordon-Web-Wolpert, spectral zeta functions, trace formulas of Poisson and Selberg.

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