Weyl's Law and Polya's Conjecture

Following Chapter 3 in Levitin--Mangoubi--Polterovich's book, we will investigate the distribution of Laplace eigenvalues on bounded domains. We will discuss several proofs of Weyl's famous law for the asymptotic distribution of high-energy eigenvalues and Polya's conjecture that the leading order term in this asymptotic series in fact provides unconditional bounds on the number of eigenvalues below any given threshold.