Polya's Conjecture for Euclidean Balls

Polya's Conjecture for Euclidean Balls

Explore a seminar on spectral geometry focusing on Polya's conjecture for Euclidean balls. Delve into the 1954 conjecture by G. Pólya regarding the estimate ND(Ω,Λ) ≤ CW Λ d/2 for all Λ greater than 0, where Ω is a bounded domain in R d, Λ is the spectral parameter, ND(Ω,Λ) is the counting function of the Laplace operator of the Dirichlet problem in Ω, and CW is the constant in the Weyl law. Learn about the proof of this conjecture for balls of arbitrary dimension, presented by Nikolay Filonov from Saint Petersburg University. Gain insights into this collaborative work with M. Levitin, I. Polterovich, and D. A. Sher, which advances our understanding of spectral geometry and mathematical analysis.