On geometric eigenvalue boundsMPIM

by Filip Pietrzak (Universität Bonn/MPIM)

Tuesday May 12, 2026, 4:30 PM → 5:30 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Seminar Room (Max Planck Institute for Mathematics)

Reading group on spectral geometry

The aim of this talk is to introduce classical methods of dealing with eigenvalues on manifolds. We will begin with variational characterization via  minimax principles, then we will talk about topological restraints arising form Courant's nodal domain theorem. From there we turn towards isoperimetric problems introducing Cheeger constant and proving Cheeger's inequality - establishing a lower bound for smallest eigenvalue. If time allows we will show Buser's upper bound for $\lambda_1$ and provide some examples.