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Mathematical Physics Seminar

Geometry of the Laplace Operator on Compact Riemannian Manifolds

Sagun Chanillo - Rutgers University

Location:  Hill 705
Date & time: Thursday, 14 November 2019 at 12:00PM - 1:00PM

Abstract:  This talk will be in part a survey of many of the results on the spectrum of the Laplace operator on compact Riemannian manifolds. In particular we will discuss the conjectures of Yau and the Courant Nodal domain theorem. We will then focus on a local version of the Courant Nodal domain theorem which was  rst investigated by Donnelley and C. Fefferman. This was improved by Chanillo-Muckenhoupt in the 1990s. Using recent work by Logunov and Mallinikova on the conjectures of Yau, we will also present near optimal versions of the local Courant theorem.

This is joint work with A. Logunov and E. Mallinikova.


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