## Speaker:

Jiaping Wang

## Institution:

University of Minnesota

## Time:

Thursday, March 31, 2022 - 4:00pm

## Host:

## Location:

ISEB 1010

The classical de Rham-Hodge theory implies that each cohomology

class of a compact manifold is uniquely represented by a harmonic

form, signifying the important role of Laplacian in geometry. The talk aims

to explain some results relating curvature to the spectrum of Laplacian. We

plan to start by a brief overview for the case of bounded Euclidean domains

and compact manifolds, highlighting some of the fundamental contributions by

Peter Li and others. We then shift our focus to the case of complete

Riemannian manifolds. In particular, it includes our recent joint work with

Ovidiu Munteanu concerning the bottom spectrum of 3-manifolds with scalar

curvature bounded below.