数学研究所

学术报告

综合报告会

Speaker: Prof. Dr. Thomas Schick(Georg-August-Universität Göttingen)

Title: The topology of positive scalar curvature

Time&Venue: 2024.12.18（星期三）15:30-17:00 & 南楼N204

Abstract: Given a smooth manifold M, geometers and topologists ask the question

"which geometries, i.e. which kind of Riemannian metrics" can one put on M?

In recent years, this problem has been studied intensively for metrics with positive scalar curvature.

The main questions are:

* is there such a metric at all?

* if so: can one "classify" these metrics?

It turns out that both questions have interesting answers.

Surprisingly, much of this turns out to be rather topological: there are well studied topological constructions

("surgery") of such metrics. There are obstructions, which are based on characterisitc classes and numbers.

This is happening in particular through the use of the spectral theory of the Dirac operator.

We will give a brief survey of what the theory and then focus on some recent developments, using higher index theory.