## Geometry Seminar - Abstracts

### Talk

Thursday 25 May 2023, 16:00 - 17:00 in HG00.065

**Anna Sakovich** (Uppsala)

*Mass and its positivity in Riemannian Geometry and General Relativity*

### Abstract

Suppose that we are given two Riemannian manifolds that 'look alike'
near infinity. Under which minimal geometric assumptions can we
determine if these two manifolds are identical or different? If one of
the two manifolds is either Euclidean space or hyperbolic space, the
answer to this question can be provided by an invariant called mass,
which was first discovered in General Relativity. In this talk we will
discuss geometry and physics behind this rather unique invariant and
review some geometric inequalities where it appears. We will conclude by
giving a brief outline of our recent proof of the positive mass theorem
in the case when the geometry at infinity is asymptotically hyperbolic.

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