## Geometry Seminar - Abstracts

### Talk

Tuesday 4 February 2020, 15:30-16:30 in HG02.802

**Saskia Roos** (Potsdam)

*Dirac operator under collapsing to a smooth manifold*

### Abstract

We consider a sequences of spin manifolds with bounded curvature and diameter that collapses to a smooth manifold. In that setting we show that a part of the spectrum of the Dirac operator converges to an explicitly given twisted Dirac operator with a symmetric potential. Moreover, we give an example of collapsing sequences where the spectrum of the Dirac operator converges to the spectrum of the Dirac operator on the limit space.

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