# Abstracts

Prof. Bernd Ammann und Mitarbeiter, Zimmer 119

### Clara Aldana, (Univ. Luxembourg; MPI Bonn; Universidad del Norte in Barranquilla, Colombia)

## Compactness of conformal metrics under critical curvature bounds

### Tuesday, 13.11.2018, 10.15 in M009

In this talk I will present recent joint work with Gilles Carron and Samuel Tapie (Université de Nantes). I will show how, using techniques from harmonic analysis, we can prove compactness of conformal metrics with critical integrability conditions on the scalar curvature. This relates to two problems in differential geometry: Pinching of the curvature and finding geometrical conditions under which a sequence of conformal metrics admits a convergent subsequence. The main tool is the use of A_{∞}-weights and strong A_{∞}-weights. I will introduce all the necessary definitions and will give a motivation of the problem.

## Existences of Dirac harmonic maps

### Tuesday, 4.12.2018, 10.15 in M009

Recently Prof. B. Ammann and N. Ginoux published their results to characterize some explicit construction of Dirac-harmonic maps. In this talk I would like to give a survey of the known results on the existence of Dirac-harmonic maps: examples, rigidity, and implicit existence and also non-existence.

## On the space of initial value pairs satifying the dominant energy condition strictly

### Tuesday, 29.1.2019, 10.15 in M009

In this talk, we want to study the space of initial value pairs satisfying the dominant energy condition strictly.
In order to do so, we introduce a kind of alpha-invariant for initial
values and compare it to its classical counterpart.
Invoking recent non-triviality results for the latter,
we will be able to conclude that the space of interest
has non-trivial homotopy groups.

Bernd Ammann, 29.01.2019

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