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## MPI-Oberseminar

The Oberseminar is a very long running seminar at MPI (‘Ober‘ standing for 'upper'). Its idea is that the guests of the MPI speak in this seminar (hopefully early in their stay) and get the chance to explain their work to the other guests.

## Friedrich Hirzebruch Lecture

The annual Friedrich Hirzebruch Lecture is a series of lectures started in 2007 on the occasion of the 80th birthday of Prof. Friedrich Hirzebruch. The lectures address a general audience and aim at illustrating the relation between mathematics and art, society and other fields.

## Metric Measure Spaces and Ricci Curvature

## Arbeitstagung 2017 on "Physical Mathematics" in honor of Yuri Manin

#### Organizers

C. Blohmann, M. Kapranov, P. Teichner, B. Vallette

#### Speakers

## Modular Forms are everywhere

## Irreducible SL(2,C)-representations of integer homology 3-spheres

We prove that the splicing of any two non-trivial knots in the 3-sphere admits an irreducible SU(2)-representation of its fundamental group. Using a result of Boileau, Rubinstein and Wang, it follows that the fundamental group of any integer homology 3-sphere different from the 3-sphere admits irreducible representations of its fundamental group in SL(2,C). Our result uses instanton gauge theory.

## tba

## Cycle classes of divisorial Maroni loci

Hurwitz spaces are the moduli spaces of covers of given genus

and degree of the projective line. There are natural divisors in these

moduli spaces that generalize the divisor that Maroni defined for

trigonal covers. The problem is to calculate the cycle classes in the

compactified Hurwitz spaces. We define effective cycles that extend

the Maroni divisors and calculate their classes. This is joint work

with Alexis Kouvidakis.

## tba

## Evolution Equations in Geometry (III)

Evolution equations have been used to address successfully key questions in Differential Geometry

like isoperimetric inequalities, the Poincaré conjecture, Thurston’s geometrization conjecture, or

the differentiable sphere theorem.

During this series of lectures we will give a general introduction to geometric flows, which are sort of

non-linear versions of the heat equation for a relevant geometric quantity. These equations should be

understood as a tool to canonically deform a manifold into a manifold with nicer properties, for instance,