Abstracts of upcoming talks at the MPIM. For an overview see also the calendar.

## Recent developments in Quantum Topology -- Cancelled --

We will review the basics of quantum topology such as the colored Jones polynomial of a knot, its standard conjectures relating to asymptotics, arithmeticity and modularity, as well as the recent quantum hyperbolic invariants of Kashaev et al, their state-integrals and their structural properties. The course is aimed to be accessible by graduate students and young researchers.

## Applications of virtual fundamental classes to enumerative geometry

The aim of this talk is to show why understanding the construction of a virtual fundamental class is useful: firstly we do this via computing these in some examples of moduli spaces of stable maps and secondly by linking these classes to Gromov-Witten invariants and thus to certain problems in enumerative geometry. I will start with a recap from the summer (17th August), when moduli spaces of stable maps were introduced, giving explicit examples along the way.

## Cut and paste invariants of manifolds via algebraic K-theory

Recent work of Campbell and Zakharevich has focused on building machinery for studying scissors congruence problems via algebraic K-theory. Their main application was the study of the Grothendieck ring of varieties. In this talk, I will present an application of their framework to the study of cut and paste invariants of manifolds. In particular, I will talk about the construction of a spectrum that recovers the classical "cut and paste" groups for manifolds on \pi_0.

## Equivariant bordism, multiplicative gerbes and topological electronic structures of crystals

In this talk I will give a short presentation of who I am and the main mathematics subjects that have interested me.

## Tame geometry and Hodge theory

Originating in Grothendieck's "Esquisse d'un programme", tame geometry has been developed by model theorists under the name "o-minimal structures". It studies structures where every definable set has a finite geometric complexity. It has for prototype real semi-algebraic geometry, but is much richer.

## An Automorphic translation of Deligne’s conjecture: Special values of L-function attached to an automorphic representation of GL_N over a number field

Zoom Meeting ID: 919 6497 4060

For password see the email or contact Pieter Moree (moree@mpim...).

## Lie algebra action

Meeting ID: 997 9940 1217

For passcode contact Christian Kaiser (kaiser@mpim...)

## Generic regularity of min-max minimal hypersurfaces

Minimal hypersurfaces in 8-dimensional Riemannian manifolds may have isolated singularities. However, it follows from the results of R. Hardt, L. Simon and N. Smale that one can perturb away singularities of an area minimizing minimal hypersurface by a small change of the metric. I will talk about a similar problem for min-max minimal hypersurfaces (joint work with Otis Chodosh and Luca Spolaor). We show that for a generic 8-dimensional Riemannian manifold with positive Ricci curvature, there exists a smooth minimal hypersurface.

## W algebras and integrable structures

https://hu-berlin.zoom.us/j/61339297016

## Beauville decomposition: proof via Fourier-Mukai

Meeting ID: 997 9940 1217

For passcode contact Christian Kaiser (kaiser@mpim...)

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