## 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.

## 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.

## Beauville decomposition: proof via Fourier-Mukai

Meeting ID: 997 9940 1217

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

## Lie algebra action

Meeting ID: 997 9940 1217

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

## Chow rings and abelian varieties

Meeting ID: 997 9940 1217

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

## 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.

## Properties of obstruction theories and virtual classes

After a recap of last week's constructions of perfect obstruction theories and virtual fundamental classes, I will discuss their properties with respect to deformation, and construct virtual pullbacks, which are bivariant classes. Then I will discuss the behaviour of virtual classes under pushforwards and give computational examples.

## Second moment of the central values of Rankin--Selberg $L$-functions

Asymptotic evaluation of higher moments of higher degree $L$-values is an interesting problem and has potential applications towards many questions in analytic theory of automorphic forms, e.g. subconvexity of the central $L$-values. In this talk I will explain a recent result on asymptotic evaluation of the second moment of $\mathrm{GL}(n) \times \mathrm{GL}(n)$ Rankin--Selberg central $L$-values where one of the forms is a fixed cuspidal representation and the other form is varying in a family containing representations with analytic conductors bounded by $X$ and $X \to \infty$.

## Holomorphic curves, boundaries, skeins, and recursion

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

## Non-abelian Abel's theorems and quaternionic rotation

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

## Macroscopic band width inequalities

Inspired by Gromov's work on 'Metric inequalities with scalar

curvature' we establish band width inequalities for Riemannian bands of

the form $(V=M\times[0,1],g)$, where $M^{n-1}$ is a closed manifold. We

introduce a new class of orientable manifolds we call 'filling

enlargeable' and prove:

If $M$ is filling enlargeable and all unit balls in the universal cover

of $(V,g)$ have volume less than a constant $\frac{1}{2}\epsilon_n$, then $width(V,g)\leq1$.

We show that if a closed orientable manifold is enlargeable or

## Topological expansions, Random matrices and operator algebras theory

In this lecture, I will discuss the remarkable connection between random

matrices and the enumeration of maps and some applications to sub-factor theory and physics.

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

## Topological expansions, Random matrices and operator algebras theory

In this lecture, I will discuss the remarkable connection between random

matrices and the enumeration of maps and some applications to sub-factor theory and physics.

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

## 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...).

## Defining perfect obstruction theories and virtual fundamental classes

I will talk about obstruction bundles and use them to give a preliminary definition of virtual fundamental classes. We will use this notion to compute the virtual fundamental class explicitly in some examples. Then, we will define virtual fundamental classes more generally as in Behrend-Fantechi using the notion of perfect obstruction theories.

## Mock Modular Forms

Meeting ID: 997 9940 1217

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

## Maass Forms and 2-dimensional Artin Representations

Meeting ID: 997 9940 1217

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

## Dynamical irreducibility of polynomials modulo primes

Zoom ID: 919 6497 4060

For password contact Pieter Moree (moree@mpim...).

## tba

## Prismatic cohomology of classifying stacks

I will tell about the theory of prismatic cohomology (developed recently by Bhatt and Scholze) and what it gives when applied to the classifying stack of a reductive group.

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