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

## Spectra, Complex Oriented Cohomology Theories, and Formal Group Laws

## From typed programming languages to synthetic homotopy theory

In this talk I'll try to give an overview of (homotopic) type theory, a theory which produces a very important link between computer science and homotopy theory and which is at the heart of modern proof assistants.

We'll start with concrete examples from computer science, which will allow us to introduce Martin-Löf's dependent type theory. We'll then talk about Voevodsky's univalence axiom and finally the interepration of this theory in simplicial sets by Voevodsky, Lumsdaine and Warren.

## Adic spaces

## The restricted lower central series spectral sequence

## Hyperbolic 4-manifolds of low volume

There is a natural interest in hyperbolic manifolds of low volume, and this talk addresses dimension four.As opposite to dimension n = 3 (Thurston's hyperbolic Dehn filling), for n > 3 the volume spectrum is discrete, and there is at most a finite number of hyperbolic n-manifolds with bounded volume (Wang's finiteness). Computing the number of hyperbolic 4-manifolds of given small (even minimal) volume appears nowadays far from reach. Counting such manifolds up to commensurability seems less unrealistic, at least by restricting the count to arithmetic manifolds.

## Intertwining Fourier-Mukai and Wehrheim-Woodward functors via mirror symmetry of tori (master's talk 1)

After a brief motivation for mirror symmetry, we will discuss how to sistematically produce the mirror symmetry functor for the product, following the paper of Abouzaid and Smith. The technology presented will help us relate Wehrheim-Woodward functors to Fourier-Mukai ones.

For the most part of the talk we will handle symplectic 2-tori, but we will ask ourselves whether what we performed holds in greater generality. Does this point towards a 2-categorical framework for mirror symmetry?

## The stack of L-parameters

## tba

## The distribution of values of $L(1,\chi)$, where $\chi$ is a cubic character over $\mathbb Q$

In this talk, I will speak about the distribution of the special values $L(1, \chi)$ as $\chi$ varies over the family $F(X)$ of cubic primitive characters of conductor less or equal to $X$, and in particular the distribution of extreme values. This is a recent joint work with Chantal David, Matilde Lalı́n, and Allysa Lumley.

## Distinguishing Brill--Noether loci

Classical Brill–Noether theory studies linear systems on a general curve in the moduli space $\mathcal{M}_g$ of algebraic curves of genus $g$. A refined Brill–Noether theory studies the linear systems on curves with a given Brill–Noether special linear system.

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