GRK Retreat 2026 Schedule

Location:

Talks:

Dimension expanders and quiver representations (Markus Reineke) slides

Abstract: We first briefly review the notion of expander graphs and its utility. Then we turn to the concept of dimension expanders of Lubotzky-Zelmanov and Wigderson. We formulate an optimal existence result, which is proved using ideas from quiver representation theory. All representation-theoretic notions will be recalled, and we give an outline of the proof. Finally, we discuss a more general notion of expander representations.

Serre's class field theory (Ismaele Vanni)

Abstract: This will be an expository talk on Serre's paper "Sur les corps locaux à corps résiduel algébriquement clos", which provides a geometric interpretation of the Galois group of the maximal abelian extension of a local field K with algebraically closed residue field, using the theory of proalgebraic groups he had previously laid down.

Functorial stratifications of singularities in characteristic 0 (Vicente Monreal)

Abstract: In this talk we will discuss existence of canonical and functorial stratifications of singularities in characteristic 0. The stratifications to be presented, called riso-stratifications, were introduced in affine contexts by Bradley-Williams and Halupczok using non-archimedean and model-theoretic methods. Recent work proved that they are embedding independent and can be computed étale locally, upgrading their construction into a canonical and functorial stratification process that works for schemes of finite type over fields of characteristic 0. We will describe the geometric ideas involved in this work and dicuss its compatiblity with classical approaches to singularities.

The derived category of coherent sheaves

1. (Jan Hennig)
2. (Julian Reichardt)
3. Fourier-Mukai transforms of abelian varieties(Fabian Rodatz)

Abstract: The derived category is constructed from the (homotopy) category of chain complexes by inverting all quasi-isomorphisms (morphisms inducing isomorphisms on cohomology groups). The derived category not only has some more desirable properties than the category of chain complexes, we can take the whole derived category associated to a variety as an invariant. The goal of this mini-course is to explore two applications of this. We start by giving an introduction to derived categories. Then we will look at what it means for two smooth projective varieties to have equivalent derived categories. The first application is a reconstruction theorem of Bondal-Orlov, which states that a variety with ample canonical or anti-canonical bundle can be reconstructed from its derived category. The second application is a theorem of Mukai, which states that the derived category of an abelian variety is equivalent to the derived category of its dual abelian variety. As there are abelian varieties not isomorphic to their dual, this gives examples of non-isomorphic varieties with equivalent derived categories.

Functional programmming and monads in Haskell (Daniel Echtler)

Abstract: Programming and mathematics have been intertwined from the beginning: In fact, computer science started out as a branch of mathematics and early on, computer scientists, like Alonzo Church, Grace Hopper, and Alan Turing, where in fact mathematicians. Nowadays, especially theoretical computer science and math are still overlapping. Whether it be word and decision problems, cryptography, graph theory, or computability theory. However, there does not seem to be a huge connection between pure mathematics and programming anymore. In this talk I will try to convince you that this connection still exists and that programming can (in some cases) be considered just mathematics! To do so, I will discuss functional programming and the usage of monads (a concept from category theory) in the Haskell programming language.

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Retreat 2025
GRK schedule summer semester 2023