Alternatively have a look at the program.

## On the Farell-Jones conjecture for localizing invariants

This is a report on a joint project with D. Kasprowski and C. Winges. To every left-exact infinity category with a G-action and a finitary localizing invariant with target C we associate a functor from the orbit category of G to C. The Farrell-Jones conjecture asserts that this functor is equivalent to the left-Kan of its restriction to the subcategory of orbits whose stabilizers are vitually cyclic. |

## Semi-topological K-theory of dg-algebras and the lattice conjecture

I will discuss the problem of constructing a natural rational structure on periodic cyclic homology of dg-algebras and dg-categories. The promising candidate is A. Blanc’s topological K-theory. I will show that it, indeed, provides a rational structure in a number of cases and I will discuss its structural properties and possible applications.

## Analytic Geometry

We will discuss some of our joint work with Dustin Clausen on Analytic Geometry, based on Condensed Mathematics.

## On the $K$-theory of $\mathbb{Z}/p^n$

I will report on joint work with Achim Krause and Thomas Nikolaus on an algorithm to compute the higher algebraic $K$-groups of rings such as $\mathbb{Z}/p^n$.

## Artin reciprocity via spheres

I will explain a very strange proof of the Artin reciprocity law. At the heart of it is the construction of a sphere from every locally compact Q-vector space.

## Elliptic Zeta functions (only remotely)

In this talk, I speak about establishing a close connection between three notions attached to a modular subgroup, namely, the set of weight two meromorphic modular forms, the set of equivariant functions on the upper half-plane commuting with the action of the modular subgroup, and the set of elliptic zeta functions generalizing the Weierstrass zeta functions. In particular, we show that the equivariant functions can be parameterized by modular objects as well as by elliptic objects.

## The homology of configuration-section spaces

Configuration-section spaces parametrise fields with singularities on a given manifold, and may be viewed as an enrichment of configuration spaces by non-local data. |

## Reflection

This talk will introduce a notion of a stratification of a (stable presentable) category. A stratification of a scheme determines a stratification of its category of quasi-coherent sheaves. A stratification of a topological space determines a stratification of its category of linear sheaves. Such a stratification determines two reconstruction theorems, each reconstructing the category in terms of its strata and gluing data. An abelian group can be reconstructed in terms of its p-completions and its rationalization, as well as from its p-torsion and its corationalization.

## Weights in homotopy theory

Weight decompositions were first introduced in the setting of rational homotopy as a tool to study p-universal spaces. The same notion may be adapted to many other algebraic contexts and, in general, positive and pure weight decompositions have strong homotopical consequences, often related to formality. A main source of weights is algebraic geometry, either via the theory of mixed Hodge structures on de Rham cohomology or the theory of Galois actions in étale cohomology.

## Gathertown "meet the speakers" moment (online)

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