Lectures WS 2025/2026

Speaker: Leon Goertz, Universität Hamburg – Invited by Catherine Meusburger

Abstract: Given a commutative Frobenius algebra A, Asaeda–Frohman and Kaiser define for every 3-manifold M a skein module of embedded A-decorated surfaces in M. These generalize structures appearing in the construction of Khovanov homology and form the state spaces of a (2,3,3+\epsilon)-dimensional TQFT. Using an inductive state-sum construction following Walker, this can be partially extended to dimension 4.

In the first part of my talk, I will sketch the general construction and explain the necessary assumptions for an extension to 4d 2-handlebodies. In the second part, I will focus on surface skein theory associated to the Frobenius algebra underlying Lee’s deformation of Khovanov homology.

Speaker: Max Demirdilek, Universität Hamburg – Invited by Catherine Meusburger

Abstract: Grothendieck-Verdier categories are monoidal categories with a duality structure generalising rigid duality. Examples include categories of bimodules, modules over Hopf algebroids, and modules over vertex operator algebras.

Unlike rigid categories, Grothendieck-Verdier categories admit non-invertible associativity constraints. These can be studied using a surface-diagrammatic calculus, extending Joyal and Street’s string-diagrammatic calculus into a third dimension. I will illustrate this calculus in the context of Frobenius algebras and higher Frobenius–Schur indicators. To make the geometry tangible, I will share 3D-printed surface diagrams created with homotopy.io.

If time permits, I will also present coherence theorems for Grothendieck-Verdier categories. These combinatorial results, from ongoing joint work with Christian Reiher and Christoph Schweigert, simplify calculations in the surface-diagrammatic calculus.

(The lecture will take place at 4:00 p.m. in lecture hall H12.)

Speaker: Joonas Vättö, Aalto University – Invited by K.-H. Neeb, M. S. Adamo

Abstract: In Segal’s axiomatisation, a chiral conformal field theory (CFT) is a projective, monoidal functor from compact Riemann surfaces to the category of Hilbert spaces and Hilbert-Schmidt maps, satisfying natural compatibility conditions under gluing and boundary reparametrisations. The formalism is constructed to capture key properties of the path integral while avoiding measure-theoretic difficulties.

Once a CFT is shown to satisfy Segal’s prescriptions, analytic control over central objects in alternative axiomatisation schemes (e.g. vertex operator algebras) is expected to follow. However, as the formalism requires nuanced interplay between disparate areas of mathematics, Segal CFTs are notoriously difficult to construct with concrete examples being few and far between. In this talk, I will review Segal’s framework and present a construction of the massless free boson CFT.

Speaker: Aidan Sims, University of New South Wales – Invited by Kang Li

Abstract: Over the course of three reasonably leisurely lectures I will develop the basics of homology and cohomology of \’etale groupoids and their relationship to associated *-algebras and C*-algebras. The rough schedule will be as follows.

In the first lecture I will discuss what an \’etale groupoid is, with particular emphasis on ample groupoids, describe some key classes of examples arising from directed graphs and their analogues, and define their homology (for this I will stick strictly to the ample case to avoid getting bogged down in technicalities) and cohomology.

Speaker: Aidan Sims, University of New South Wales – Invited by Kang Li

Abstract: Over the course of three reasonably leisurely lectures I will develop the basics of homology and cohomology of \’etale groupoids and their relationship to associated *-algebras and C*-algebras. The rough schedule will be as follows.

In the second lecture I will introduce the *-algebras and C*-algebras of a groupoid, and outline how cohomology can be used to twist such C*-algebras, including an overview of their structure theory, and how homology relates to some of the classical algebraic invariants of a groupoid C*-algebra.

Speaker: Aidan Sims, University of New South Wales – Invited by Kang Li

Abstract: Over the course of three reasonably leisurely lectures I will develop the basics of homology and cohomology of \’etale groupoids and their relationship to associated *-algebras and C*-algebras. The rough schedule will be as follows.

In the third lecture I will describe techniques for computing the homology of a groupoid and indicate how these computations can be used to recover some well-known computations of K-theory. I will also discuss the idea of an equivalence of ample groupoids, and discuss the relationship between groupoid equivalence and groupoid homology.

Speaker: Jacopo Bassi, Università degli Studi di Roma Tor Vergata – Invited by Kang Li

Abstract: After a review of some basic constructions and results in Analytic Group Theory, I will introduce possible candidates of hyperbolicity of a discrete group from the analytic point of view. These are biexactness, the (AO)-property and solidity of the von Neumann algebra of the group. An interesting problem is to understand whether these concepts are different. If time permits I will discuss how the dynamics on non-standard extensions of the Stone-Cech boundary of the group enables to study the possible gap between biexactness and the (AO)-property.