talks & conferences
Overview of talks, conferences, and seminars.
2026
Tensor categories in representation theory & vice versa Uppsala University, Uppsala, Sweden August 24–27, 2026 · Conference
Lightning Talk (Title TBA)
Seminar der Arbeitsgruppen Diskrete Mathematik/Geometrie & Diskrete Geometrie TU Berlin, Germany August 5, 2026 · Seminar
Circular double leaves in the diagrammatic Hecke category
Oberseminar Darstellungstheorie Max Planck Institute for Mathematics (MPIM), Bonn, Germany June 26, 2026 · Seminar
The Zamolodchikov relation
The Hecke algebra is categorified in two ways. Firstly algebraically by Soergel bimodules, secondly diagrammatically by the diagrammatic Hecke category. The latter category is generated by strands in one color for every generating reflection of the underlying Coxeter group, subject to certain one-color, two-color and three-color relations. While in type $A_3$ and $B_3$ Elias–Williamson gave an exact description of the three-color (also called Zamolodchikov) relation, there is still a gap in type $H_3$. Each diagrammatic relation is a certain equality of two morphisms between Bott-Samelsons. We will explain how one can go in-between the algebraic and diagrammatic world to compute how these morphisms factor over all indecomposable summands of these Bott-Samelsons. For this we need to explain the construction of idempotents inside the diagrammatic category. As a consequence we can 1. describe a fake Zamolodchikov relation in $A_3$, 2. analyse all possible variants of Zamolodchikov relations in type $A_3$ and $B_3$, and 3. describe how one could find the missing gap in $H_3$, as well as showing how far computer calculations already came.
International Workshop on quantum groups, categorification and related topics Tianyuan Mathematical Research Center, Kunming, Yunnan, China June 07–12, 2026 · Conference
The Zamolodchikov relation
The diagrammatic Hecke category categorifies the category of Soergel bimodules. For every generating reflection of the underlying Coxeter group we have one color of strands in the diagrammatic category. They satisfy certain one-color, two-color and three-color relations. The latter is also called Zamolodchikov relation. While in type $A_3$ and $B_3$ Elias–Williamson gave an exact description there is still a gap in type $H_3$. We will explain how a solution can look like; what happens in type $A_3$ and $B_3$ for variants of the original Zamolodchikov and how far the calculation in type $H_3$ has come.
Mini-conference: Categorification University of East Anglia, Norwich, UK January 12–13, 2026 · Conference
Idempotents and dimensions in the asymptotic Hecke category
The diagrammatic Hecke category, introduced by Elias–Williamson, provides a categorical framework for studying Soergel bimodules through diagrams. We present results from recent joint work with Ben Elias and Dani Tubbenhauer. Our main contributions includes an algorithmic construction of idempotents, as well as the computations of the dimensions of objects inside the asymptotic Hecke category. We show these with many diagrammatic examples.
| Event | Slides |
2025
Joint Block Seminar on Category Theory University of Zurich, Switzerland December 2, 2025 · Seminar
Computing Idempotents and Dimensions in the Asymptotic Hecke Category
The diagrammatic Hecke category, introduced by Elias and Williamson, provides a categorical framework for studying Soergel bimodules using diagrams. We present results from recent joint work with Ben Elias and Dani Tubbenhauer on idempotents, traces, and dimensions in Hecke categories.
We begin by motivating general string-diagram notation for monoidal categories. We then define the diagrammatic Hecke category of Soergel bimodules and illustrate it with numerous examples. The main contribution of the paper is an algorithmic construction of clasp idempotents. Using these new idempotents, we define the asymptotic Hecke category and compute the dimensions of objects within it.
Annual Meeting 2025 of the SFB TRR 195 University of Tübingen, Germany September 22–25, 2025 · Conference
Computing in the asymptotic Hecke category
The diagrammatic Hecke category, introduced by Elias–Williamson, provides a categorical framework for studying Soergel bimodules through diagrams. We present results from recent joint work with Ben Elias and Dani Tubbenhauer on idempotents, traces, and dimensions in Hecke categories. Our main contributions include an algorithmic construction of clasp idempotents, which we will present here, as well as a variety of examples in many different types of Coxeter groups. Furthermore, we construct the asymptotic Hecke category, a categorification of Lusztig’s asymptotic Hecke algebra. We present methods to compute categorical dimensions of objects in this monoidal category.
2023
Block Seminar, SFB 195 Graduate Programme Trippstadt, Germany September 18–22, 2023 · Organized event
An Introduction to Categorification
Starting from the very definition of a category, we will look at the idea of the categorification of an algebraic object. This turned out to be a powerful method in a variety of mathematical contexts in the last decades. One classical example will be Khovanov Homology, a categorification — and more powerful version — of the Jones-polynomial for links. To this end we introduce specific topics of homological algebra, links, diagrammatic algebras and put it all together into a connecting framework.