### Overview

## About

Broadly speaking, I’m interested in representation theory, its interaction with geometry, and computer-algebraic aspects. My main focus is on what may be called **algebraic Lie theory**. Explicitly, I’m interested in/working on the following (the numbers in brackets refer to my publications):

- Rational Cherednik algebras, Calogero–Moser spaces, and Poisson deformations in general [1,2,4,5,6]
- Flat families of finite-dimensional algebras [3,7]
- Computational aspects in ring and representation theory [2]
- Coxeter groups, Kazhdan–Lusztig theory, Hecke algebras [5]
- Complex reflection groups [1,5]
- Highest weight categories, cellular algebras [8]
- Soergel bimodules
- Tensor categories

It is not so obviously visible in this list but one of my main motivations is actually (in the very long run) to better understand finite reductive groups and their representations. I’m also particularly interested in the *spetses program* by Broué–Malle–Michel and the *Calogero–Moser vs. Kazhdan–Lusztig program* initiated by Gordon–Martino and Bonnafé–Rouquier. The idea is roughly to generalize finite groups of Lie type to objects having a *complex* reflection group as “Weyl group”. Hecke algebras and the more recent rational Cherednik algebras play a key role in this. In the introduction of [4] I give some details.

### Short CV

Here is a short CV, you can find the full one here.

- Since Apr 2017: Research Fellow in Algebraic Geometry and Lie Theory at
**University of Sydney** - Mar 2016–May 2016: Research stay at
**Glasgow University**(supported by Edinburgh Mathematical Society). - Jul 2014: PhD in pure mathematics at
**University of Kaiserslautern**with thesis*On restricted rational Cherednik algebras*. Supervisors: Gunter Malle and Raphaël Rouquier. - Oct 2012–Mar 2017: Research assistant of Meinolf Geck at
**University of Stuttgart**. Between Jul 2014 and Jul 2016 funded by DFG SPP 1489*Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory*. - Nov 2009–Sep 2012: Research assistant of Gunter Malle at
**University of Kaiserslautern**. Funded by DFG SPP 1388*Representation Theory* - Nov 2009: Diplom in mathematics (with specialization in algebraic number theory and with physics as minor) at
**University of Kaiserslautern**with thesis*Mackey functors and abelian class field theories*. Supervisor: Gunter Malle. - Sep 2007–Feb 2008: Visiting graduate student at
**Harvard University**.

### Current favorite quote

*That same answer — the unique thing at the center of all these cohomology theories — was what Grothendieck called a “motive.” “In music it means a recurring theme. For Grothendieck a motive was something which is coming again and again in different forms, but it’s really the same,” said Pierre Cartier, a mathematician at the Institute of Advanced Scientific Studies outside Paris and a former colleague of Grothendieck’s.*

—In “Strange Numbers Found in Particle Collisions” by Quanta Magazine