### Overview

## About

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
- Digital signal processing (that’s a hobby!)

One of my “hidden” 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