I’m a member of the Algebra, Geometry and Computer Algebra group at the University of Kaiserslautern. My main research focus lies in algebraic geometry, representation theory, and (higher) category theory—mostly in the context of algebraic Lie theory. I also develop computer algebraic methods. Specific topics I am interested in are:
- Symplectic algebraic geometry (symplectic singularities, Poisson deformations, symplectic duality, minimal model program; symplectic reflection algebras, rational Cherednik algebras, Calogero–Moser spaces)
- Coxeter groups, Kazhdan–Lusztig theory, Hecke algebras; complex reflection groups, cyclotomic Hecke algebras, spetses
- Highest weight categories, cellular algebras
- Soergel bimodules
- Categorial structures in representation theory
- Geometric methods in representation theory
- Tensor categories
- Computer algebra
If you are a student, check out my information for students.
News and schedule
- May 9–13: Counting conjectures and beyond, Isaac Newton Institute for Mathematical Sciences, Cambridge (second try)
- Apr 4–8: Symplectic singularities in geometry and representation theory, Luminy
- Jan 21: I’m giving a talk in the Oberseminar Darstellungstheorie, Bonn
- Oct 14: v0.2 of my lecture notes on Commutative Algebra
- Sept 13–Sept 16: Fifth annual conference of the SFB-TRR 195
- Aug 27: I’m giving a (virtual) talk in the representation theory seminar at Academia Sinica, Taiwan
- Aug 19: Next term, I’ll be teaching Commutative Algebra
- Aug 15–21: Workshop Computational Group Theory, Oberwolfach
- Jul 19: New preprint Cellularity of Endomorphism Algebras of Tilting Objects (with G. Bellamy)
- Jul 14: Vorstellung Fachpraktikum “Implementierung von Iwahori–Hecke Algebren“
- Jul 8: I’m giving a (virtual) talk in the SMRI Algebra and Geometry Online seminar, Sydney
- Jul: I’m member of the evaluation panel of the Breakthrough Junior Challenge, part of the Breakthrough Prize
- May 31: I totally forgot that almost 20 years ago I became a titan!
- May 17: Our paper Towards the classification of symplectic linear quotient singularities admitting a symplectic resolution (with G. Bellamy and J. Schmitt) will appear in Math. Z.
- Mar 23: I have released v1.0 of Magma-UT
- Feb 18: I’m giving a talk in the Birmingham-Warwick algebra seminar (virtual)
- Feb 17: First version v0.1 of my lecture notes Introduction to Commutative Algebra (182pp)
- Feb 17: First (very early!!) version v0.1 of my lectures notes Introduction to Categorical Thinking and Categorification (74pp)
- Feb 10: Vorstellung Fachpraktikum “Kombinatorische Algorithmen“
- Feb 3: I have released the first version v0.1 of JuLie!
- Jan 24: Next term, I’ll be teaching Elementary Number Theory and organize a Proseminar Symmetrie: Einstieg in die Lie-Theorie
See here for previous years.
- Since Aug 2019: Professor for “Algebra” at the University of Kaiserslautern (press release)
- Nov 2020: Principal Investigator in three projects within the DFG SFB-TRR 195: 1) Towards unipotent character sheaves associated to Coxeter groups, 2) Conjectures and new examples in birational geometry (with V. Lazić and F.O. Schreyer), 3) Gröbner techniques for PBW deformations: parametrization, representations, applications (with G. Fourier and E. Zerz).
- Apr 2019–Jul 2019: ARC Early Career Researcher at the University of Sydney
- Apr 2017–Mar 2019: Research Fellow in “Algebraic Geometry and Lie Theory” at the University of Sydney. Supervisor: Anthony Henderson. Supported by an ARC Discovery Project of Anthony Henderson, Gus Lehrer, and Geordie Williamson.
- Oct 2012–Mar 2017: Research and teaching assistant at the University of Stuttgart. Supervisor: Meinolf Geck. Between Jul 2014 and Jul 2016 supported by DFG SPP 1489 Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory.
- Mar 2016–May 2016: Research stay at the University of Glasgow. Supported by a Research Support Fund from the Edinburgh Mathematical Society.
- Jul 2014: Award of the University of Kaiserslautern for “outstanding achievements as doctoral student at the department of mathematics” (press release).
- May 2014: PhD in pure mathematics at University of Kaiserslautern. Supervisor: Gunter Malle, Referee: Raphaël Rouquier. (I moved to Stuttgart in between)
- Nov 2009–Sep 2012: Research fellow at the University of Kaiserslautern. Supervisor: Gunter Malle. Supported by DFG SPP 1388 Representation Theory.
- Nov 2009: Diplom (Master’s equivalent) in pure mathematics (with physics as minor) at the University of Kaiserslautern.
- Sep 2007–Feb 2008: Visiting student at Harvard University.
University of Kaiserslautern
Department of Mathematics
Office: 48.416 (Gottlieb-Daimler-Straße, 67663 Kaiserslautern)
Email: thiel at mathematik.uni-kl.de
Tel: +49 631 205 2258