Ulrich Thiel bio photo

Ulrich Thiel

Research Fellow, Algebra Group, University of Sydney

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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.

For leaving early one day. Sydney is a tough workplace...

Short CV

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

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