Research area
Our research focus is set on the theory of finite and algebraic groups and complex algebraic geometry with applications. For instance, we work on
- algebraic groups and finite groups of Lie type
- applications of algebra and geometry to theoretical biology and physics
- automorphism groups of algebraic and geometric objects
- Brauer algebras
- Calabi-Yau and hyperkähler varieties
- representation theory
- geometric analysis and PDEs
- moduli spaces of Higgs bundles
- Kazhdan-Lusztig theory
- K3, Enriques and elliptic surfaces
- combinatorial methods in algebra
- rational Cherednik algebras, symplectic mirror algebras and associated geometric structures
- mirror groups and Hecke algebras
- symbolic computation
- toric geometry
- Zopf groups
Further information on our research can be found on the personal pages of the institute members and on our project page.
Discrete structures and symbolic computation form an important touchpoint of our research activities. This comprises also the development of constructive methods and efficient software.
The aim of symbolic computation is to provide exact instead of numerical / approximative solutions. In this sense, symbolic computation is complementary to scientific computing. Symbolic computation allows, for instance, to carry out substantial experiments with abstract mathematical structures thus providing counterexamples to conjectures, specifications of working hypotheses or even hints to previously undiscovered relationships. Ultimately, symbolic computation helps to establish general theorems whose proof has been reduced to the consideration of finitely many cases. During the process new significant theoretical results as well as innovative algorithms often emerge which are helpful for further investigations.
Discrete structures underline on one hand side the complementary character of symbolic computation compared to numerical-approximative methods. On the other, it encompasses the areas of mathematics in which algebraic and geometric methods are successfully applied.
| Year | Title |
|---|---|
| 2024 PhD |
Toric Cohiggs Bundles (supervised by Prof. Frederik Witt) |
| 2023 PhD |
Characters and Character Sheaves of Finite Groups of Lie Type (supervised by Prof. Meinolf Geck) |
| 2021 Habilitation | On some enumerative problems on K3 surfaces |
Contact persons
Meinolf Geck
Prof. Dr.Professor - Chair of Algebra
Frederik Witt
Prof. Dr.Professor - Chair of Differential Geometry