Selected Publications
- Representations of quantum groups at a p-th root of unity and of semi-simple groups in characteristic p: Independence of p; Coauthors: Henning Haahr Andersen and Jens Carsten Jantzen, Astérisque 220 (1994), 1-320
- Koszul duality patterns in representation theory, Coauthors: Alexander A. Beilinson and Victor Ginzburg, JAMS 9 (1996), 473-527
- Langlands’ philosophy and Koszul duality, Algebra-Representation Theory (2001), 379-414; Editor: Roggenkamp and Stefanescu, Proceedings of NATO ASI 2000 in Constanta, Kluwer
- Kazhdan-Lusztig-Polynome und unzerlegbare Bimoduln über Polynomringen, JMIJ 6 (2007), 501-525
- Perverse motives and graded derived category Coauthor: Matthias Wendt, JMIJ (2017), 1-49
FRIAS Project
Cohomology in Algebraic Geometry and Representation Theory.
The Research Focus with Annette Huber-Klawitter (Theory of Numbers), Stefan Kebekus (Algebraic Geometry) and Wolfgang Soergel (Representation Theory) as principal investigators deals with a topic from Pure Mathematics. The linking element of their work in different sub-disciplines of mathematics is cohomology, a concept that originally served to explore geometrical spaces with the help of linear algebraic structures. A particular challenge in mathematics is to explain when two things (for example, two geometrical objects) are “different”. One possibility to show these differences is to simply count holes. While a circle has one hole, the geometrical form of the number 8 has two. The same applies to spheres and toruses (which has the form and surface of a bagel). Cohomology enables mathematicians to give a systematic definition of the illustrative concept of “holes” and provides methods for their analysis and calculation. In this way, it provides answers to questions like “What happens when we ‘glue’ two spaces together?”, “When do new holes emerge?”, or “How many holes does a complex space have?”. This is especially interesting when analysing high-dimensional spaces, which easily exceed human imagination.
The Research Focus aims to use cohomology as a common ground for “Algebraic Geometry”, “Representation Theory” and “Number Theory,” and to exchange ideas across these mathematic disciplines together with the guest researchers of the group. The Research Focus will invite a number of fellows and guest researchers and will also closely collaborate with the Mathematical Research Institute in Oberwolfach and the DFG Research Training Group 1821.