The category of Soergel bimodules, which bears the name of German mathematician Wolfgang Soergel, serves as a central element in modern representation theory. Born in Geneva in 1962, Soergel has developed a career centered on geometry and the foundational aspects of mathematics, contributing to the understanding of Koszul duality and Kazhdan-Lusztig theory through his extensive research.
Academic Background
Wolfgang Soergel attended the University of Hamburg, where he completed his PhD in 1988. His doctoral dissertation, titled Universelle versus relative Einhüllende: Eine geometrische Untersuchung von Quotienten von universellen Einhüllenden halbeinfacher Lie-Algebren, was written under the supervision of Jens Carsten Jantzen. This early work focused on the geometry of quotients within universal envelopes of semi-simple Lie algebras.
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Following his doctoral studies, Soergel held postdoctoral positions at Harvard University, MIT, and UC Berkeley. He finished his Habilitation at the University of Bonn in 1991. In 1994, he accepted a professorial chair at the University of Freiburg. During that same year, he contributed as an invited speaker at the International Congress of Mathematicians held in Zurich. His influence in the field is further reflected in his membership within the German Academy of Sciences Leopoldina and the Heidelberg Academy of Sciences and Humanities, the latter of which he joined in 2008.
Research Contributions
Soergel is credited with authoring or coauthoring more than 30 research articles throughout his career. His work on representation categories, perverse sheaves, and modules over coinvariants of the Weyl group has addressed significant questions in abstract algebra. Collaborations have included work with researchers such as Alexander Beilinson, Victor Ginzburg, Henning H. Andersen, and Jens C. Jantzen. These efforts have yielded insights into quantum groups and representation theory that remain relevant to current mathematical inquiries.
Mentorship
Beyond his individual research, Soergel has supervised the work of various doctoral students who have continued into the field of mathematics. Among those he has mentored are Karen Günzl, Peter Fiebig, Catharina Stroppel, and Geordie Williamson.
Fast facts
- Born: 12 June 1962, Geneva
- Citizenship: Germany
- PhD: University of Hamburg, 1988
- Current Employer: University of Freiburg
- Field: Geometry and representation theory
- Memberships: German Academy of Sciences Leopoldina; Heidelberg Academy of Sciences and Humanities
Questions readers ask
What is the focus of Wolfgang Soergel's research?
He specializes in geometry and representation theory, with specific contributions to Koszul duality, Kazhdan-Lusztig theory, and the development of Soergel bimodules.
Where has Wolfgang Soergel held academic appointments?
He has held postdoctoral positions at UC Berkeley, Harvard University, and MIT, and has served as a professor at the University of Freiburg since 1994.
Achievements
- Held posts at University of Freiburg
