Research Groups in Pure Mathematics

 

Algebra / Number Theory
Professors:
Prof. Dr. M. Reineke
Prof. Dr. K. Bongartz
Prof. Dr. W. Borho
Prof. Dr. R. Huber

Description:
Below you will find some key words describing research interests of members of the research group.
  • Algebraic combinatorics
  • Algebraic groups
  • Enveloping algebras of semisimple Lie algebras
  • Equivariant Cohomology
  • Equivariant K-theory
  • Etale cohomology of adic spaces
  • Geometric representation theory
  • Geometry of repesentations of finite dimensional algebras
  • Geometry of Schubert varieties
  • Invariant theory
  • Kac-Moody groups
  • Kazhdan-Lusztig theory
  • Non-commutative algebra
  • Representation theory of finite dimensional algebras
  • Representations of quantum groups
  • Rigid analytic spaces
  • Ramification theory
  • Spherical varieties

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Functional Analysis
Professors:
Prof. Dr. B. Jacob
Prof. em. Dr. D. Vogt

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Complex Analysis
Professors:
Prof. Dr. N. Shcherbina
Prof. Dr. K. Fritzsche
Apl. Prof. Dr. G. Herbort
Prof. em. Dr. K. Diederich

Description:
Research Interests:
The research interests of the group lie in the area of Geometric and Quantitative Complex Analysis using in particular many methods of real analysis. This is an area in which geometry, analysis, topology and algebra come to work together creating a rich set of phenomena which still have to be understood. Applications of the results of the research in this area can be found in many other directions of Pure Mathematics (like in Algebraic Geometry, Number Theory, Topology etc.), but also in recent Theoretical Physics and in the area of Scientific Computing.

Major topics of research are:
  • Geometry of real, in particular pseudoconvex hypersurfaces
  • Solution of the Cauchy-Riemann equations with estimates
  • Extension of holomorphic functions
  • Pluripotential theory and its Greene functions
  • Quantitative aspects of the Bergman theory
  • Regularity of holomorphic and of CR maps with applications
  • The Levi problem for complex spaces with singularities
The research group is since a long time part of a european research network in Complex Analysis and Analytic Geometry comprising other groups in universities in
  • Bonn, Berlin, Pisa, Florence, Rome, Grenoble, Paris 6, Göteborg, Stockholm
Furthermore, there are permanent active research relations to groups at
  • Lille (France)
  • University of Michigan, Ann Arbor (USA)
  • Indiana University, Bloomington (USA)


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Real Analysis
Professors:
Prof. Dr. H. Pecher
Prof. em. Dr. M. Reeken

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Topology / Geometry
Professors:
Prof. Dr. K. Knapp
Prof. em. Dr. E. Ossa

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