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You are here: FRIAS Fellows Fellows 2016/17 Prof. Dr. Stefan Kebekus

Prof. Dr. Stefan Kebekus

University of Freiburg
Complex and Algebraic Geometry
Internal Senior Fellow
October 2017 - September 2018

Room 01 012
Phone +49 (0)761-203 5536
Fax +49 (0)761-203 97451


Stefan Kebekus, born 1970, is Professor of Mathematics at the University of Freiburg. His research interests lie in Complex Geometry, a branch of Pure Mathematics with connections to Number Theory, Cryptography, Theoretical Physis, and many other fields.

Kebekus studied Mathematics at the Ruhr-Universität Bochum and also obtained his PhD there in 1996. Subsequent to his studies, he was Scientific Assistant at the University of Bayreuth, Guest Researcher at Kyoto University, Visiting Professor at the University of Washington in Seattle, Professeur Invite at Strasbourg, Grenoble and Rennes, and Heisenberg-fellow of the DFG. He obtained his Habilitation in 2001 from the University of Bayreuth.

From 2003-2008, Kebekus was Professor of Mathematics the University of Cologne. He moved to Freiburg in 2008.

Kebekus is an editor of the journal „Algebraic Geometry“. He is currently vice director of the Graduiertenkolleg 1821 „Cohomologische Methoden in der Geometrie“. From 2006 to 2008, Kebekus was director of the Graduiertenkolleg 1269 „Global Structures in Geometry and Analysis“. He was a member of the Mathematical Sciences Research Institute in Berkely in 2009.

Selected Publications

  • Étale fundamental groups of Kawamata log terminal spaces, flat sheaves, and quotients of Abelian varieties (with Daniel Greb und Thomas Peternell). Duke Math. J., Volume 165, Number 10 (2016), 1965-2004. DOI:10.1215/00127094-3450859. Preprint arXiv:1307.5718.
  • Singular spaces with trivial canonical class (with Daniel Greb und Thomas Peternell). in “Minimal Models and Extremal Rays (Kyoto, 2011)”.
  • Advanced Studies in Pure Mathematics 70, Pages 67-113, Mathematical Society of Japan, Tokyo, 2016. Preprint arXiv:1110.5250.
  • Differential Forms on Log Canonical Spaces (with Daniel Greb, Sándor Kovács and Thomas Peternell). Publications Mathématiques de l’IHÉS, Volume 114, Number 1 (2011), 87-169. DOI:10.1007/s10240-011-0036-0. Preprint arXiv:1003.2913 contains an extended version with additional graphics.
  • Families of canonically polarized varieties over surfaces (with Sándor Kovács). Inventiones Mathematicae, Vol. 172, No. 3, pp. 657-682, 2008. DOI:10.1007/s00222-008-0128-8. Preprint arXiv:math/0511378.
  • Projective Contact Manifolds  (with Thomas Peternell, Andrew J. Sommese and Jarosław A. Wiśniewski). Inventiones Mathematicae, Vol. 142, No. 1, pp. 1-15, 2000. DOI:10.1007/PL00005791. Preprint arXiv:math/9810102.

FRIAS Research 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.