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You are here: FRIAS Fellows Fellows 2017/18 Prof. Dr. Annette Huber-Klawitter

Prof. Dr. Annette Huber-Klawitter

University of Freiburg
Mathematics
Internal Senior Fellow
October 2017 - July 2018

Room 01 011
Phone +49 (0)761 203-97319
Fax +49 (0)761 203-97451

CV

Annette Huber-Klawitter works in number theory, i.e, on questions about properties of the integers. She follows the very modern and successfull approach ofarithmetic geometry: equations are seen as describing geometric objects, which are then studied by methods of algebraic geometry. Prof. Huber-Klawitter works in particular on motives (a conjectural universal cohomology theory), periods and special values of L-functions.

As a high school student she was a three times winner of the Bundeswettbewerb Mathematik. She then studied mathematics and physics in Frankfurt, Cambridge and Münster. In 1994 she obtained a doctorate from the University of Münster in mathematics under the supervision of Christopher Deninger. After her habilitation in 1999, also at Münster, she was appointed full professor at the University of Leipzig. She moved to Freiburg in 2008. Since 2012 she leads the Graduiertenkolleg Cohomolgical Methods in Algebraic Geometry.

In 2002, she was an invited speaker at the ICM in Beijing. In 2008 she was elected member of the Deutsche Akademie der Naturforscher Leopoldina and in 2012 Fellow of the AMS.

Annette Huber-Klawitter is married with two children.

Selected Publications

  • A. Huber, S. Müller-Stach, with contributions of Benjamin Friedrich and Jonas von Wangenheim, Periods and Nori motives, Springer Verlag, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 65, 2017.
  • A. Huber, C. Jörder, Differential forms in the h-topology, (pdf) Algebraic Geometry, Volume 1, Issue 4 (October 2014), 449-478.
  • A. Huber, G. Kings. Equivariant Bloch-Kato conjecture and non-abelian Iwasawa Main Conjecture. Proceedings of the ICM, Beijing 2002, vol. II, pp. 149-162. Higher Education Press, Beijing, 2002.
  • A. Huber, G. Kings. Degeneration of l-adic Eisenstein classes and of the elliptic polylog. Inventiones Mathematicae 135(3): 545-594, 1999.
  • A. Huber. Mixed motives and their realization in derived categories. Lecture Notes in Mathematics 1604. Springer-Verlag, Berlin, 1995.

FRIAS Rersearch Project

Cohomological Methods in Algebraic Geometry and Representation Theor

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.