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 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.