Kai Behrend
Kai Behrend (* 1961 ) is a German mathematician who deals with algebraic geometry .
Behrend studied at the University of Bonn with a diploma in 1987 with Günter Harder ( Moduli spaces for vector bundles with level structures on algebraic curves ) and received his doctorate in 1991 at the University of California, Berkeley , with Arthur Ogus (and Günter Harder) ( The Lefschetz Trace Formula for the Moduli Stack in Principal Bundles ). He was a post-doctoral student at the Massachusetts Institute of Technology . He is a professor at the University of British Columbia .
He dealt with module spaces of algebraic curves, algebraic stacks, Gromov-Witten invariants , Donaldson- Thomas invariants. These research areas are topical in the field of string theory .
Partly with Barbara Fantechi and Yuri Manin , he used the theory of stacks to determine the virtual fundamental class of modular spaces of stable mappings and thus its Gromov-Witten invariants with applications in enumerative algebraic geometry. Further fundamental work concerned Differential Graded Schemes and the proof that Donaldson-Thomas invariants (which in turn have connections to Gromov-Witten invariants) are related to the Euler characteristic of their modular spaces.
In 2001 he received the Coxeter James Prize and 2011 Jeffery Williams Prize . In 2014 he was invited speaker at the ICM in Seoul (On the virtual fundamental class). For 2015 he was awarded the CRM Fields PIMS Prize . He is a fellow of the American Mathematical Society .
Fonts
- Gromov-Witten Invariants in algebraic geometry, Inventiones Mathematicae, Volume 127, 1997, pp. 601-617, Arxiv
- with Barbara Fantechi: The intrinsic normal cone, Inventiones Mathematicae, Volume 128, 1997, pp. 45-88, Arxiv
- with Yuri Manin : Stacks of stable maps and Gromov Witten Invariants, Duke Mathematical Journal, Volume 85, 1996, pp. 1-60, Arxiv
- Derived l-adic categories for algebraic stacks, Memoirs of the American Mathematical Society, 2003
Web links
Individual evidence
| personal data | |
|---|---|
| SURNAME | Behrend, Kai |
| BRIEF DESCRIPTION | German mathematician |
| DATE OF BIRTH | 1961 |