Kai Behrend

Kai Behrend is a German mathematician who deals with algebraic geometry.

Behrend studied at Bonn University with a diploma in 1987 with Günter Harder ( moduli spaces for vector bundles with level structures on algebraic curves ) and in 1991 received his doctorate at the University of California, Berkeley, with Arthur Ogus ( and Günter Harder ) (The Lefschetz trace Formula for the moduli stack in principal bundles). As a post - graduate student, he was at the Massachusetts Institute of Technology. He is a professor at the University of British Columbia.

He dealt with moduli spaces of algebraic curves, algebraic stacks, Gromov -Witten invariants, Donaldson -Thomas invariants. These research areas are currently in the field of string theory.

Partly with Barbara Fantechi and Yuri Manin, he used the theory of stacks around the virtual fundamental class of moduli spaces of stable pictures to determine and thus its Gromov -Witten invariants with applications in enumerative algebraic geometry. More fundamental research focused on graduate schemes Differential (Differential Graded Schemes ) and the evidence that Donaldson -Thomas invariants (which in turn links to Gromov -Witten invariants have ) related to the Euler characteristic of their moduli spaces.

In 2001 he received the Coxeter - James Prize and 2011 Jeffery -Williams Prize.

Writings

  • Gromov - Witten Invariants in algebraic geometry, Inventiones Mathematicae, Volume 127, 1997, pp. 601-617, Arxiv
  • 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, vol 85, 1996, pp. 1-60, Arxiv
  • Derived l - adic categories for algebraic stacks, Memoirs of the American Mathematical Society, 2003
Gromov–Witten invariant Simon Donaldson Coxeter–James Prize Jeffery–Williams Prize
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