The Behrend function serves as a significant marker in the field of algebraic geometry, representing a core contribution to the development of Donaldson–Thomas theory. Born in Hamburg in 1961, this German mathematician focused his academic career on the complex structural properties of algebraic stacks, earning recognition through various mathematical honors for his research in geometry.
Academic Formation and Career
Kai Behrend completed his graduate education at the University of California, Berkeley. Following his academic training, he secured a position at the University of British Columbia in Vancouver, Canada. Throughout his tenure, he has served as a university teacher while conducting specialized research in geometry and algebraic geometry.
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His research focuses on the theory of algebraic stacks and Gromov–Witten invariants. Among his notable outputs is Behrend's formula, which provides a generalization of the Grothendieck–Lefschetz trace formula specifically applied to algebraic stacks. His technical publications include 'Motivic degree zero Donaldson–Thomas invariants' and 'The intrinsic normal cone,' both of which appear in the journal Inventiones Mathematicae.
Professional Recognition
The mathematical community has awarded several prizes for his research. He received the Coxeter–James Prize in 2001 and the Jeffery–Williams Prize in 2011. In 2015, he was awarded the CRM-Fields-PIMS prize. Additionally, he holds membership in the American Mathematical Society, having been elected to the class of fellows in 2018.
Fast facts
- Born: 1961, Hamburg
- Citizenship: Germany
- Alma Mater: University of California, Berkeley
- Primary Field: Algebraic geometry
- Employer: University of British Columbia
- 2015 Award: CRM-Fields-PIMS prize
- 2018 Status: Fellow of the American Mathematical Society
- Languages: German, English
Questions readers ask
What is the Behrend function?
It is a mathematical concept associated with his research in Donaldson–Thomas theory.
Where is Kai Behrend based?
He is a professor located in Vancouver, British Columbia, working at the University of British Columbia.
Achievements
- CRM-Fields-PIMS prize — 2015
- Coxeter–James Prize
- Held posts at University of British Columbia
- Fields: algebraic geometry, geometry and mathematics
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