2015 CRM-Fields-PIMS Prize Recipient
Kai Behrend (University of British Columbia) [ français ]
Professor Behrend will give his lecture on September 10, 2015.
Professor Behrend is an internationally recognized leader in the field of
algebraic geometry, whose contributions to the subject are noted both
for their depth and scope. He has obtained fundamental results in the
theory of algebraic stacks, Gromov-Witten theory and the study of
Donaldson-Thomas invariants. In particular, his pioneering works on the
construction of a "virtual fundamental class" played a key role in laying
the algebraic foundations of the Gromov-Witten theory. Later, he made a
breakthrough in the study of the Donaldson-Thomas invariants by showing
that, for certain spaces, the degree of the virtual fundamental class
could be expressed as the topological Euler characteristic weighted by a
natural constructible function, depending only on the intrinsic properties
of the space. This function is now widely known as Behrend's
function. It allowed the use of motivic methods to compute Donaldson-Thomas
invariants, and made it possible to obtain their categorified and
motivic versions, which is currently among the hottest trends in the
subject. In his earlier work, Professor Behrend obtained an important
generalization of the Lefschetz trace formula for algebraic stacks,
presently known as Behrend's trace formula. The ideas put forward by Kai
Behrend have already proven to be immensely influential and will
undoubtedly have a lasting impact on this area of mathematics.
Kai Behrend received a Ph.D. in 1991 at the University of California,
Berkeley. He joined the faculty of the University of British Columbia in
1994. Professor Behrend has received numerous recognitions for his
research, including the 2001 Coxeter-James Prize and the 2011
Jeffery-Williams Prize of the Canadian Mathematical Society, as well as an
invitation to speak at the International Congress of Mathematicians
in Seoul in 2014.
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