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CMS Coxeter-James Lecture / Conférence Coxeter-James de la SMC


KAI BEHREND, University of British Columbia
Quantum Cohomology and the virtual fundamental class or ``how to count properly''

Motivated by the desire to have beautiful formulas, mathematicians have realized time and again that it is necessary to change the meaning of the ``number of solutions'' to a problem. The simplest case is maybe the introduction of the complex numbers in order for the theorem ``any quadratic equation has two solutions'' to become true. The introduction of Gromov-Witten invariants (i.e., quantum cohomology) into algebraic geometry can be understood as another step in this program. This talk is meant to be a somewhat leisurly introduction to some of the ideas involved in this long story.

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