Special Colloquium

Speaker: Alex Petrov (MIT)
Title: Topology of algebraic varieties in positive characteristic
Abstract: One fruitful way to analyze the topology of an algebraic variety over complex numbers is to consider its cohomology groups; at least if one is content with disregarding torsion in cohomology, these groups can be expressed in terms of algebraic differential forms on the variety, via an algebraic analog of de Rham cohomology. When applied to algebraic varieties in positive characteristic, de Rham cohomology exhibits behavior that in several ways is qualitatively different from the situation in characteristic zero. I will discuss some recent progress in understanding these differences which have to do with the failure of Hodge decomposition in positive characteristic. The methods used turn out to also be helpful for studying torsion in cohomology of families of varieties in characteristic zero.

Date and Time: Wednesday, January 22 @ 4:30PM
Location: 520 Mathematics

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