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Colloquium – Talk by Mark de Cataldo: April 17, 2025

Posted by on Thursday, May 8, 2025 in Colloquium.

April 17, 2025 (Thursday), 4:10 pm

Mark de Cataldo, Stony Brook University

The P=W Conjecture in Non Abelian Hodge Theory

The classical de Rham and the Hodge Decomposition theorems deal with the singular cohomology of a projective manifold with coefficients in the non-zero complex numbers C*. Non abelian Hodge theory seeks to generalize this picture, with complex reductive groups, such as the general linear group, playing the role of the abelian C*. Instead of cohomology groups, we obtain complex algebraic varieties and their singular cohomology groups carry additional structures. The P=W Conjecture seeks to relate two of these non-classical structures. This talk is devoted to introducing the audience to this circle of ideas and related developments.