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