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Séminaire Bourbaki du vendredi

Mirko Mauri — A gentle introduction to the P = W conjecture


The P=W conjecture states the equality of two filtrations of very different origin on the cohomology of the moduli space of representations of the fundamental group of a compact complex curve. This has been recently proved by Maulik-Shen and Hausel-Mellit-Minets-Schiffmann, under the assumption that the moduli space is smooth. In this talk I will discuss motivations for the conjecture, and present some toy examples.