Class Central is learner-supported. When you buy through links on our site, we may earn an affiliate commission.

YouTube

P=W via H2 - Moduli Space of Stable Twisted Higgs Bundles

M-Seminar, Kansas State University via YouTube

Overview

Explore a lecture on the $P=W$ conjecture in algebraic geometry, focusing on its connection to the Lie algebra $H_2$ of polynomial Hamiltonian vector fields on the plane. Delve into the moduli space of stable twisted Higgs bundles on algebraic curves, examining two natural filtrations on its cohomology: the weight filtration W from the Betti realization and the perverse filtration P induced by the Hitchin map. Discover how computations in Khovanov-Rozansky homology of links motivate the search for an $H_2$ action on the cohomology of the moduli space. Investigate the algebra generated by tautological classes and Hecke operators, and learn how both P and W coincide with the filtration associated with an $sl_2$ subalgebra of $H_2$. Gain insights into this joint work with Hausel, Minets, and Schiffmann, building upon the proof by De Cataldo, Hausel, and Migliorini for rank 2 cases and exploring the conjecture for arbitrary ranks.

Syllabus

Anton Mellit - $P=W$ via $H_2$

Taught by

M-Seminar, Kansas State University

Reviews

Start your review of P=W via H2 - Moduli Space of Stable Twisted Higgs Bundles

Never Stop Learning.

Get personalized course recommendations, track subjects and courses with reminders, and more.

Someone learning on their laptop while sitting on the floor.