Hitchin Fibrations and P=W

The goal of this reading seminar is to understand the statement and proof of the P=W conjecture: we will use the third proof given in the paper of Maulik-Shen-Yin. We will also spend some time understanding the paper of Hausel-Thaddeus.

We will meet on Mondays from 1:00PM to 2:30PM at MIT 2-255, for a 75 min talk followed by a 15 minute discussion session. The 15 minutes is for overflow time, so you should plan your talk to be an hour and expect questions. 

A tentative schedule for the reading seminar can be found here. The schedule for the talks for week 7-11 are subject to change, depending on audience interests. Possible topics include: Arinkin's paper and MSY in the full support compactified Jacobian case, de Cataldo-Maulik-Shen (tautological classes are in correct perversity), Ngo support theorems and Springer theory.

If you have any questions or would like to join the mailing list, please email the organizers Yonghwan Kim (yonghkim@mit.edu) and Anne Larsen (annelars@mit.edu).

Suggested references

Arinkin - Autoduality of compactified Jacobians for curves with plane singularities

Beauville - Sur la cohomologie de certains espaces de modules de fibres vectoriels

de Cataldo, Maulik, Shen - Hitchin fibrations, abelian surfaces, and the P=W conjecture

de Cataldo, Migliorini - The decomposition theorem, perverse sheaves, and the topology of algebraic maps

Hausel, Thaddeus - Mirror symmetry, Langlands duality, and the Hitchin system

Hoskins - Two proofs of the P=W conjecture

Markman -  Generators of the cohomology ring of moduli spaces of sheaves on symplectic surfaces

Maulik, Shen, Yin -  Perverse filtrations and Fourier transforms

Mellit - Cell decompositions of character varieties

Shende - The weights of the tautological classes of character varieties

Schedule

Week 1 (Sep 21) Overview (Leonid) Notes

Week 2 (Sep 28) Spectral curves and Hitchin fibers (Kaiyi) Notes

Week 3 (Oct 5) Duality, Gerbes, and Mirror symmetry (Yonghwan) Notes

Columbus day

Week 4 (Oct 19) Weight filtrations and mixed Hodge structures (Merrick)

Week 5 (Oct 26) Perverse sheaves and perverse filtration (Yutong)

Week 6 (Nov 2) Tautological classes generate (Dylan)

Week 7 (Nov 9) Overview of the Maulik-Shen-Yin proof (Anne)

Week 8 (Nov 16)

Thanksgiving

Week 9 (Nov 30) Arinkin's paper (Xinchun)

Week 10 (Dec 7)

Week 11 (Dec 14)