Benedict Morrissey

We are first finishing up some loose ends from the P=W seminar. We are then going to look at Stokes data, the wild Riemann Hilbert Correspondence, and (Mixed) Hodge Modules.

We meet in 3E6A at Monday 10:30AM.

References

Cohomology of GL(n) Hitchin fibers

  • Maulik "Stable Pairs and the HOMFLY polynomial"
  • Maulik--Yun "Macdonald formula for curves with planar singularities"

For Shalika germs: Kottwitz "Harmonic analysis on reductive p-adic groups and Lie algebras"

Multiplicative Hitchin systems and applications

  • Ngo--Frenkel "Geometrization of Trace Formulas"
  • Bouthier -- various papers
  • Jingren Chi -- "Geometry of Kottwitz--Viehmann Varieties"
  • Elliott--Pestun "Multiplicative Hitchin Systems and Supersymmetric Gauge theory"

Riemann--Hilbert Correspondence

Regular Riemann Hilbert Correspondence, 6 functors for D-modules, and for constructible sheaves, Deligne's Extension results, analytic vs algebraic D-modules

  • Hotta Tanisaki Takeuchi "D-modules, perverse sheaves and representation theory"
  • Deligne "Equations differentielles a points singuliers reguliers"
  • Gaitsgory--Rozenblyum
  • Relative Riemann Hilbert functor: Fiorot--Fernandes--Sabbah "Relative Regular Riemann--Hilbert Correspondence"
  • Paulin: "The Riemann--Hilbert Correspondence for algebraic stacks"

Wild Ramification: Stokes Structures

  • Witten (a nice concrete exposition) "Gauge Theory and Wild Ramification"
  • Wasow "Asymptotic expansions for ordinary differential equations"
  • Malgrange "Equations Differentielles a Coefficients Polynomiaux"
  • **Sabbah "Introduction to Stokes Structures" [This seems to be the most comprehensive introduction to the topics]
  • Deligne--Malgrange--Ramis "Singularites Irreguliere: Correspondance et documents"
  • D'Agnolo--Kashiwara "Riemann--Hilbert Correspondence for holonomic D-modules"

Fourier Transforms:

  • Malgrange, "Equations Differentielles a Coefficients Polynomiaux"
  • Sabbah, "Fourier Transformation and Stokes Structures," "Fourier--Laplace Transform of a variation of polarized complex Hodge structure II"
  • Mochizuki, "Stokes Shelles and Fourier Transform"

Filtered D-modules and Mixed Hodge Modules

  • Saito, "Modules de Hodge polarisables," "Mixed Hodge Modules"
  • Schnell "An overview of Morihiko Saito's Theory of Mixed Hodge Modules"
  • Sabbah--Schnell "The MHM project (Version 2)"

Proof of decomposition theorem via Mixed Hodge Modules.

See above.

Description of the higher residue pairing via Mixed Hodge modules

See work of M. Saito

Non-abelianization as Stokes decomposition.

To appear.