Seminar on mixed Hodge modules
Seminar on Mixed Hodge modules at the MPI in 2015.
Abstract:
Yohan and I plan on organising an informal seminar on Hodge modules
over the coming months. I think it is unreasonable to have as goal to
"really understand Hodge modules". However I do think it is possible
to have a productive seminar where we see some examples and perhaps
approximate the theory a little better in our minds.
A list of some literature we found useful:
- Deligne, Theorie de Hodge I, II and II
- The first chapter of Period mappings and Period Domains by Carlson, Müller-Stach and Peters.
- A.H. Durfee, A naive guide to mixed Hodge theory, Singularities, Part 1 (Arcata, Calif., 1981), 313-320, Proc. Sympos. Pure Math., 40, Amer. Math. Soc., Providence, RI, 1983.
- Cattani, Eduardo; Kaplan, Aroldo, Degenerating variations of Hodge structure.Actes du Colloque de Théorie de Hodge (Luminy, 1987). Astérisque No. 179-180 (1989), 9, 67--96.
- Deligne, Pierre, Structures de Hodge mixtes réelles.
Motives (Seattle, WA, 1991), 509-514, Proc. Sympos. Pure Math., 55,
Part 1, Amer. Math. Soc., Providence, RI, 1994.
Somewhat
ironically only seems to be about complex mixed Hodge structures!
Available here.
- Deligne, Le Groupe Fondamental de la Droite Projective Moins
Trois Points, http://www.math.ias.edu/files/deligne/GaloisGroups.pdf
- Deligne, Travaux de Griffiths, Bourbaki seminaire.
- Philippe Maisonobe, Zoghman Mebkhout, Le théorème de
comparaison pour les cycles évanescents, here.
- Schmid, Variation of hodge structure: The singularities of
the period mapping, Invent. Math., 1973.
- Steven Zucker, Hodge theory with degenerating coefficients. L^2 cohomology in the Poincaré metric, Ann. of Math. (2) 109 (1979), no. 3, 415-476.
Assorted references for D-modules:
Thanks to Asilata Bapat and Leonardo Patimo for providing notes!
Wed, 18 Feb:
Geordie Williamson,
Nearby and vanishing cycles for perverse sheaves
Wed, 25 Feb:
Leonardo Patimo,
Introduction to mixed Hodge structures
Wed, 04 Mar: Leonardo Patimo,
Introduction to mixed Hodge structures II (See previous link
for notes.)
Wed, 11 Mar:
Clément Dupont and Dragos Fratila,
Variations of Hodge Structures
Wed, 25 Mar:
Clément Dupont and Dragos Fratila,
Variations of Hodge structures
Wed, 25 Mar:
Johannes Kübel,
Recollections on D-modules
Wed, 15 Apr:
Johannes Kübel,
Review of D-modules II
Wed, 22 Apr:
Geordie Williamson,
Riemann-Hilbert correspondence for curves
Wed, 29 Apr:
Stefan Schreieder,
Vanishing cycles for D-modules
Wed, 06 May:
Stefan Schreieder,
Vanishing cycles for D-modules, II
Wed, 20 May:
Yohan Brunebarbe,
Nearby and vanishing cycles for D-modules (III)
Wed, 27 May:
Yohan Brunebarbe,
Regular holonomic D-modules in dimension 1
Wed, 27 May:
Asilata Bapat,
The Bernstein-Sato polynomial and the V-filtration
Wed, 10 Jun:
Yohan Brunebarbe,
Variations of Hodge structures on the punctured disk
Wed, 17 Jun:
Yohan Brunebarbe,
Variations of Hodge structures on the punctured disk (II)
Wed, 17 Jun:
Geordie Williamson,
Some examples
Wed, 24 Jun:
Christian Kaiser,
Direct image theorem for curves
Here are is a big file of notes from
Leonardo in case there are holes above.