Reading Seminar on D-Modules and Perverse Sheaves

Fall 2018 and Spring 2019

Main Reference: R. Hotta, K. Takeuchi, and T. Tanisaki, D-Modules, Perverse Sheaves, and Representation Theory, Prog. Math. 236, Birkhäuser, 2008.

Organizer: Kai-Wen Lan

Time / Location: 2:30pm (on most Fridays) / Vincent Hall 313

Schedule

(In each day listed, there will be about two hours of lectures, except when we have conferences or outside speakers)

• Sep 14, Kai-Wen Lan: Overview; Preliminary Notions (Ch. 1): Differential Operators (1.1); D-modules—warming up (1.2)
• Sep 21, Kai-Wen Lan: Inverse and direct images (1.3); Some categories of D-modules (1.4); Inverse images and direct images II (1.5)
• Sep 28: no meeting (because of the Yamabe Memorial Symposium: Moduli Spaces in Algebraic Geometry)
• Oct 5, Kai-Wen Lan: Inverse images and direct images II (1.5) (cont.)
• Oct 12, Zhilin Luo: Kashiwara's equivalence (1.6); A base change theorem for direct images (1.7); Dihua Jiang: Some motivations from representation theory; Coherent D-modules (Ch. 2): Good filtrations (2.1); Characteristic varieties (singular supports)
• Oct 19, Dihua Jiang: Characteristic varieties (singular supports) (cont.); Zhilin Luo: Dimensions of characteristic varieties (2.3)
• Oct 26, Daniel Jonestone: Inverse images in the non-characteristic case (2.4); (outside speaker: Shizhang Li, Columbia)
• Nov 2, David Sherman: Proper direct images (2.5), Duality functors (2.6); Daniel Jonestone: Relations among functors (2.7)
• Nov 9, Daniel Jonestone: Relations among functors (2.7) (cont.); (outside speaker: Rong Zhou, IAS)
• Nov 16: no meeting (because of the Sixth Abel Conference: A Mathematical Celebration of Robert P. Langlands)
• Nov 30: Cheng Chen: Holonomic D-modules (Ch. 3): Basic results (3.1); Functors for holonomic D-modules (3.2); Zhilin Luo: Finiteness property (3.3)
• Dec 7: Zhilin Luo: Minimal extensions (3.4); (outside speaker: Koji Shimizu, Berkeley)
• Jan 25: Shengkai Mao: Analytic D-modules and the de Rham functor (Ch. 4): Analytic D-modules (4.1); Solution complexes and de Rham functors (4.2); Peihang Wu: Cauchy–Kowalevski–Kashiwara theorem (4.3); Cauchy problems and micro-supports (4.4)
• Feb 1: Peihang Wu: Cauchy problems and micro-supports (4.4) (cont.); Daniel Jonestone: Constructible sheaves (4.5); Kashiwara's constructibility theorem (4.6)
• Feb 8: Kai-Wen Lan: Kashiwara's constructibility theorem (4.6) (cont.); David Sherman: Analytic D-modules associated to algebraic D-modules (4.7)
• Feb 15: David Sherman: Analytic D-modules associated to algebraic D-modules (4.7) (cont.); (outside speaker: Lue Pan, U. Chicago)
• Feb 22: David Sherman: Theory of Meromorphic Connections (Ch. 5): Meromorphic connections in the one-dimensional case (5.1); Zhilin Luo: Regular meromorphic connections on complex manifolds (5.2)
• Mar 1: Zhilin Luo: Regular meromorphic connections on complex manifolds (5.2) (cont.); Kai-Wen Lan: Regular integrable connections on algebraic varieties (5.3)
• Mar 8: Cheng Chen: Regular Holonomic D-Modules (Ch. 6): Definition and main theorems (6.1); Proof of main theorems (6.2)
• Mar 15: Zhilin Luo: Riemann–Hilbert Correspondence (Ch. 7): Commutativity with de Rham functors (7.1); Riemann–Hilbert correspondence (7.2); Comparison theorem (7.3)
• Mar 29: Shenkai Mao: Perverse Sheaves (Ch. 8): Theory of perverse sheaves (8.1): t-structures (8.1.1)
• Apr 5: Peihang Wu: Perverse sheaves (8.1.2)
• Apr 12: Daniel Jonestone: Intersection cohomology theory (8.2)
• Apr 19: David Sherman: Intersection cohomology theory (8.2) (cont.)