The aim of this working seminar is to give an introduction to Intersection (Co)Homology, Perverse Sheaves, the Decomposition Theorem, and end up with a tour of some classical and modern applications and conjectures. We will try to develop as much as possible "ground up", so no particular pre-knowledge is assumed.
All talks taking place Tuesdays, 1-2pm, in JCMB 5326.
Organisation and introduction (Martina Lanini)
12th January 2016, 1:00pm to 2:00pm
Introduction to Intersection Homology (Johan Martens)
19th January 2016, 1:00pm to 2:00pm
Sheaf cohomology (Tim Weelinck)
26th January 2016, 1:00pm to 2:00pm
Introduction to Derived Categories & the 6 functor formalism (Jenny August)
2nd February 2016, 1:00pm to 2:00pm
t-structures & perverse sheaves (Matt Booth)
9th February 2016, 1:00pm to 2:00pm
More on t-structures & perverse sheaves (Matt Booth)
23rd February 2016, 1:00pm to 2:00pm
Deligne's construction of Intersection Cohomology (Salvatore Dolce)
1st March 2016, 1:00pm to 2:00pm
Decomposition Theorem - Statement + Examples (David Jordan)
8th March 2016, 1:00pm to 2:00pm
Comments on the proof of the Decomposition Theorem using Hodge Theory
15th March 2016, 1:00pm to 2:00pm
The P=W conjecture (Johan Martens)
12th April 2016, 10:30am to 12:00pm JCMB 5327
The literature on this topic is vast. The three main sources we will use for the bulk of the seminar are:
- M.A. de Cataldo and L. Migliorini, The decomposition theorem, perverse sheaves and the topology of algebraic maps. Bull. Amer. Math. Soc. (N.S.) 46 (2009), no. 4, 535–633. Available online.
- F. Kirwan and J. Woolf, An introduction to intersection homology theory. Second edition. Chapman & Hall/CRC, Boca Raton, FL, 2006. Book website.
- Georgie Williamson, An illustrated guide to perverse sheaves, unpublished notes, available online.
Other useful references will be pointed out during the semester.
The seminar is coordinated by Martina Lanini and Johan Martens. All are welcome to attend. If you want to be included in the mailing list please email johan.martens at ed.ac.uk.