Geometric extensions

Geordie Williamson (Sydney Mathematical Research Institute)

16-Sep-2021, 21:00-22:00 (3 years ago)

Abstract: The Decomposition Theorem is probably my favourite theorem. I'll start by recalling the statement and trying to explain a little of why it is so remarkable. One consequence is that one could imagine an alternate history of the subject, in which intersection cohomology complexes were discovered without knowing about perverse sheaves. I'll explain how this might have occurred, and how it led Soergel and Juteau-Mautner-Williamson to the study of parity sheaves. Parity sheaves need strong parity vanishing assumptions, which somewhat restrict their utility (particularly for applications outside of geometric representation theory). The final goal of my talk is to explain a recent theorem (joint with Chris Hone) which proves the existence and uniqueness of "geometric extensions" in broad generality. The upshot is that parity sheaves probably don't need parity after all.

algebraic geometry

Audience: researchers in the topic


ZAG (Zoom Algebraic Geometry) seminar

Series comments: Description: ZAG seminar

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Organizers: Jesus Martinez Garcia*, Ivan Cheltsov*, Jungkai Chen, Jérémy Blanc, Ernesto Lupercio, Yuji Odaka, Zsolt Patakfalvi, Julius Ross, Cristiano Spotti, Chenyang Xu
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