Sheaves behaving badly

Abstract: This talk is about singularities of Schubert varieties, studied via sheaf-theoretic invariants like intersection cohomology and parity sheaves. The motivation comes from the use of these sheaves in representation theory, which began with the celebrated proof of the Kazhdan-Lusztig conjectures by Beilinson-Bernstein localisation. We will present examples of poor behaviour (in particular exhibit non-perverse parity sheaves), which thwart historic overly-optimistic conjectures on the singularities of Schubert varieties.

mathematical physicsalgebraic geometrydifferential geometrygeometric topologyoperator algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

Geometry, Physics, and Representation Theory Seminar

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