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Author ORCID Identifier

https://orcid.org/0009-0002-6814-2526

AccessType

Open Access Dissertation

Document Type

dissertation

Degree Name

Doctor of Philosophy (PhD)

Degree Program

Mathematics

Year Degree Awarded

2023

Month Degree Awarded

September

First Advisor

Ivan Mirkovic

Subject Categories

Algebra | Algebraic Geometry | Harmonic Analysis and Representation

Abstract

ABSTRACT SEMI-INFINITE FLAGS AND ZASTAVA SPACES SEPTEMBER 2023 ANDREAS HAYASH, B.A., HAMPSHIRE COLLEGE M.S., UNIVERSITY OF MASSACHUSETTS AMHERST Ph.D, UNIVERSITY OF MASSACHUSETTS AMHERST Directed by: Professor Ivan Mirković We give an interpretation of Dennis Gaitsgory’s semi-infinite intersection cohomol- ogy sheaf associated to a semisimple simply-connected algebraic group in terms of finite-dimensional geometry. Specifically, we construct machinery to build factoriza- tion spaces over the Ran space from factorization spaces over the configuration space, and show that under this procedure the compactified Zastava space is sent to the support of the semi-infinite intersection cohomology sheaf in the Beilinson-Drinfeld Grassmannian. We also construct a partial resolution of singularities of the compact- ified Zastava space and show that the Zastava version of the semi-infinite intersection cohomology sheaf is pulled back to the ordinary (perverse) intersection cohomology sheaf of the partial resolution. Lastly, we show that there is a monad acting on sheaves over the resolution whose category of modules embeds fully faithfully in sheaves on the affine Grassmannian.

DOI

https://doi.org/10.7275/35989596

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