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SEMI-INFINITE FLAGS AND ZASTAVA SPACES

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dc.contributor.advisorIvan Mirkovic
dc.contributor.authorHayash, Andreas
dc.contributor.departmentUniversity of Massachusetts Amherst
dc.date2024-03-27 19:15:10
dc.date.accessioned2024-04-26T16:01:44Z
dc.date.available2024-04-26T16:01:44Z
dc.date.submittedSeptember
dc.date.submitted2023
dc.description.abstractABSTRACT 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.
dc.description.degreeDoctor of Philosophy (PhD)
dc.description.departmentMathematics
dc.identifier.doihttps://doi.org/10.7275/35989596
dc.identifier.orcidhttps://orcid.org/0009-0002-6814-2526
dc.identifier.urihttps://hdl.handle.net/20.500.14394/19271
dc.relation.urlhttps://scholarworks.umass.edu/cgi/viewcontent.cgi?article=4074&context=dissertations_2&unstamped=1
dc.source.statuspublished
dc.subjectgeometric Langlands program
dc.subjectAlgebra
dc.subjectAlgebraic Geometry
dc.subjectHarmonic Analysis and Representation
dc.titleSEMI-INFINITE FLAGS AND ZASTAVA SPACES
dc.typeopenaccess
dc.typedissertation
digcom.contributor.authorisAuthorOfPublication|email:andreashayash@gmail.com|institution:University of Massachusetts Amherst|Hayash, Andreas
digcom.identifierdissertations_2/2892
digcom.identifier.contextkey35989596
digcom.identifier.submissionpathdissertations_2/2892
dspace.entity.typePublication
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