Equivariant quantum cohomology and the geometric Satake equivalence
Name
958670562-MIT.pdf
Description
Full printable version
Size
1.69 MB
Format
Adobe PDF
Checksum (MD5)
c61d4334144c8dd19b18d91b5ecce8e8
Author(s)
Viscardi, Michael
Advisor(s)
Roman Bezrukavnikov.
Date Issued
2016
Publisher
Massachusetts Institute of Technology
Abstract
Recent work on equivariant aspects of mirror symmetry has discovered relations between the equivariant quantum cohomology of symplectic resolutions and Casimir-type connections (among many other objects). We provide a new example of this theory in the setting of the affine Grassmannian, a fundamental space in the geometric Langlands program. More precisely, we identify the equivariant quantum connection of certain symplectic resolutions of slices in the affine Grassmannian of a semisimple group G with a trigonometric Knizhnik-Zamolodchikov (KZ)-type connection of the Langlands dual group of G. These symplectic resolutions are expected to be symplectic duals of Nakajima quiver varieties, and thus our result is an analogue of (part of) the work of Maulik and Okounkov in the symplectic dual setting.
Description
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2016.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 41-45).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
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