2026-09-20T12:12:24Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/1553222024-06-28T03:48:27Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Bezrukavnikov, Roman
Krylov, Vasily
Massachusetts Institute of Technology. Department of Mathematics
2024-06-27T19:44:52Z
2024-06-27T19:44:52Z
2024-05
2024-05-15T16:20:34.977Z
https://hdl.handle.net/1721.1/155322
This thesis studies the geometry and representation theory of various symplectic resolutions of singularities from different perspectives. Specifically, following the ideas of Bellamy, Hilburn, Kamnitzer, Tingley, Webster, Weekes, and Yacobi, we establish a general approach to attack the Hikita-Nakajima conjecture and illustrate this approach in the example of ADHM spaces. We also study minimally supported representations of the quantizations of ADHM spaces and provide explicit formulas for their characters. Lastly, we describe the monodromy of eigenvalues of quantum multiplication operators for type A Nakajima quiver varieties by examining Bethe subalgebras in Yangians and linking their spectrum with Kirillov-Reshetikhin crystals.
Ph.D.
Massachusetts Institute of Technology
In Copyright - Educational Use Permitted
Copyright retained by author(s)
https://rightsstatements.org/page/InC-EDU/1.0/
Geometry and representation theory of symplectic singularities in the context of symplectic duality
Thesis
application/pdf
Doctoral
Doctor of Philosophy
Publication
unknown
unknown
<Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="3b7dddcd-45b8-4106-b653-027e505cc3af">
<Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type>
<Title>Geometry and representation theory of symplectic singularities in the context of symplectic duality</Title>
<PublishedIn>
<Publication>
</Publication>
</PublishedIn>
<PublicationDate>2024-05</PublicationDate>
<Authors>
<Author>
<DisplayName>Krylov, Vasily</DisplayName>
<Affiliation>
<OrgUnit>
</OrgUnit>
</Affiliation>
</Author>
</Authors>
<Editors>
</Editors>
<Publishers>
<Publisher>
<DisplayName>Massachusetts Institute of Technology</DisplayName>
<OrgUnit />
</Publisher>
</Publishers>
<License>https://rightsstatements.org/page/InC-EDU/1.0/</License>
<Abstract>This thesis studies the geometry and representation theory of various symplectic resolutions of singularities from different perspectives. Specifically, following the ideas of Bellamy, Hilburn, Kamnitzer, Tingley, Webster, Weekes, and Yacobi, we establish a general approach to attack the Hikita-Nakajima conjecture and illustrate this approach in the example of ADHM spaces. We also study minimally supported representations of the quantizations of ADHM spaces and provide explicit formulas for their characters. Lastly, we describe the monodromy of eigenvalues of quantum multiplication operators for type A Nakajima quiver varieties by examining Bethe subalgebras in Yangians and linking their spectrum with Kirillov-Reshetikhin crystals.</Abstract>
<Access xmlns="http://purl.org/coar/access_right"
>
</Access>
</Publication>