2026-09-18T22:00:16Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/1269342026-06-17T14:46:46Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Davesh Maulik.
Pădurariu, Tudor(Tudor Gabriel)
Massachusetts Institute of Technology. Department of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2020-09-03T16:41:54Z
2020-09-03T16:41:54Z
2020
2020
https://hdl.handle.net/1721.1/126934
1191267620
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, May, 2020
Cataloged from the official PDF of thesis.
Includes bibliographical references (pages 167-171).
Given a quiver with potential (Q, W), Kontsevich-Soibelman constructed a Hall algebra on the cohomology of the stack of representations of (Q, W). As shown by Davison-Meinhardt, this algebra comes with a filtration whose associated graded algebra is supercommutative. A special case of this construction is related to work of Nakajima, Varagnolo, Maulik-Okounkov etc. about geometric constructions of Yangians and their representations; indeed, given a quiver Q, there exists an associated pair (Q̃, W̃) for which the CoHA is conjecturally the positive half of the Yangian Y[subscript MO]([subscript gQ]). The goal of this thesis is to extend these ideas to K-theory. More precisely, we construct a K-theoretic Hall algebra using category of singularities, define a filtration whose associated graded algebra is a deformation of a symmetric algebra, and compare the KHA and the CoHA using the Chern character. As before, we expect our construction for the special class of quivers (Q̃, W̃) to recover the positive part of quantum affine algebra U[subscript q]([subscript gQ]) defined by Okounkov-Smirnov, but for general pairs (Q, W) we expect new phenomena.
by Tudor Pădurariu.
Ph.D.
Ph.D. Massachusetts Institute of Technology, Department of Mathematics
171 pages
eng
Massachusetts Institute of Technology
MIT theses may be protected by copyright. Please reuse MIT thesis content according to the MIT Libraries Permissions Policy, which is available through the URL provided.
http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
K-theoretic Hall algebras for quivers with potential
Thesis
application/pdf
2020-09-03T16:41:53Z
Publication
Doctoral
Math
unknown
unknown
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<Abstract>Given a quiver with potential (Q, W), Kontsevich-Soibelman constructed a Hall algebra on the cohomology of the stack of representations of (Q, W). As shown by Davison-Meinhardt, this algebra comes with a filtration whose associated graded algebra is supercommutative. A special case of this construction is related to work of Nakajima, Varagnolo, Maulik-Okounkov etc. about geometric constructions of Yangians and their representations; indeed, given a quiver Q, there exists an associated pair (Q̃, W̃) for which the CoHA is conjecturally the positive half of the Yangian Y[subscript MO]([subscript gQ]). The goal of this thesis is to extend these ideas to K-theory. More precisely, we construct a K-theoretic Hall algebra using category of singularities, define a filtration whose associated graded algebra is a deformation of a symmetric algebra, and compare the KHA and the CoHA using the Chern character. As before, we expect our construction for the special class of quivers (Q̃, W̃) to recover the positive part of quantum affine algebra U[subscript q]([subscript gQ]) defined by Okounkov-Smirnov, but for general pairs (Q, W) we expect new phenomena.</Abstract>
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