K-theoretic Hall algebras for quivers with potential

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.

Name thesis:degree_name

Doctoral

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Mathematics

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2020

Author dc:creator

• Pădurariu, Tudor(Tudor Gabriel)

Advisor dc:contributor.advisor

• Davesh Maulik.

• Mathematics.

Statement dc:rights

• 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.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

https://hdl.handle.net/1721.1/126934

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/126934