Quantum theta bases for quantum cluster algebras
Travis Mandel (Oklahoma)
Abstract: One of the central goals in the study of cluster algebras is to better understand various canonical bases and positivity properties of the cluster algebras and their quantizations. Gross-Hacking-Keel-Kontsevich (GHKK) applied ideas from mirror symmetry to construct so-called "theta bases" for cluster algebras which satisfy all the desired positivity properties, thus proving several conjectures regarding cluster algebras. I will discuss joint work with Ben Davison in which we combine the techniques used by GHKK with ideas from the DT theory of quiver representations to quantize the GHKK construction, thus producing quantum theta bases and proving the desired quantum positivity properties.
algebraic geometrycombinatorics
Audience: researchers in the topic
Online Nottingham algebraic geometry seminar
Series comments: Online geometry seminar, typically held on Thursday. This seminar takes place online via Microsoft Teams on the Nottingham University "Algebraic Geometry" team.
For recordings of past talks, copies of the speaker's slides, or to be added to the Team, please visit the seminar homepage at: kasprzyk.work/seminars/ag.html
| Organizers: | Alexander Kasprzyk*, Johannes Hofscheier*, Erroxe Etxabarri Alberdi |
| *contact for this listing |