The structure of Grassmanian cluster categories
Lead Research Organisation:
University of Bath
Department Name: Mathematical Sciences
Abstract
Grassmannian cluster categories were introduced in 2016 by Jensen--King-Su as categories of Cohen-Macaulay modules for certain algebras. Also in 2016, Baur-King-Marsh showed how these are related to dimer models on a disc. However, many questions remain about the structure and properties of these categories and how these are reflected in the dimer model. Amongst these are:
-Find a good combinatorial formula for the dimensions of Ext groups between modules, using the dimer model combinatorics.
-Find the relationship between a categorical formula for cluster characters introduced more recently by Jensen-King-Su and a combinatorial formula of Lam.
-Find a categorical interpretation of the quadratic form on the Grothendieck group of the category that seems (experimentally) to constrain the existence of indecomposable modules.
-Find a good combinatorial formula for the dimensions of Ext groups between modules, using the dimer model combinatorics.
-Find the relationship between a categorical formula for cluster characters introduced more recently by Jensen-King-Su and a combinatorial formula of Lam.
-Find a categorical interpretation of the quadratic form on the Grothendieck group of the category that seems (experimentally) to constrain the existence of indecomposable modules.
Organisations
People |
ORCID iD |
Alastair David King (Primary Supervisor) | |
Ellis CAIRD (Student) |
Studentship Projects
Project Reference | Relationship | Related To | Start | End | Student Name |
---|---|---|---|---|---|
EP/R513155/1 | 01/10/2018 | 30/09/2023 | |||
2749834 | Studentship | EP/R513155/1 | 01/10/2022 | 31/03/2026 | Ellis CAIRD |