Cluster algebras and representation theory
| Created: | 2021-09-14 09:21 |
|---|---|
| Institution: | Isaac Newton Institute for Mathematical Sciences |
| Description: | Programme theme
The theory of cluster algebras is one of the most active research areas in Mathematics over the last 18 years. Introduced by Fomin and Zelevinsky in 2002 in the context of Lie theory and total positivity, cluster algebras quickly developed deep connections to different disciplines such as representation theory, combinatorics, algebraic, hyperbolic and symplectic geometry, dynamical systems, topology and string theory. Among the major applications of cluster algebras are the construction of part of Lusztig's dual semicanonical basis in Lie theory, the discovery of generalized associahedra in combinatorics, the development of cluster-tilting theory in the representation theory of finite dimensional algebras, the proof of Zamolodchikov's periodicity conjecture in conformal field theory, the development of a new approach to Teichmüller theory and the discovery of a fundamental relationship with Donaldson-Thomas invariants and wall-crossing in algebraic geometry. Much work on cluster algebras has centred around applications to the representation theory of finite dimensional algebras. These grew from categorical models for cluster algebras. In particular, the cluster-tilted algebras arising from cluster categories have given new insights into classical tilting theory. The interaction is in both directions, with the representation-theoretic models also being used to answer fundamental questions about cluster algebras. This programme will focus on interactions between cluster algebras and representation theory as well as interdisciplinary applications of cluster algebras. |
Media items
This collection contains 83 media items.
Media items
\tau-exceptional sequences
Professor Bethany Marsh (University of Leeds)
5th October 2021 16:00 - 17:00
Collection: Cluster algebras and representation theory
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Fri 8 Oct 2021
Connectedness of the Support Tau-Tilting Graph of a Gentle Algebra
Yu Zhou Tsinghua University
21 September 2021 – 13:45 to 14:15
Collection: Cluster algebras and representation theory
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Wed 22 Sep 2021
Silting theory and stability conditions
David Pauksztello Lancaster University
16 September 2021 – 13:00 to 13:45
Collection: Cluster algebras and representation theory
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Fri 17 Sep 2021
A cluster character for y-variables
Matthew Pressland University of Leeds
23 September 2021 – 14:45 to 15:15
Collection: Cluster algebras and representation theory
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Fri 24 Sep 2021
An Algebraic Variety Related to Tau-Tilting Theory
Dr Hugh Thomas (Université du Québec à Montréal)
8th November 2021 | 13:00 - 13:30
Collection: Cluster algebras and representation theory
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Wed 10 Nov 2021
An Introduction to Extriangulated Categories
Yann Palu Université de Picardie Jules Verne
14 September 2021 – 16:05 to 16:50
Collection: Cluster algebras and representation theory
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Fri 17 Sep 2021
An Introduction to Extriangulated Categories
Yann Palu Université de Picardie Jules Verne
16 September 2021 – 15:05 to 15:50
Collection: Cluster algebras and representation theory
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Fri 17 Sep 2021
Bongartz Completion Via C-Vectors
Dr Peigen Cao (Hebrew University of Jerusalem)
10th November 2021 | 15:30 - 16:00
Collection: Cluster algebras and representation theory
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Thu 11 Nov 2021
Bracelets are theta functions
Professor Fan Qin (Shanghai Jiao Tong University)
11th November 2021 | 13:45 - 14:15
Collection: Cluster algebras and representation theory
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Fri 12 Nov 2021
Categorification of Perfect Matchings
Professor Alastair King (University of Bath)
10th November 2021 | 13:00 - 13:30
Collection: Cluster algebras and representation theory
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Thu 11 Nov 2021
Cluster Adjacency for amplitudes from Gröbner bases
Professor James Drummond (University of Southampton)
8th November 2021 | 15:30 - 16:00
Collection: Cluster algebras and representation theory
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Wed 10 Nov 2021
Cluster Algebra Via Non-Archimedean Enumerative Geometry
Professor Tony Yue Yu (Université Paris Saclay)
9th November 2021 | 15:30 - 16:15
Collection: Cluster algebras and representation theory
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Wed 10 Nov 2021
Cluster algebras generated by projective cluster variables
Alireza Nasr-Isfahani University of Isfahan; IPM - Institute for Research In Fundamental Sciences
23 September 2021 – 13:45 to 14:15
Collection: Cluster algebras and representation theory
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Fri 24 Sep 2021
Cluster algebras with coefficients and relative cluster categories - Series Talk 1of 3
Professor Bernhard Keller (Université Paris 7 - Denis-Diderot)
6th October 2021 14:00 - 15:00
Collection: Cluster algebras and representation theory
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Fri 8 Oct 2021
Cluster algebras with coefficients and relative cluster categories - Series Talk 2 of 3
Professor Bernhard Keller (Université Paris 7 - Denis-Diderot)
13th October 2021 15:00 - 16:00
Collection: Cluster algebras and representation theory
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Mon 18 Oct 2021
Cluster algebras with coefficients and relative cluster categories Series talk 3 of 3
Professor Bernhard Keller (Université Paris 7 - Denis-Diderot)
20th October 2021 | 15:00 - 16:00
Collection: Cluster algebras and representation theory
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Mon 8 Nov 2021
Cluster Algebras, Augmentations, and Legendrian Knots
Professor Linhui Shen (Michigan State University)
9th November 2021 | 14:30 - 15:00
Collection: Cluster algebras and representation theory
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Wed 10 Nov 2021
Cluster Combinatorics of SLk Skein Algebras in the Presence of Punctures
Chris Fraser Michigan State University
21 September 2021 – 14:45 to 15:15
Collection: Cluster algebras and representation theory
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Wed 22 Sep 2021
Cluster Structures
Emine Yildirim Isaac Newton Institute; University of Cambridge
21 September 2021 – 15:30 to 16:00
Collection: Cluster algebras and representation theory
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Wed 22 Sep 2021
Counting tau-exceptional sequences for Nakayama algebras
Dixy Msapato, University of Leeds, 14/12/2021
Collection: Cluster algebras and representation theory
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Mon 20 Dec 2021