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Cluster algebras and representation theory

Participation in INI programmes is by invitation only. Anyone wishing to apply to participate in the associated workshop(s) should use the relevant workshop application form.

Programme
6th September 2021 to 17th December 2021

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. 

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons