Departmental Seminar

Discrete integrable systems from cluster algebras

Professor Andrew H Hone
University of Kent
Cluster algebras are a new class of commutative algebras that were introduced by Fomin and Zelevinsky in 2000, and soon became the hottest topic in algebra, with applications in diverse areas of mathematics and topic in algebra and theoretical physics (Lie theory, Teichmuller theory, discrete integrable systems and the thermodynamic Bethe ansatz, to name but a few). In this talk we give a brief introduction to cluster algebras, and explain how discrete integrability can appear in this context, using Somos sequences, QRT maps and discrete Painleve equations as the main examples.

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