# Manchester Geometry Seminar 2014/2015

**Thursday 7 May 2015. ** *The Frank Adams Room (Room 1.212), the Alan Turing Building. 4.15pm*
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Cluster Algeras of Finite Mutation Type

Anna Felikson (University of Durham)

`anna.felikson@durham.ac.uk`

Cluster algebras were introduced by Fomin and Zelevinsky in 2002 for
studying total positivity of Grassmannians.
Very soon after that it turned out that the notion is connected to
numerous different fields in mathematics (such as Poisson geometry,
representation theory, integrable systems, combinatorics of polytopes,
Teihmuller theory, dilogorithm identities and many others).
In this talk we will introduce cluster algebras and show some
connections to Coxeter groups. More precisely, we will see how an
experience in classification of Coxeter hyperbolic polytopes helped to
solve some classification problem in cluster algebras.
The work is joint with Pavel Tumarkin and Michael Shapiro.