Pure Maths Colloquium: Cluster Algebras via reflection groups
19 October 2015 16:00 in CM221
Cluster Algebras are a class of commutative rings introduced by Fomin and Zelevinsky as a tool to model positivity phenomena naturally arising on various varieties connected to Lie groups. Since their inception, they have given insights on a wide spectrum of problems often coming from previously unrelated branches of mathematics like Poisson geometry, discrete integrable systems, quiver representations, Calabi-Yau categories, and
Teichmüller theory just to name a few. This makes them a formidable tool to have at hand.
Unfortunately the general definition of Cluster Algebra is quite technical and the standard examples are usually not so illuminating. In this talk we will present a simple minded combinatorial model that is sophisticated enough to capture the key features of the construction while using only some basic linear algebra constructions.
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