Pure Maths Colloquium: Gradings on cluster algebras and associated combinatorics
28 April 2014 16:00 in CM221
When studying any class of rings or algebras, the existence of
a grading often has a big impact on what can be said about the members
of the class. In the few years since their inception, cluster algebras
have been found in numerous places and have been shown to be responsible
for a plethora of combinatorial patterns, but until very recently
gradings on cluster algebras have not been considered in any detail.
In this talk, we will introduce gradings on cluster algebras in a very
natural way and show how the intricate structure and combinatorics
associated to cluster algebras allows us to find and classify gradings.
We will look at cluster algebras of finite type and examine the gradings
they admit, making use of cluster categories. Conversely, the gradings
bring out some beautiful combinatorics of their own, as we will see.
Finally, we will conclude with a more algebraic application of gradings
to a problem of the existence of certain (quantum) cluster algebra
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