Department of Mathematics
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Quiver representations are some of the simplest examples of modules over a noncommutative algebra (in this case, the path algebra of a quiver, or directed graph). In this talk, I will give a short introduction to quiver representations, and explain how they came up in our study of the combinatorics of the noncrossing partitions associated to a finite reflection group. The main result which I will discuss is a new proof that the noncrossing partitions form a lattice, the first computer-free proof of which was given by Brady and Watt in 2005.

This is joint work with Colin Ingalls (UNB), and is based on work presented in arXiv:math/0612219.