Graph Representations and Dynkin Diagrams -- Ben Elias
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A representation of a graph assigns a vector space to each
vertex, and a linear map to each edge.  Simple enough.  Now classify
these!  I will give an overview of graph representations, how to
think about simple and irreducible representations, and present the
key result: somehow it is only feasible to classify the irreducible
representations for certain specific graphs - namely, the Euclidean
and Affine Dynkin Diagrams!