Colloquium: Dr. Nicholas Mayers

Seaweed algebras form a class of Lie algebras for which a number of algebraic invariants can be computed combinatorially. One such invariant is the index, an important algebraic invariant which is notoriously difficult to compute. Defining seaweed algebras originally as subalgebras of gl(n), Dergachev and Kirillov found that their index could be computed combinatorially by counting paths and cycles in a corresponding planar graph called a meander. Since then, the notion of a seaweed algebra has been extended to the classical Lie algebras (types A, B, C, and D), and the likewise extended notion of their associated meanders have been shown to hold much algebraic information. The goal of this talk is to give a tour of these combinatorial results over both gl(n) as well as the classical types. No prior knowledge is necessary for this talk. Open problems will be sprinkled throughout.

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