Matt SZCZESNY - Toric Hall Algebras and infinite-dimentional Lie algebras
Channel: Institut des Hautes Études Scientifiques (IHÉS)
Date: 2020-11-29

The process of counting extensions in categories yields an associative (and sometimes Hopf) algebra called a Hall algebra. Applied to the category of Feynman graphs, this process recovers the Connes-Kreimer Hopf algebra. Other examples abound, yielding various combinatorial Hopf algebras. I will discuss joint work with J. Jun which attaches a Hopf algebra to a projective toric variety X. This Hopf algebra arises as the Hall algebra of a category of coherent sheaves on X locally modeled on n-dimensional skew partitions.


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