Speaker: Professor Ezra Getzler (Northwestern University)

Title: Generalizing Lie theory to higher dimensions – the De Rham theorem on simplices and cubes

Abstract: There is a generalization of Lie theory from Lie algebras to differential graded Lie algebras. Ordinary Lie theory involves first order ordinary differential equations. Higher Lie theory may be understood as a non-linear generalization of the de Rham theorem on simplicial complexes (in Dupont’s formulation), as against graphs. In this talk, we present an alternate approach to this theory, using the more elementary de Rham theorem on cubical complexes.
Along the way, we will need an interesting relationship between cubical and simplicial complexes, which has recently become better known due to its use in Lurie’s theory of straightening for infinity categories.

Mathematics Hall, room 407 from 4:30 – 5:30pm

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