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# Topology, Algebraic Geometry, and Dynamics Seminar (TADS): How to differentiate a Lie infinity-group

Nov 1, 2024, 1:30 - 2:30 PM

**Speaker:** Chris Rogers, University of Nevada

**Title:** How to differentiate a Lie infinity-group

**Abstract:** Lie infinity-groups are reduced simplicial manifolds which satisfy a geometric version of the Kan condition from simplicial homotopy theory. In analogy with the correspondence between finite-dimensional Lie groups and Lie algebras, the infinitesimal counterpart of a finite-dimensional Lie infinity-group is a Lie infinity-algebra. This is a finite-type graded real vector space equipped with operations which satisfy the axioms of a differential graded Lie algebra, but only up to coherent homotopy. In recent work (arXiv:2409.08957) with Jesse Wolfson (UCI), we proved that every such Lie infinity-algebra integrates to a finite-dimensional Lie infinity-group. This talk will concern the inverse operation: differentiation. We will describe a homotopically well behaved differentiation functor for Lie infinity-groups that is tractable, yet sufficiently explicit, and which bypasses the technical complications surrounding similar constructions appearing in the recent literature. This is joint work in progress with Jesse Wolfson.

**Time:** Friday, November 1, 1:30pm – 2:30pm

**Place:** Exploratory Hall, room 4208