Quantum Mathematics Seminar: Joost Nuiten (Toulouse)

Physics B21
Monday 24th April 2023 (14:00-15:00)

Robert Laugwitz (organizer)

Alex Schenkel (host)


Quantum Maths Seminar, external speaker

Joost Nuiten (Université de Toulouse)

Title: Lie algebroids as curved Lie algebras

Abstract: Differential graded Lie algebras play an important role in deformation theory as algebraic objects classifying the infinitesimal neighbourhoods of moduli spaces around a basepoint. An informal principle asserts that geometric objects without a fixed basepoint should admit a similar description in terms of curved Lie algebras, which have a `differential' whose square is controlled by a curvature element. In this talk, I will discuss the relation between two algebraic models for the formal neighbourhood of a moduli space around a variety, rather than around a single point: in terms of dg-Lie algebroids and in terms of curved Lie algebras over the de Rham complex. In particular, I will describe an embedding of the homotopy category of dg-Lie algebroids into the homotopy category of such curved Lie algebras. Joint work with Damien Calaque and Ricardo Campos.

School of Mathematical Sciences

The University of Nottingham
University Park
Nottingham, NG7 2RD

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