Geometry when commutativity fails, a groupoid approach

par Mathis Alleysson (IMT)

jeudi 23 avr. 2026, 14:00 → 16:00 Europe/Paris

Pellos (1R2)

A powerful idea in modern geometry is that a space can be encoded by its functions. In this talk, we begin by recalling this correspondence, which associates to each topological space its commutative algebra of continuous functions. 

We then introduce groupoids as a natural generalization of both spaces and groups, illustrated by examples. To each groupoid, one can associate an algebra, which is, in general, noncommutative. This procedure recovers both classical commutative algebras and some noncommutative examples, such as matrix algebras. If time permits, we will conclude with a fundamental example at the interface of dynamics and operator algebras: the noncommutative torus, which captures many of the central ideas of the theory.

Despite appearances, no prior background in geometry will be assumed.