Higher Structures in Algebra, Geometry, and Topology

Talk by Bruno Vallette (Université Sorbonne Paris Nord), at the Antwerp Algebra Colloquium on April 23, 2021.

The goal of this talk will be to introduce the audience with higher structures (homotopy algebras, operadic calculus and higher categories). These structures and the way to work efficiently with them were extensively studied over the past 30 years. We will show that their consideration is mandatory to formulate and to establish some open conjectures in Algebra, Geometry, and Topology.