Program on Higher Structures in Geometry and Physics

Background and goal

One of the classical prerogatives of mathematics is to understand, distinguish and classify its objects. This is favorably achieved by considering naturally appearing additional structures. In recent times, great progress has been made on this front. These leaps in understanding have been so successful, that there is a growing need to understand the different structures themselves and their interplay using higher or meta-structures. Examples from this can be found in algebra, geometry and physics, such as higher homotopies and coherences, the objects governing these, the use of higher categories in quantum field theory and derived algebraic and differential geometry. These higher structures also appear in the very foundations of mathematics in the guise of univalent foundations and homotopy type theory.

The activity aims to bring together researchers from the various areas above that are working on related and interlinked problems albeit so far in their own respective languages. The intention is an exchange of techniques and ideas which will aid current research and help to focus and shape future directions.

Related events

There will be an opening conference in the week January 18-22, a workshop on homotopy type theory and higher structures in the second week of February (Feb. 10-14) and a closing conference on March 18-22.

Advisory board

Y. Manin, P. Teichner

Participants