Higher Structures and Field Theory

The programme is devoted to the fruitful interaction between the theory of higher structures and mathematical approaches to field theory. This interaction goes in both directions.

On the one hand, field theory constantly inspires new developments in almost all fields of mathematics. And higher stuctures including the modern homotopy theory and supergeometry are among the first recepients of these ideas. There is also a renewed interest in mathematical approaches to field theory including algebraic perturbative quantum field theory, factorization homology etc.

On the other hand, many tools of the higher stucture theory naturally enter the language of quantum field theory. Among the examples are A-infinity and L-infinity stuctures, Batalin-Vilkovisky structures (first discovered in physics, they made their home in mathematics, and are now back on the physics arena) and many others. An impressive recent development is the use of higher structures in the classification of states of matter.

The programme will bring together specialists in higher structures and classical and quantum field theory to create more interaction on these exciting topics. Among the highlights of the programme are a focus week on the use of higher structures for a classification of states of, what is called, topological matter (during week 1), a workshop on higher structures (week 3), a focus week on the interaction between quantum field theory and higher structures (week 5), and a focus week on supergeometry and gauge theory (week 7). Among the programme events there will be mini-courses on perturbative algebraic quantum field theory, BV-methods, factorization algebras, and supergeometry (see below for a detailed description).



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At a glance
Thematic Programme
Aug. 1, 2022 — Aug. 26, 2022
ESI Boltzmann Lecture Hall
Anton Alekseev (U Genève)
Stefan Fredenhagen (U Vienna)
Nicolai Reshetikhin (UC, Berkeley)
Thomas Strobl (U Lyon)
Chenchang Zhu (U Göttingen)