Global Categorical Symmetries

Simons Collaboration in Mathematics and Physics

14 October 2021
Tangles as defects describing E_2-structures such as braidings

The Simons Collaboration on Global Categorical Symmetries brings together a group of physicists and mathematicians who aim to unlock the power of symmetry in its broadest, most general form – across disciplinary boundaries.

Professor Claudia Scheimbauer from the Technical University of Munich (TUM) is one of the principal investigators of this new Simons Collaboration. The collaboration directed by Professor Constantin Teleman from the University of California, Berkeley. Its members come from various institutions around the world.

PostDoc position at TUM

The Simons Foundation will support this effort by providing a grant of 8 million USD for four years, renewable for 3 additional years. The collaboration will create a prestigious Simons Foundation postdoctoral position at the TUM. It will also fund yearly conferences, summer schools, and various meetings per year.

The Kick-Off Meeting of the Collaboration took place on 11-13 October at a bicoastal meeting at the Simons Center in Stonybrook, New York, and at the International Centre for Mathematical Sciences in Edinburgh. As one of the keynote speakers, Prof. Claudia Scheimbauer talked on "Higher categorical tools for defects and boundary theories". Watch the talk by Claudia Scheimbauer here.

Exploring quantum field theory with symmetry

The aim of the Simons Collaboration is to enhance our understanding of symmetry. Symmetry is a powerful tool for organizing physical phenomena and anchors our understanding of the laws of nature.

The notion of symmetry, however, has evolved dramatically since the emergence of groups and representations as the language for describing symmetries in geometry and mechanics. Galvanized most recently by advances in mathematics and physics, much of this evolution has been driven by the quest to achieve a deeper understanding of quantum field theory – the universal language of modern theoretical physics.

Connecting topology and symmetry

From a modern point of view, quantum field theory associates to every symmetry a topological "defect", which acts on local and extended observables. These defects can be described by methods of topology, using the mathematics of topological quantum field theory.

This connection to topology has recently led to the discovery of new higher notions of symmetry, which in turn has shed new light on some of the most mysterious and profound phenomena described by quantum field theory, such as the so-called color confinement in non-abelian gauge theories or duality.

For more information on the research topics, members, events and positions, visit the Simons Collaboration on Global Categorical Symmetries website.