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Kavli Institute for Theoretical Physics, Santa Barbara

Generalized symmetries have recently emerged as a unifying theme in high energy theory, phenomenology, condensed matter physics, mathematics, and quantum gravity. This field has witnessed a literal explosion of new results within all these different areas. This program will bring together experts from this diverse set of fields, to first consolidate recent progress and more importantly, to find common ground to explore, across disciplines, the exciting physical implications of generalized symmetries. To date, the isolated development has led to several related concepts being developed independently, in different contexts and without much cross-interaction. The program aims to consolidate these divergent approaches and foster interactions between researchers in high energy, condensed matter physics and mathematics, hopefully identifying synergies that drive future joint developments. Due to the truly interdisciplinary character of this subject, this program will convene scientists to discuss 1. Generalized Symmetries: hep-th meets cond-mat 2. Non-Invertible Symmetries 3. Topological Order 4. Generalized Symmetries in String Theory, Holography and Quantum Gravity 5. Phenomenological Applications, and, 6. Mathematics, in particular Higher Category Theory.

The Department of Mathematics and Statistics at the University of Massachusetts Amherst will host its fourth annual summer school on Physical Mathematics of Quantum Field Theory during the week of June 9 - 13, 2025. The aim of the workshop is to introduce young researchers on the boundary between mathematics and physics to recent ideas in classical and quantum field theory using notions from complex geometry and algebraic topology. This year there is a focus on 4d gauge theories and their relationship with representation theory, algebraic geometry, and topology. The target audience of the workshop is advanced graduate students and post-docs, from both mathematics and theoretical physics. The schedule will be designed to include a large amount of time for participants to interact. We hope especially to encourage conversations between mathematicians and physicists.

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