17 September 2026

Photo: UHH/ Görtz

Group Photo from the CRC 1624 Summer School

Three weeks, 17 speakers from around the world, and over 120 participants gathered in Hamburg for an intensive program at the frontier of mathematics and theoretical physics.

The CRC 1624, "Higher Structures, Moduli Spaces and Integrability", is a joint initiative of Universität Hamburg, DESY Hamburg, and TU Munich. It held a major scientific gathering this summer: a three-week school bringing together some of the most active research directions at the intersection of modern mathematics and theoretical physics. The themes of the summer school were of particular interest also for an interdisciplinary part of the Cluster of Excellence Quantum Universe. CRC1624 and Quantum Universe share common overarching themes, and complement each other in the specific goals and methods.

The summer school covered topics ranging from topological quantum field theory and conformal field theory to supersymmetry, generalized geometry, integrable models, and the geometry of moduli spaces, across more than 60 lectures, colloquia, and poster sessions. These areas sit at the intersection of modern mathematics and theoretical physics, with direct connections to quantum field theory and string theory.

An International Community

Seventeen internationally renowned speakers from institutions across the world delivered lecture series at the school, covering fields ranging from vertex algebras and generalized symmetries to the geometry of quantum field theories. They were joined by over 120 participants ranging from master's students to professors, the majority traveling from outside Germany.

The program was designed to give early-career researchers genuine opportunities to present and develop their own work alongside leading experts. One popular format was the Gong Show: five minutes per speaker to present a result or open problem, which regularly sparked focused discussions between participants comparing thoughts and approaches. For many, the school offered not only new scientific input but also direct exchange with established researchers and a chance to find new directions for their own work.

A Field in Motion

The research areas covered by the school are developing rapidly. Generalized symmetries, higher categorical structures, and their role in quantum field theory and string theory are transforming significant parts of both mathematics and theoretical physics, and the school reflected that momentum. For many participants, the three weeks offered not only new mathematical and physical input, but also the connections and collaborations that sustain long-term research careers.

The summer school was held as a highlight event for the first funding period of the CRC 1624. All lectures are recorded and available on the summer school website.