19 June 2026

Photo: Hofstetter/Goertz

The sixth edition of „Topology between the waves (TBTW)” was held in Fréjus, France, on May 10 – 15, 2026. Every year, the TBTW workshop series brings together young researchers to spend one week studying and presenting a topic in low-dimensional and quantum topology. The title of the 2026 edition was „The Volume Conjecture: From Some TQFTs to Recent Developments”. The CRC 1624 co-organized the workshop and seven CRC 1624 early career researchers, as well as one UHH master's student, were involved in the event.

The volume conjecture relates quantum invariants of knots and manifolds with an invariant of a very different kind: the hyperbolic volume. The first part of the workshop addressed the construction of the Reshetikhin–Turaev and Turaev–Viro invariants and their corresponding TQFTs. In the second part of the workshop hyperbolic geometry and several formulations of the volume conjecture were introduced. The last part of the week was devoted to understanding recent advances in the volume conjecture, using the RT-TV correspondence. Each presentation was followed by ample discussion time, to delve into the topics and foster interactions between participants.

The workshop provided an opportunity for the training of early career researchers and offered insight into an important research area in quantum topology. UHH master's student Alexander Tishchenko shared his experience as one of the youngest participants of this edition: "During my stay, I had the opportunity to connect and socialize with fellow students and researchers in a spectacular location. I particularly valued the open and collaborative atmosphere, which exposed me to new ways of thinking about mathematics and deepened my interest in the field."