Conformal Field Theory, Integrability, and Geometry: March 11-15, 2024

Quantum Field Theory (QFT) is an indispensable tool in modern theoretical physics. It is essential to the study of particle physics and critical phenomena and finds numerous applications in other areas such as many-body systems, turbulence, cosmology, etc. As the list of topics in which QFT plays an important role continue to expand, we are forced to constantly revise our fundamental understanding of the topic and develop new sophisticated mathematical techniques. Two dimensional Integrable Models (IMs) and Conformal Field Theories (CFTs) constitute the perfect laboratories to explore and probe the frontiers of our knowledge of QFT. The presence of a large, oftentimes infinite, set of symmetries in IMs and CFTs allows for the use of powerful non-perturbative and exact methods. In turn this elevated degree of control led– and is still leading – to profound insights on many important physical phenomena. Two celebrated examples are the features of universality classes of 2nd order phase transitions and the nature of dimensional transmutation. Additionally, being founded on beautiful and profound mathematical structures, IMs and CFTs are amongst the most active fields of Mathematical Physics. The intense exchange of ideas and results between the research in these topics and Pure Mathematics brought about many remarkable achievements in both fields such as the discovery of Quantum Groups and considerable advancements in the Langlands program.

In 2024, it will be exactly 40 years since the publication of the influential article ‘Infinite conformal symmetry in two-dimensional quantum field theory’ by A. Belavin, A. Polyakov and A. Zamolodchikov. Seizing this happy occasion, the workshop aims to bring together experts in conformal field theory, integrable systems and string theory, who will share their insights, report on recent developments, and trace new avenues of research.