SCIENTIFIC PROGRAM

Quantum Field Theories (QFT) provide the basic framework for the study of physical systems with infinite number of degrees of freedom. They model interactions of elementary particles, and phase transitions in condensed matter and non-equilibrium systems such as turbulence in fluid flow. In mathematics, the quest of finding rigorous and satisfactory formulations of QFT has led to successes and development in many areas, including Probability Theory and Geometry (the key aspects of this CJM Program) as well as Algebra and Representation Theory, Functional Analysis, and General Topology. As fixed points of the renormalisation flow, Conformal Field Theory (CFT) plays a special role in the QFT landscape. Our CJM Program envisions to bring together people with a wide range of backgrounds, ranging from Probability, Analysis, Geometry, to Theoretical Physics in order to make substantial progress in the study of CFT. It has become clear in the recent decades that combinations of different techniques are necessary to address the difficult technical and conceptual challenges in the rigorous and satisfactory formulations of CFT and its relation to lattice models in Statistical Physics and to Random Geometry. We have therefore paid particular attention to planning lectures and mini-courses that serve as a platform for establishing a common language between communities, as well as a training ground for young researchers to tackle the hard problems in the mathematics of CFT. Our main research topics will be :   

•  Logarithmic CFT
•  Minimal Models and BRST Reduction
• Connections with SLE/CLE
• Boundary Liouville CFT and JT Gravity
• Quantization of Teichmüller Space