Two dimensional conformal field theories (CFTs) are ubiquitous in mathematical physics and as such provide surprising connections between different areas of research. The past decade has seen a surge of powerful techniques using supersymmetry, integrability, and more recently, random geometry/probability to study different aspects of CFTs. For instance, the task of explicitly computing conformal blocks is crucially important, but often very difficult.
Building a dictionary between such techniques often leads to a web of dualities, which have the potential to translate any result obtained in one of these fields into new nontrivial results in the others. A prime example is that of supersymmetric (SUSY) partition functions. On the one hand, their equivalence to conformal blocks resulted in explicit and elegant expressions for Painlev´e tau-functions. On the other hand their connection to quantum integrable systems has led to solutions for a new class of spectral problems, including the one appearing in black hole perturbation theory. Likewise, a recent connection between CFT and the Gaussian Free Field has led to a rigorous formulation of the 2D Liouville path integral and bounds on the radius of convergence of the corresponding conformal blocks in certain cases. Moreover, Schramm-Loewner evolution and conformal loop ensembles have led to the construction of new CFTs and the link with the conformal blocks is yet to be discovered.
The purpose of this workshop is to bring together young researchers and experts from the three communities mentioned above, to share their techniques and insights, and work towards a unified framework.
