Recent years have seen a regain of interest in the use of Poisson-Lie group and quantum group structures in the foundations of quantum gravity with a cosmological constant. Witten opened the field at the end of the 80's by cracking the quantization of 3d-gravity, through a Chern-Simons formulation. A related, though somewhat complementary, line of research was born soon after with the discovery that the Turaev-Viro state sum encodes 3d quantum geometries. Using loop quantum gravity related techniques, new progress has been recently achieved in this direction by explicitly working out the relation between curved discrete (quantum) geometries and Poisson-Lie (quantum-) group structures. This year an analogous construction has been proposed in the 4d context. Interestingly, this proposal hints toward the need in 4d of an extension of the standard quantum group framework. Indeed, the quantization of the simplicial geometry, and the consequent correspondence with the discrete Einstein-Hilbert-Regge action, is obtained by means of a complex Chern-Simons theory where appropriate boundary conditions are imposed. Coincidently, such a theory has also experienced a recent boost in its comprehension, actually made possible by the application of string theoretical ideas and techniques. At the intersection between these two lines of research lies the new, and still largely unexplored, proposal that a specific class of holomorphic blocks from 3d N=2 gauge theories are the wave functions of quantum 4d simplicial geometries.

The aim of the workshop is to bring together mathematicians and mathematical physicists from different backgrounds and generations to discuss these new developments and to foster an exchange of points of view and mathematical techniques. To make this possible, ample room for discussions will be left in between the talks. Also, to effectively introduce the youngest researchers to such a technical field, renowned experts will be asked to hold four mini-courses of two lectures each on the main topics of the conference. Note that these courses are also of interest to a wider spectrum of students and young researchers than quantum gravity researchers and mathematicians. Indeed, quantum groups have become crucial tools in some areas of quantum information theory and condensed matter.