Quantization in Derived Algebraic Geometry and Representation Theory (21w5145)


(Università di Pisa)

(Università degli Studi di Parma)

Mauro Porta (Université de Strasbourg)

Olivier Schiffmann (Université Paris-Saclay)


The Casa Matemática Oaxaca (CMO) will host the "Quantization in Derived Algebraic Geometry and Representation Theory" workshop in Oaxaca, from May 2 to May 7, 2021.

An essential paradigm in science is solving a problem through the study of its symmetries. Whether dealing with a chemical, physical, or mathematical system, its symmetries are intimately related to the conservation laws characterizing the system itself. Therefore, their study leads us to its full understanding. Quantum groups are deformations of the most elementary symmetries in Nature, describing, for example, infinitesimal layers of ice. They first appeared in the eighties as symmetries of one and two-dimensional statistical mechanical models and are nowadays ubiquitous objects in mathematics.

Quantum groups represent only an instance of the more general Theory of Quantization, in which the procedure of "deforming" classical structures gives rise to their "quantum" analog. This theory proved soon to have spectacular connections with many and only apparently unrelated areas of mathematics and physics, especially in representation theory (as described above), algebraic geometry (in particular the theory of moduli spaces), and theoretical physics (e.g. gauge theory). The present workshop aims to provide a survey of the state of the art of the Quantization Theory, with a special emphasis on using advanced techniques from (derived) algebraic geometry to the realm of Quantization.

The Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, are collaborative Canada-US-Mexico ventures that provide an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station in Banff is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT). The research station in Oaxaca is funded by CONACYT