Moduli, Motives and Bundles – New Trends in Algebraic Geometry (22w5187)

The Casa Matemática Oaxaca (CMO) will host the "Moduli, Motives and Bundles – New Trends in Algebraic Geometry" workshop in Oaxaca, from September 18 to September 23, 2022.

Classification problems are doubtless some of the most important problems in mathematics. Normally objects are classified with respect to a notion of symmetry, equivalence or isomorphism. As geometers, we are really happy when the classifying set of symmetries turns out to be a geometric object as well. When this is the case, the geometry of this classifying object tells us something about the classification problem itself, basically points of this geometric object correspond to the isomorphism classes of the structures one wants to classify. These classifying or moduli spaces can then be studied themselves with methods from algebraic geometry. Nowadays, apart from the classical techniques such as invariant theory developed during the 19th and 20th century to study these moduli spaces, other new techniques are used such as derived categories or motivic homotopy theory. A problem arises when the classification problem gives rise to too many symmetries and no moduli space can be directly constructed. A modern way to deal with this problem is to use the language of algebraic stacks, which intrinsically allows to keep track of all the isomorphisms and gives rise to the notion of a moduli stack, a more abstract categorified version of a moduli space, but nevertheless tractable with methods from algebraic geometry. Fundamentally important in geometry, topology, arithmetic and physics is the classification of vector bundles and principal bundles over a fixed algebraic variety and the associated moduli spaces and moduli stacks have very rich geometric structures. This school and workshop intends to give fresh insights into new methods and techniques for the study of these moduli spaces and moduli stacks including GIT methods, derived categories and motivic homotopy theory.

Organised in partnership with the Clay Mathematics Institute and the Foundation Compositio.

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