<p>Illustrated by Rok Gregoric</p>

This program is organized around key themes of “higher” quantization and mirror symmetry as they impact and elucidate a wide variety of questions in representation theory. The program will bring together experts and young researchers from algebra, geometry, physics and number theory to help develop and disseminate this unified vision of a rapidly evolving field, exploring the mathematical consequences of the examples, structures, and dualities discovered in physics.

Tremendous progress has been made using motivic techniques in geometric questions for affine algebraic varieties, especially those involving algebraic vector bundles. Computations in classical algebraic topology have been improved by motivic techniques, e.g., related to the problem of computing homotopy groups of spheres. Moreover, the theory has identified new structures of interest in arithmetic situations. Transformative recent progress in motivic homotopy theory has only broadened the scope for potential applications of motivic techniques, as well as new avenues of interaction with other areas of mathematics. This program will build on previous successes, explaining the tools that have been developed and how to use them, analyzing questions of the sort described above and identifying new domains where motivic techniques will be successful.

The Complementary Program has a limited number of memberships that are open to mathematicians whose interests are not closely related to the core programs; special consideration is given to mathematicians who are partners of an invited member of a core program.

Under the light of suspended spheres, the QFT wizard dangles groups and their duals over a boiling cauldron of motives. (Drawn by Rok Gregoric)

The goal of this introductory workshop is to showcase some of the recent developments in motives and quantum field theory, with a focus on giving a high-level, but "outsider-friendly" introduction to both subjects. It will feature lectures introducing the modern formalism of sheaf theories, supersymmetric gauge theories, geometric representation theory and motivic spectra.