Workshop

While motives and quantum field theory have two rather disparate origins in mathematics, they share many of the ideas, themes and even have direct influence on each other. In the theory of motives and motivic homotopy theory, old conjectures have now been toppled which has given rise to swaths of new structures and objects. The latter interacts, in often surprising ways, with commutative algebra, enumerative geometry, p-adic Hodge theory and classical algebraic topology. Interactions between representation theory and quantum field theory triggered a development of the new field of 3-dimensional mirror symmetry with connections to both the classical 2d mirror symmetry and the geometric Langlands program. The goal of this introductory workshop is to showcase some of the recent developments in both fields, 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.