Speaker
Description
This talk is an overview of recent progress in applying techniques from arithmetic geometry to physics. Many interesting physics constructions in various theories, such as CFTs and SUGRAs, can be related to non-trivial Hodge theoretic problems. Some number theoretic results and conjectures, generalising the celebrated modularity theorem in various directions, imply that these problems can be solved by using arithmetic geometry. After reviewing these connections, I give a quick overview of techniques I have developed together with collaborators to efficiently compute arithmetic geometry data, and give various examples of applications to physics.
Time permitting, I will give some comments on recent work, questions, and speculation on how the correspondence between arithmetic geometry and physics can be taken beyond the context of Hodge theory.