PIMS Workshop in Mathematical Physics at Heidelberg University

From June 12 to 16, 2023, the Mathematical Physics group in the Mathematisches Institut at Universität Heidelberg, will host a workshop on topics at the intersection of physics and pure mathematics, focused special emphasis on algebra, representation theory, and complex and algebraic geometry.

Calabi-Yau manifolds have played a pivotal role in the fruitful exchange between theoretical high-energy physics and algebraic geometry since the 1980’s. Seeded by a handful of examples in the context of heterotic string theory, and fueled by the discovery of mirror symmetry and other dualities around the turn of the Millennium, the range of questions about Calabi-Yau manifolds that are studied in both physics and mathematics has diversified considerably over the last decade. For the phenomenology of the string landscape, the finiteness of the number of string vacua remains of central importance, and Calabi-Yau flux compactifications the basic paradigm. On the theoretical end, recent years have seen a surge of interest in understanding the relevance of number theoretic methods in physics, and of techniques of quantum theory for arithmetic geometry. These methods have also found common ground in unravelling the structure of scattering amplitudes in perturbative quantum field theory. The Algebraic Geometry group at Alberta and the Mathematical Physics group at Heidelberg share a broad range of interests and expertise revolving around Calabi-Yau manifolds and their moduli spaces. The topics also resonate with interests of several other groups, both within the MAThematics Center Heidelberg and the Institute for Theoretical Physics at Heidelberg, and at the Pacific Institute for Mathematical Sciences at its various sites. The environment in Heidelberg also includes the STRUCTURES Cluster of Excellence, one of whose aims is to uncover deep new relations between mathematical and physical structures.

We hope that this joint MATCH-PIMS workshop will serve both to further connect the different topics to one another, and also to foster interactions and connections between the diverse participants.