Special Functions: From Geometry to Fundamental Interactions

Fertile common ground has emerged for the mathematical structures that control perturbative calculations in different domains of fundamental physics – quantum field theory, general relativity, and their extension to string theory. This program brings together experts in these various domains of physics, as well as mathematicians with expertise in higher-genus surfaces and Calabi-Yau periods. Through an in-depth exchange among these communities, we aim to: · trigger technology transfer for advancing the precision frontier in perturbative quantum field theory and string theory, leading to insights that will impact both phenomenology, such as collider and gravitational-wave physics, and formal theory, such as string dualities and holography; · chart a course towards new understanding of the role of special functions in high energy physics, opening new avenues to reformulate quantum field theory and string theory to manifest the similarities of their mathematical structures.