Special Functions: From Geometry to Fundamental Interactions

5 - 30 August 2024

Lorenzo Tancredi, Ruth Britto, Henrik Johansson, Oliver Schlotterer, Matthias Wilhelm

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.


Week 1: Monday: welcome and discussion, Tuesday-Thursday: topical workshop “Elliptics and Beyond ‘24", Friday: discussion


Week 2: Topics: Properties of Calabi-Yau varieties and Higher genus Riemann surfaces, iterated integrals defined on Calabi-Yaus and Higher genus surfaces, realizations & applications in string theory, quantum field theory and gravity


Week 3: Topics:  Special functions and special numbers in gravity, the standard model of particle physics and super Yang-Mills theories; algebraic methods (generalization of symbol map, motivic coaction, single-valued periods)


Week 4: Topics: Application to multi-scale problems in QFT and Gravity,  algorithms for symbolic manipulation and analytic continuation, algorithms for numerical evaluation of collider and gravitational wave observables