25th Geometry and Physics Colloquia

Programme

13:30-14:30 Lecture by Prof. Eric D'Hoker (UCLA, USA)

Title: Mathematical adventures of a theoretical physicist, from string theory to modular graph forms, modular tensors and polylogarithms

Abstract: Modular forms have played a central role in string theory since its inception. The low energy limit of string amplitudes at one loop order has recently led to introducing infinite families of non-holomorphic modular forms known as modular graph forms. They generalize non-holomorphic Eisenstein series and have sparked recent developments at the interface of algebraic geometry and number theory. Perturbative string amplitudes at higher loop order suggest a further generalization in terms of modular tensors on Riemann surfaces of higher genus. Variants of the modular tensors encountered in string amplitudes lead to an explicit construction of higher-genus polylogarithms and associated function spaces which close under integration. An overview of these developments to date will be presented and some open problems for future investigations will be outlined.

14:30-15:00 Coffee and tea

15:00-16:00 Lecture by Prof. Nikita Nekrasov (Simons Center for Geometry and Physics, USA):

Title: Yang-Mills theory and condensed matter physics: many-body systems, strings, and graphene

Abstract: Quantum Yang-Mills theory is the fundamental ingredient of the Standard Model of particle physics, in 3+1 spacetime dimensions. I will describe the much simpler version of Yang-Mills theory, two dimensional gauge theory, which, despite its simplicity, bears a lot of interesting structure. From dynamics of many-body systems to magic angles in twisted bilayered graphene, various aspects of Yang-Mills theory, classical and quantum, will prove relevant for description of observed and expected phenomena of superconductivity and quantum Hall effect.

Welcome to join!

This colloquia is organised by the Centre for Geometry and Physics.