Dispersionless Integrable Equations and Modular Forms

Explore the fascinating connection between dispersionless integrable equations and modular forms in this comprehensive lecture by E. Ferapontov from Loughborough University, UK. Delve into two key examples: dispersionless Hirota equations with theta constants, and first-order integrable Lagrangians with Picard modular forms. Gain insights from joint work with F. Clery, L. Hadjikos, K. Khusnutdinova, A. Odesskii, and D. Zagier. Learn about the general phenomenon of expressing coefficients of various classes of dispersionless integrable PDEs in 3D using modular forms. Understand the context of this lecture within the SCREAM project, focusing on Cartan and parabolic geometries, and their applications in mechanical systems, integrable systems, and Penrose's Conformal Cyclic Cosmology programme.

E. Ferapontov (Loughborough University, UK): Dispersionless integrable equations and modular forms