Sep 2 – 6, 2019
Institut de Mathématiques de Bourgogne
Europe/Paris timezone

Integrable Lagrangians and Picard modular forms

Sep 5, 2019, 3:15 PM
Amphi Paris

Amphi Paris


Evgeny Ferapontov (Loughborough University)


We consider first-order Lagrangians whose Euler-Lagrange equations belong to the class of 3D dispersionless integrable systems. Our main results can be summarised as follows:
(1) A link between integrable Lagrangians and Picard curves/Picard modular forms studied by E. Picard as far back as in 1883 is established.
(2) A parametrisation of integrable Lagrangian densities by generalised hypergeometric functions (solutions of the Picard-Fuchs system governing periods of Picard curves) is obtained.
(3) Conjectured theta representations and power series expansions of the integrable Lagrangian densities are proved.
(based on joint work with F. Cl\'ery A. Odesskii and D. Zagier)

Primary author

Evgeny Ferapontov (Loughborough University)

Presentation materials