8–11 Sept 2025
Opava, Czech Republic
Europe/Prague timezone

Towards a Construction of Algebro-Geometric Solutions for Integrable Vortex Equations

11 Sept 2025, 14:00
45m
Lecture hall of Institute of Mathematics (Opava, Czech Republic)

Lecture hall of Institute of Mathematics

Opava, Czech Republic

Na Rybníčku 626/1, 746 01 Opava 1

Speaker

Kaoru Miyamoto (Japan)

Description

The integrable vortex equations, which were originally motivated by models of superconductivity, can be explicitly solved using Liouville’s equation. While integrable vortices are known to exist on surfaces of non-zero genus (e.g., a torus), concrete vortex solutions and detailed studies of their analytic properties on higher-genus surfaces remain limited. Within the theory of integrable systems, the finite-gap (or algebro-geometric) method provides a powerful technique for constructing explicit solutions on Riemann surfaces of genus g. In this talk, we apply the finite-gap method to Liouville’s equation and construct a finite-gap vortex solution, as a step towards a systematic construction of integrable vortices on higher-genus surfaces.

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