Overview 

Dates:　　March 16--March 19,  2027

Venue:　Takigawa Hall, Kobe University

Moduli spaces of stable parabolic connections on algebraic curves with regular or irregular singularities have been constructed as smooth quasiprojective varieties, and through an analysis of the Riemann–Hilbert correspondence, the geometric Painlevé property of the isomonodromic differential equations has been established. Since the phase spaces of Painlevé-type equations have thus been understood globally as moduli spaces of stable parabolic connections, detailed study of these phase spaces has become possible. A wide range of research is now developing, including the symplectic structure of the moduli spaces, the theory of canonical coordinates via apparent singularities, asymptotic expansions of solutions and τ-functions of Painlevé-type equations, WKB analysis and the theory of topological recursion, non-abelian Hodge theroy,  Geometric Langlands program,  and connections with mathematical physics.  This conference will feature lectures and discussions on research integrating algebraic geometry and integrable systems, as well as on related topics.

Supported by Research Grand in Aid, JSPS Kakenhi: 22H00094