Curve/Jacobian correspondenceLecture

by Dr Younghan Bae

Monday Nov 2, 2026, 3:00 PM → 3:45 PM Europe/Berlin

Endenicher Allee 60/1-016 - Lipschitzsaal (Mathezentrum)

To every smooth projective complex curve C of genus g, one associates a g dimensional complex torus J(C), called its Jacobian. Classical Abel-Jacobi theory reveals precise connections between the geometry and topology of C and J(C). How do these connections extend when smooth curves degenerate to singular curves?

In this talk, we extend this correspondence over the moduli space of stable curves. We construct an algebra isomorphism between the cohomology of universal compactified Jacobians and a quotient of the cohomology of moduli spaces stable curves with additional symmetrized markings. Our construction is motivated by recent progress on the P=W conjecture and logarithmic Abel-Jacobi theory. This isomorphism allows us to transfer structures between two sides, leading to several applications. This is joint work in progress with Aaron Pixton.