Calabi-Yau metrics with full moduli dependence

Luca Nutricati (U of Oxford)

Jul 10. 2026, 12:15 — 13:00

Modern approximate constructions of Ricci-flat metrics on compact Calabi-Yau manifolds typically fall into two complementary categories: highly flexible numerical methods, which are not easily interpretable, and analytic ansätze, which are often tied to a fixed Kähler class. This becomes particularly restrictive when seeking explicit Kähler moduli dependence, since varying the moduli generally requires changing the ansatz itself. I will describe a hybrid strategy that uses machine-learned Ricci-flat metrics as data and reconstructs explicit symbolic expressions with moduli-dependent coefficients. The resulting approximate analytic metrics exhibit explicit dependence on both Kähler and complex-structure moduli, providing a bridge between numerical metric learning and analytic approaches to Calabi-Yau geometry.

Further Information
Venue:
ESI Boltzmann Lecture Hall
Associated Event:
The Unreasonable Effectiveness of Toric Geometry: Bridging Mathematics, Computation, and String Theory (Thematic Programme)
Organizer(s):
Magdalena Larfors (Uppsala U)
Gary Shiu (U of Wisconsin-Madison)
Harald Skarke (TU Wien)
Michael E. Stillman (Cornell U, Ithaca)