Machine and human learning the geometry of Calabi–Yau manifolds

Vishnu Jejjala (U of Witwatersrand)

Jul 06. 2026, 11:30 — 12:15

Using physics informed neural networks, we construct numerical approximations to Ricci-flat Calabi–Yau metrics. This allows for the calculation of Yukawa couplings in the low-energy effective N=1 theories obtained upon heterotic compactification. In explicit examples, hierarchies arise from excursions away from symmetric points in complex structure moduli space. While numerical Ricci-flat metrics on Calabi–Yau manifolds are becoming increasingly accurate and useful, they lack the interpretability required to extract theoretical insights. From a variant of Donaldson's algorithm, we establish that the metric parameters obey novel power laws near the large complex structure limit.

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)