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Résumé |
Finding Ricci-flat metrics is a long standing problem in geometry with deep
implications for string theory and model building. A new attack on this problem
uses neural networks to engineer numerical approximations to the Ricci-flat
metric on a Calabi–Yau manifold within a given Kähler class. As case studies, we
investigate numerical Ricci-flat metrics over smooth and singular K3 surfaces
and Calabi–Yau threefolds such as the quintic. Using persistent homology, we
show that high curvature regions form clusters near the singular points.
Finally, we discuss how good the current state-of-the-art numerical metrics are
for phenomenology. |
