Seminar Announcement
Date: Tuesday, 07 November 2023
Time: 02:00 PM
Venue: Lecture Hall 801
Approximate Ricci-flat metrics on Calabi–Yau geometries
Vishnu Jejjala
University of the Witwatersrand, South Africa.
07-11-23

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Abstract

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.