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Computational Differential Geometry and it’s Applications in Physics: November 14- 18, 2022

Participant List

Organized by:

Rodrigo Barbosa (SCGP)
Simon Donaldson (SCGP)
Michael R. Douglas (CMSA and SCGP)
Burt Ovrut (U Penn)

The workshop “Computational Differential Geometry and its Applications in Physics” grows out of recent work using machine learning techniques to solve geometric PDEs such as those determining Ricci-flat Kähler metrics in four and higher dimensions.

The mathematical focus will be on computational methods for Riemannian geometry: methods to represent and compare metrics, to find structures such as geodesics or minimal cycles, and to obtain explicit Einstein metrics, metrics of G2 and special holonomy and complex structures. The physics focus will be on using these explicit expressions for metrics, gauge connections, moduli potentials and so on to solve for physically relevant quantities in supergravity and string theory compactifications, such as Yukawa couplings and matter Kähler potentials in realistic superstring vacua. We also hope to stimulate discussion on the foundations of such work and the use of verified numerical results in rigorous proof.