Computational Differential Geometry and its Applications in Physics: November 14-18, 2022

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Danfords Shuttle

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.

Talk Schedule

Time Title Speaker Location
8:30am Breakfast N/A SCGP Cafe
9:30am Review of some numerical approaches to Kahler-Einstein metrics and other special metrics on complex projective varieties Simon Donaldson SCGP 102/ZOOM
10:30am Coffee Break N/A SCGP Cafe
11:00am Calabi-Yau metrics with neural networks Sven Krippendorf SCGP 102
12:00pm Lunch N/A SCGP Cafe
1:15pm Relations between numerical geometry and machine learning Michael Douglas SCGP 102
2:15pm Break N/A SCGP Cafe
2:30pm Non-commutative optimization – geodesic 1st and 2nd order methods for moment maps and polytopes Rafael Oliveira SCGP 102
3:30pm Tea Time N/A SCGP Cafe
4:00pm Computational Riemannian geometry applied to the physics of the AdS-CFT correspondence Toby Wiseman SCGP 102

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