Math 281Y: Topics in Differential Geometry (Spring 2020)

Class Time: Tuesdays and Thursdays 12-1:15pm, Science Center 310

Instructor: Sébastien Picard
Email: spicard@math
Office: Science Center 235
Office hours: Tuesdays and Thursdays 1:15-2:15pm, or by appointment

Course Description: An introduction to non-Kahler complex geometry and the Hull-Strominger system.

References:

Notes and Books:

o Becker-Becker-Schwarz. String Theory and M-theory: A modern introduction. Cambridge University Press, 2006.
Relevant sections: 9.4 and 10.4

o Sebastien Picard - Calabi-Yau Manifolds with Torsion and Geometry Flows (Link)
My notes on non-Kahler geometry and the Anomaly flow

o Jose M Figueroa-O'Farrill - Course on Spin Geometry (Link)
Good place to learn about spinors

Research Papers:

o M.L. Michelsohn. "On the existence of special metrics in complex geometry." Acta Mathematica 149 (1982), 261-295.
Introduces balanced metrics

o S. Donaldson. "Anti Self‐Dual Yang‐Mills Connections Over Complex Algebraic Surfaces and Stable Vector Bundles." Proceedings of the London Mathematical Society 3.1 (1985), 1-26.
Obtains Hermitian-Einstein connections via heat flow

o A. Strominger. "Superstrings with torsion." Nuclear Physics B 274.2 (1986), 253-284.
Introduces Hull-Strominger system

o C. Hull. "Compactifications of the Heterotic Superstring." Phys. Lett. 178 B (1986) 357-364.
Introduces Hull-Strominger system