Geometric flows from unified string theories

Abstract

A survey of new geometric flows motivated by string theories is provided. Their settings can range from complex geometry to almost-complex geometry to symplectic geometry. From the PDE viewpoint, many of them can be viewed as intermediate flows between the Ricci flow and the Kähler-Ricci flow, albeit often coupled to flows of additional fields. In particular, a survey is given of joint works of the author with Tristan Collins, Teng Fei, Bin Guo, Sebastien Picard, and Xiangwen Zhang.

Contribution to Surveys in Differential Geometry, "Forty Years of Ricci flow", edited by H.D. Cao, R. Hamilton, and S.T. Yau