Ricci Flow and Complex Geometry

Valentino Tosatti | Courant Institute School of Mathematics, Computing, and Data Science - New York University: Ricci Flow and Complex Geometry.

Abstract: Ricci flow is a geometric analogue of the heat conduction equation: it evolves the geometry of a curved space with the aim of making its curvature more uniform. Introduced by Richard Hamilton in 1982, it was the key tool in Perelman’s proof of the Poincaré conjecture, a century-old problem about the shape of three-dimensional spaces. But this evolution need not simply smooth things out: singularities can develop. What determines how a space evolves, and what can this evolution reveal about its geometry? This talk explores these questions for geometric spaces defined using complex numbers, describing what is known and what remains conjectural.

Event in presence and also available on Zoom