Mathematics Graduate Student Colloquium

MGSC Website: http://math.uci.edu/~mgsc/

On a Calabi-type Estimate for Pluriclosed Flow

Josh Jordan
Tuesday, March 3, 2020
1:00 pm - 1:50 pm
RH 340P

Talk Abstract:

The regularity theory for pluriclosed flow hinges on obtaining C^\alpha regularity for the metric assuming uniform equivalence to a background metric. This estimate was established by Streets in an adaptation of ideas from Evans-Krylov, the key input being a sharp differential inequality satisfied by the associated 'generalized metric' defined on T \oplus T^*. In this work, we give a sharpened form of this estimate with a simplified proof. To begin, we show that the generalized metric itself evolves by a natural curvature quantity, which leads quickly to an estimate on the associated Chern connections analogous to, and generalizing, Calabi-Yau's C^3 estimate for the complex Monge Ampere equation.

About the Speaker:

Josh is a 3rd year graduate student working on geometric analysis with a focus on non-Kahler geometry.

Refreshments:

Pizza will be served after the talk.