The Monge-Ampere equation is fundamental in geometry and analysis, and the regularity of solutions has been studied by many leading mathematicians.

In the last three decades applications in optimal transportation has drawn increasing attentions and the regularity is again a key issue in the theory.

In this talk we discuss the global regularity of solutions to the Monge-Ampere equation subject to a natural boundary condition arising in optimal transportation.

In particular we will discuss the regularity of free boundaries arising in optimal transport problems.

Bio：汪徐家，1979年进入浙江大学数学系学习，在浙江大学获得本科硕士博士学位，并留校工作。1995年至今在澳大利亚国立大学数学中心工作。2009年当选澳大利亚科学院院士。主要研究领域为偏微分方程，特别是Monge-Ampere方程，及其在几何与物理中的应用。