Geometry of low dimensional manifolds

Abstract: I will start the talk by reviewing some classical theories on Riemann surfaces and their recent variations in geometric analysis. Then we discuss Perelman's work on geometrization of 3-manifolds. Finally, I will survey some recent progress on 4-manifolds. I hope that this talk will show some clues how geometric equations can be applied to studying geometry of underlying spaces.

Refreshments will be served at 3:45 p.m. (MATX 1115, Math Lounge).