Back to Departmental Colloquium: Fall 2006
Departmental Colloquium
Date: Thursday, Oct 19, 2006
Time: 4:00PM - 5:00PM
Location: JWB 335
Special Colloquium
James McKernan
University of California, Santa Barbara
Title |
Geometry of Algebraic Curves and Birational Geometry |
Abstract |
Everyone knows how to integrate However it is impossible to integrate using only elementary functions. In this talk we will show that the reason for this is due to the geometry of the underlying algebraic curve, most especially the meromorphic forms on the curve. We will then show how the behaviour of the holomorphic forms on any algebraic curve controls the geometry, differential geometry, topology, and arithmetic of the curve. Finally we will explain how recent progress in higher dimensional geometry shows that the relatively simple picture for curves carries over to birtional geometry in higher dimensions. |
Number Theory
Algebraic Geometry
Topology