Professor Sheng-Li Tan
Abstract
In
recent years, some long-studied problems on complex algebraic surfaces have
been solved by using Bogomolov’s inequality for semistable rank two vector bundles. In these two lectures,
we are going to present systematically this powerful method. Precisely, we will
give a simple proof of the inequality, an explicit construction of rank two
vector bundles from the cohomology classes and a
proof of the most general optimal bound. We will also talk about the possible
generalization of the vector bundle method to higher dimensional manifolds from
the point of view of the representation theory of the general linear groups.
|
Lecture 1: |
November 2, 2004 (Tuesday) |
|
|
Lecture 2: |
November 4, 2004 (Thursday) |
|
All
are welcome
|