Series of Lectures for ICTP Math Diploma Programme - 19-23 June, by Luca Di Cerbo

[ICTP Math Section]

Series of Lectures for Math Diploma Programme

by Luca DI CERBO (University of Florida)


Teaching schedule:

- (Monday 19 - Friday 23), at 10:00:  1 lecture per day of 2 hours every 
morning
- Examples/exercises session every  afternoon (1 hour), at 14:30

Title: An Introduction to Harmonic Functions on Riemannian Manifolds

Abstract:   This class is an introduction to geometric analysis at the 
graduate level. Geometric analysis plays a central role in modern 
mathematics, and it experienced a tremendous growth in the last forty 
years. It also figures prominently in many other areas of mathematics, 
such as mathematical general relativity, mathematical string theory, and 
geometric topology. It is also essential in many applications; e.g., 
image analysis and geometric data analysis. More specifically, we will 
first introduce the foundational aspects of geometric analysis on 
manifolds. In particular, we will define the Laplace operator on a 
Riemannian manifold by using the Riemannian metric and the associated 
Levi-Civita connection. After reviewing some of the most important 
features of harmonic functions on the flat Euclidean space, we then 
develop some basic aspects of the theory of harmonic functions on 
Riemannian manifolds. This will include the proof of the non-existence 
of non-constant L2-harmonic functions on complete Riemannian manifolds 
(a celebrated result of S.-T. Yau, 1976).

-- 
Koutou Mabilo
ICTP Mathematics Group
Leonardo Da Vinci Building
Strada Costiera no. 11
34151 Trieste, Italy
Tel. no.: +39-040-2240455

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