7th European
Intensive Course on Complex Analysis
“Complex
Analysis and its Generalizations (with applications to partial differential
equations)”
Departamento
de Matemática, Universidade de Coimbra,
Portugal
With support from CMUC (Centro de Matemática da Universidade de Coimbra), UI&D "Matemática e Aplicaçőes" da Universidade de Aveiro, and the Socrates programme
Registration Form 
This intensive course will have a total of 40 hours of lectures and is at postgraduate level. Lecturers will have time available to discuss with the students. Successfully participating students will get a certificate. This course is organized by the Universities of Coimbra and Aveiro with the same goals as the ones organized under the programme Socrates, and is open to all young mathematicians interested in Complex Analysis and its applications.
There will be an Workshop on "Applications and Generalizations of Complex Analysis" on the 23th and 24th of March.
19 March 
20 March 
21 March 
22 March 
23 March 

Opening session 
9h9h30m 
* 
* 
* 
* 
9h30m12h30m 
9h12h30m 
9h12h30m 
* 
* 

15h 17h 
15h 17h 
* 
10h 12h  15h  17h 
10h 12h 
26 March 
27 March 
28 March 
29 March 
30 March 

10h12h 
10h12h 
10h12h 
10h12h 

15h 17h 
15h 17h 
* 
15h 17h 
15h 17h 
OPERATOR THEORY AND MOMENT PROBLEMS
 Francisco Marcellán (Univ. Carlos III, Madrid,
Spain)
Abstract: The aim of this course is to introduce the stateofthe art of moment problems from the perspective of the theory of finite
difference operators in the scalar and in the matrix case, respectively. One the advantages of this approach is that the
Nevanlinna functions appear as elements of a transfer matrix and the Padé approximants are the resolvents of a finite
matrix approximation to a infinite Jacobi matrix.
Contents:
Basic references that will be distributed to the participants in the course.
[1]. A. I. Aptekarev, E. M. Nikishin, The scattering problem for a discrete SturmLiouville operator, Mat. USSR Sbornik 49
(1984) 325355.
[2]. B. Beckermann, Complex Jacobi matrices. Journal of Computational and Applied Mathematics. 2001. To appear.
[3]. B. Simon, The classical Moment Problem as a Self Adjoint Finite Difference Operator, Advances in Mathematics 137
(1998) 82203
INTRODUCTION TO COMPLEX DIFFERENTIAL EQUATIONS
 Ilpo Laine (Univ. Joensuu, Finland)
Abstract: These lectures offer a short introduction to differential equations
in the complex domain through the following subtitles: Local existence theorems,
linear differential equations (theorem of Wittich, basic value distribution of
solutions), oscillation properties of solutions of f" + A(z)f = 0, first
order algebraic differential equations (theorems of Gol'dberg and Malmquist),
Riccati differential equation, Painlevé differential equations
(meromorphic nature of solutions and their value distribution), differential
equations in the unit disk.
CONFORMAL INVARIANCE IN CLIFFORD ANALYSIS
 Vladimir Soucek (Charles University, Czech Republic)
Abstract: The series of lecture will contain a discussion of simplest conformally invariant first order differential equations and basic properties of their solutions. The principle example will be the Dirac operator on domains in Euclidean space. The main points of the series of lectures can be summarized as follows:
AN INTRODUCTION TO SEVERAL COMPLEX VARIABLES
 Chris Boyd (Univ. College, Dublin, Ireland)
Abstract: We begin by showing how certain classical results from one complex variable
(e.g. The Open Mapping Theorem, The Identity Principle and Montel's Theorem) generalise to several complex variables. The
Riemann Mapping Theorem is one of the fundamental results of single variable complex analysis. We will show that
for n >= 2 this result is no longer true. To obtain this result we examine groups of biholomorphic mappings on domains in
C^{n}. In the process of our investigations we obtain results such as Cartan's Uniqueness Theorem and
Poincar\'e's Theorem for the Polydisc.
This intensive course follows the six held in Coimbra and Aveiro from 1995 to 1999 and there are plans for intensive courses in the following years. The lecture notes of some of the courses have been published in Coimbra and others are in print.
Living expenses can be partially covered for some students if they do not have support from their own institution and if there is enough money available.
Helmuth Malonek (Departamento de Matemática da Universidade de Aveiro)
J. Carvalho e Silva (Departamento de Matemática Universidade de Coimbra)
Amilcar Branquinho (Departamento de Matemática Universidade de Coimbra)