Title:  Course Operator Theory 
Lecturers:  M.A. Kaashoek, (); S.M. Verduyn Lunel, () 
Time and place:  3 hours per week, from the beginning of September until the beginning of December; Vrije Universiteit Amsterdam 
Contents:  This course treats various topics from the theory of nonselfadjoint operators with the aim to develop a qualitative theory for concrete classes of integral and (functional) differential equations. A strong interaction with complex function theory is typical; operators are studied using analytic functions (determinant functions, characteristic matrix functions, symbols) which appear in a natural way. Often operators will be considered as maps generated by dynamical systems. Much attention will be given to the analysis of particular families of solutions (existence, asymptotic behaviour etc.). The list of topics for this year includes the following subjects. The resolvent operator and the RieszDunford calculus, in particular for unbounded operators, spectral theory of strongly continuous semigroups and the corresponding generators, in connection with this the development of a perturbation theory (variation of constants formula), completeness of systems of eigenfunctions and generalised eigenfunctions, aiming at a qualitative theory of dynamical systems, applications to functional differential equations. 
Literature:  O. Diekmann, S.A. van Gils, S.M. Verduyn Lunel and H.O. Walther, Delay Equations: Functional, Complex, and Nonlinear Analysis, SpringerVerlag, New York, 1995, and I. Gohberg, S. Goldberg, M.A. Kaashoek, Classes of Linear Operators I, Birkha"user Verlag, 1990 (to acquire in consultation with the lecturers). 
Prerequisites:  introduction to functional analysis and complex function theory 
Examination:  via exercises and/or presentations 
Remark :  the first six weeks of this course also serve as a preparation for the workshops on "Dynamics of Differential Equations with Delays" and "Operators and Dynamical Systems" which will be held at Leiden University from 1315 and 2326 October, respectively. 
Title:  Seminar Analysis and Linear Operators 
Organiser:  M.A. Kaashoek, () 
Time and place:  Each Thursday morning from 9.15  11.30 a.m., Vrije Universiteit Amsterdam, room R2.40 of the building De Boelelaan 1081 
Contents:  Various research topics from Analysis, Operator Theory, and related fields. See the announcements in ETNA. 
Title:  Course computer algebra algorithms for special functions 
Lecturer:  T.H. Koornwinder (), (http://turing.wins.uva.nl/~thk/). 
Time and place:  Trimester I, 1997, University of Amsterdam 
Aim:  Zeilberger and Gosper algorithms and applications 
Contents:  There exists a large number of sums of products of binomial coefficients equal to some elementary expression. Such combinatorial identities can be rewritten in terms of socalled hypergeometric functions. The classical analytic proofs of such identities have recently been supplemented with algorithmic proofs that can be implemented in computer algebra systems such as Maple or Mathematica. These algorithmes have been developed by Gosper and Zeilberger and they are the starting point for much new research. In this course various aspects are discussed: from the underlying mathematical theory to the computer implementation. The related special functions are being discussed whenever they come along. Depending on their interests and previously followed courses, students may put the emphasis either on the various computer algebra aspects or on the theoretical background and special functions. 
Structure:  lectures 
Literature:  M. Petkovsek, H.S. Wilf and D. Zeilberger, ``A=B'', published by A.K. Peters, Wellesley, Massachusetts, 1996. 
Prerequisite:  Calculus, Linear Algebra, some familiarity with Maple or Mathematica Suited for 4th year math students, graduate students, also for other students interested in computer algebra. 
Examination:  handin exercises (both theoretical and computer) and/or take home exam and/or oral exam 
Title:  Course advanced Theory of Functions 
Lecturer:  Dr. J.J.O.O. Wiegerinck ( ) 
Time and place:  trimester 1, 4 hours each week (probably Tuesday 911 and Wednesday 1315; will be announced later). location:UvA 
Contents:  The aim of this course is the derivation of a theory of functions on open Riemann surfaces. Specific attention will be paid to the Riemann mapping theorem, multiply connected domains, uniformising Riemann surfaces, harmonic and subharmonic functions, Hardy spaces on the disk and on open Riemann surfaces. 
Literature:  lecture notes (by J. Korevaar) for the first part, furthermore Ahlfors L. en Sario: Riemann Surfaces Princeton, 1960. Fisher, S. D.: Function theory on planar domains, Wiley, 1983. [additional material will be indicated later] 
Title:  Course finite groups of Lie type 
Lecturers:  H.T. Koelink (), (http://turing.wins.uva.nl/~koelink/) and E.M. Opdam () 
Time and place:  Tuesday 11.1513.00 & 14.1516.00 Spring semester 1998 First meeting January 20, 1998. Mathematical Institute, Leiden University 
Aim:  Understand character theory of finite groups of Lie type 
Contents:  Apart from a few exceptions (cyclic and alternating groups and a finite list of sporadic groups) the finite groups arise from simple Lie groups defined over a finite field. These finite groups of Lie type have a rich structure, and this enables us to understand the characters of these groups. In this course we discuss the relation between the character theory and geometric structures (orbits). We also study HarishChandra induction, which gives all characters, except to socalled cuspidal characters, if we assume that the characters of certain subgroups are known. If possible the DelignLusztig induction functor will be discussed. Other keywords for this course are Weyl groups, BNpairs and Hecke algebras 
Structure:  lectures 
Literature:  R.W. Carter, ``Finite Groups of Lie Type'', Wiley, 1985 
Prerequisite:  Some acquaitance with Lie groups and Lie algebras. Suited for 4th year math students and graduate students. 
Examination:  take home exam and/or oral exam 
Title:  International Workshop 1997 Twente Conference on Lie Theory 
Organisors:  UT, KUN, UU, RUG, RUL, UvA. 
Coordination:  G.F. Helminck (UT) () 
Time and place:  December 1518, 1997, Twente University. 
More information:  http://www.math.utwente.nl/~lie/ 
Title:  International Summer School European School of Group Theory 
Contact:  G. van Dijk, () 
Time and place:  June 21  July 4, 1998, Lorentz Center, Leiden. 
Contents:  The summer school is organised on yearly basis by European mathematians working in Group Theory. In 1997 the summerschool was held in Luminy, France, and in 1996 it was held in Schloss Hirschberg, Germany. 
Title:  Seminar Analysis on Lie Groups 
Organisors:  E.P. van den Ban, G.J. Heckman, E.M. Opdam, (), T.H. Koornwinder (), 
Time and place:  Twoweekly seminar on Friday at Utrecht University starting January or Februaryr 1998 
Contents:  The subject will be vertex algebras and some related papers by Borcherds. 
Literature:  V.G. Kac, ``Vertex Algebras for Beginners'', 141 pp, AMS, 1997. R.E. Borcherds, ``Automorphic Forms and Lie Algebras'', Current Developments in Mathematics, 1996, pp. 127. 
More information:  http://turing.wins.uva.nl/~thk 
Title:  Course Functional Analytic Methods for Partial Differential Equations. 
Lecturers:  Ph. Clement, () ; B. de Pagter, () . 
Time and place:  4 hours weekly, 2x7 weeks. (the precise schedule and location will be announced later) Technische Universiteit Delft. 
Aim:  To introduce the students in certain functional analytic methods in the study of partial differential equations. 
Contents:  This course will consist of two parts: (1) Bifurcation theory; (2) Sobolev spaces and regularity theory. The following topics will be covered: (1) Differential calculus in Banach spaces;  Implicit function theorem  Bifurcation theorem of Crandall Rabinowitz;  Brouwer and LeraySchauder degree;  Global bifurcation theorem of Rabinowitz; (2) Definition and elementary properties of Sobolev spaces;  Embedding theorems;  The trace operator;  regularity theory for elliptic problems. 
Prerequisites:  It is assumed that the students are familiar with the basic principles of functional analysis and operator theory. 
Examination:  oral examination. 
Title:  Course Modern Computational Fluid Dynamics 
Lecturer:  B. Koren () 
Time and place:  Second half 1997, on Thursday, 13.4515.30 h. (starting from October 2, 1997) Mathematical Institute, Niels Bohrweg 1, Leiden 
Aim:  Getting insight into theoretical and practical aspects of modern computational fluid dynamics 
Contents: 

Course material:  Reprints of papers and reports (to be distributed during the course) 
Literature:  1. Ch. Hirsch: Numerical Computation of Internal and External Flows, Volumes 1 and 2, Wiley, Chichester (1988 and 1990). 2. R.J. LeVeque: Numerical Methods for Conservation Laws, Birkhauser, Basel (1990). 3. P. Wesseling: An Introduction to Multigrid Methods, Wiley, Chichester (1992). 
Prerequisites:  Basic theory of partial differential equations 
Examination:  oral or takehome exam 
Title:  Defect Correction and Multigrid Methods 
Lecturer:  Prof.dr P.W.Hemker (P.W.Hemker@cwi.nl) 
Time and place:  (probably) Trimester I, 1997  1998 (septnov,1997) Thursday 15h15  17h00 Gebouw Euclides, Plantage Muidergracht 24 1018 TV Amsterdam 
Aim:  To acquire a working knowledge of the use of multigrid techniques for the solution of elliptic partial differential equations. 
Contents: 
Starting from the defect correction principle, in this course its use for the construction of accurate discretisation methods for PDEs and the construction of fast iterative processes will be treated. The course consists of the following chapters:

Literature:  Special lecture notes for the course will be available. P. Wesseling: Introduction to Multigrid Methods, Wiley, 1992. W. Hackbusch: Multigrid Methods and Applicatios, Springer, 1985. 
Prerequisites:  Elementatry knowledge of functional analysis. Principles of numerical mathematics. Some experience in computer programming in a procedural language 
Examination:  To conclude the course, the student is asked to write a paper on an exercise problem. 
Title:  Course Numerical analysis and dynamical systems 
Lecturer:  K.J. in 't Hout, () 
Time and place:  Thursday 11.15  13.00, Fall semester, Leiden University, starting October 2, 1997 
Contents: 
A fundamental question in the numerical solution of initial value problems for ordinary differential equations is whether the longtime dynamics of ordinary differential equations are preserved under numerical discretization. For example one can think of the convergence of solutions to an equilibrium point or a periodic orbit, or of a particular (physical) quantity that remains constant through time. In this course, the above question is addressed. In particular the following topics are covered:

Literature:  A.M. Stuart & A.R. Humphries: Dynamical systems and numerical analysis. Cambridge University Press, 1996. 
Prerequisites:  Some knowledge about differential equations and their numerical solution is assumed 
Title:  Conference of the Dutch Community of Numerical Mathematicians 
Time and place:  September 24, 25 and 26 of 1997, the Woudschoten Conference Centre, Zeist, the Netherlands. 
Invited speakers are:
Contributed, 25minute presentations:
The programme allows incorporation of about four contributed presentations by participants, relevant to either of the conference topics.
Conference fees, due upon registration, are
Registration and optional submission of a contributed presentation can be done by mailing the registration form ultimately on 22 August 1997 (the form is in Dutch, it is obvious that the information needed includes name, address, optional title of contributed presentation, fee category, dietary requirements and signature; when using the URL given below, after completion of the form, please press [click hier] and print the appearing page, the print can then be signed and sent in.
Title and abstract of a contributed presentation in a LaTeX file must be emailed to the secretary no later than 18 August.
For further information please apply to the secretary of the organizing committee:
Jan Kok
CWI  Centrum voor Wiskunde en Informatica
Organizing committee Woudschoten Conference
P.O. Box 94079
NL1090 GB Amsterdam
Telephone: +31 20 592 4107
This information and a (clickable) registration form can be reached using:
http://WWW.cwi.nl/~jankok/woudschoten.html