August 24-30, 2001, Malta

The 10th international meeting organized by the European Women in Mathematics (EWM) took place in Malta, starting on Friday 24 August to Thursday 30 August. The conference was open to members and non-members of EWM. A brief report of the conference can be downloaded.

The University of Malta was started by the Jesuits in the 16th century and is the oldest University in the Commonwealth outside Britain. The Department of Mathematics has two main areas of research: algebraic graph theory and combinatorics, and mathematical physics.

Organizing committee

Christine Bessenrodt (Germany),
Laura Fainsilber (Sweden),
Tatiana Ivanova (Russia),
Emilia Mezzetti (Italy),
Marie-Francoise Roy (France),
Irene Sciriha (Malta),
Tsou Sheung Tsun (United Kingdom, chair)

TIMETABLE

PROGRAMME

1. 2001 EMS Lectures, by Michele Vergne (Paris).
2. Pure session on “Cohomology theories” organized by Barbara Fantechi, with speakers Chiara de Fabritiis (Ancona) and Yukari Ito (Japan).
3. Applied session on “Mathematics applied to finance”, organized by Francine Diener (Nice), with Monique Pontier (Toulouse) and Nadine Bellamy (Evry).
4. Interdisciplinary session on “The Uses of Geometry”, organized by Tsou Sheung Tsun, with speakers Xenia de la Ossa (Oxford), Caroline Series (Warwick) and Asia Weiss (Canada).
5. Socio-political Session on “Mathematics outside the classroom: cultural differences”, organized by Marie-Francoise Roy, Laura Fainsilber, and Rosa Maria Spitaleri, with speakers Mireille Chaleyat Maurel (Paris) and Franka Miriam Bruckler (Croatia). We also had Claudine Hermann (Paris), a representative from the ETAN project, to give a talk and initiate a discussion on the socio-political dimension of gender inequalilty, with also a short talk by Rosa Maria Spitaleri.
6. Poster session, organized by Tatiana Ivanova: all participants were encouraged to present their work this way. There were about 35 posters in all.
7. In addition to the scheduled sessions, there were spontaneously generated round-tables (in particular, one on the ethics of using mathematics in finance), and various discussion groups. In particular, there was a discussion session on the `Questionnaire project’ initiated by Emilia Mezzetti (Trieste) on behalf of the EMS `Women and Math’ Committee.

MAIN TALKS AND ABSTRACTS

• Nadine Bellamy: Portfolio optimization in finance: an introduction
  Let us consider an economic agent, who invests in the assets of a financial market. The agent is faced with optimal consumption and investment decisions, and wants to maximize his portfolio. The optimization problem is usually dealt with one of the following criterions :

• The mean-variance analysis
• The concept of utility functions

We recall the main tools, such as the method of Lagrange multipliers and the dynamic optimization (Bellman’s equation). Then we give explicit expressions for the optimal strategy in some usual cases.

• Franka Miriam Buckler: Popularization of mathematics: local and not so local perspective
  The problems with popularization of mathematics are mostly the same in Croatia as in many other countries, though the reasons may be somewhat different. These problems include the lack of interest for studying mathematics, the often unattractive and too technical presentation of mathematics in schools and the public opinion of mathematics as a too complicated and/or dull dicipline.In the last few years much is done to improve the image of mathematics and break the usual picture most people have of it: the Mathematical Departments in Zagreb and Osijek present themselves at the University Fairs in a very cheerful and attractive way, lectures for high school students are held in Zagreb by mathematicians on topics which show the uses, the importance and the beauty of mathematics, the Mathematical Colloquium in Osijek is advertized by (mostly humorous) posters etc.
• Mireille Chaleyat-Maurel: Raising Public Awareness in Mathematics: the WMY2000 experience
• Chiara de Fabritiis: Analytical and geometrical features of de Rham and Dolbeault cohomology
• Xenia De La Ossa: Geometry in string theory
• Francine Diener: Derivatives: a scientific revolution of the seventies
  In the seventies, three economists-mathematicians, Black, Scholes and Merton, discover how one can hedge and price new financial assets, called derivatives (in fact a large part of the story was present in the thesis of Bachelier (1900) but nobody took care of it). Since this time, many financial institutions need mathematicians to create and price new derivatives. My aim is to explain what are derivatives, why they are used, the main ideas behind there pricing and hedging and which mathematical tools they involve.
• Claudine Hermann: Women in Science in Europe and in France
• Yukari Ito: The McKay correspondence — a bridge from Algebra to Geometry
  In this talk, I would like to explain a relation between a finite group and the quotient singularity, the so-called McKay correspondence. This phenomenon was observed by J. McKay in 1979 and proved in several ways.Geometrically, it is a correspondence between the group theory (representation or conjugacy class) and the topology of a resolution of the singularity. Recently we have many generalization of this correspondece, not only in Mathematics but also in Physics.

I will talk on a brief history of the McKay correspondence and introduce a way to calculate the cohomological invariants using group theoretical objects. In this process, we will meet various topics, i.e., algebraic geometry, representation theory, combinatorics, and so on. However, I will try to talk on the correspondence without assuming any special knowledge of them.

• Monique Pontier: Why heavy tails in financial series ? estimation and tests
  Students’s works about modelling and fitting are exposed. A first try to fit the Black-Scholes model is done with estimations of trend and volatility, test of normality, estimations of Hölder exponent in case of a driving fractionnal Brownian motion. Otherwise, the stationnarity of the return logarithm is studied and non-parametrix estimation of the autocovariance function is tried. Finally, in the Diffusion-Jumps mixed model, an algorithm is done to detect jumps in a financial series and tests are done for the mixing of two (or more) Gaussian laws hypothesis.Data are these of “Bourse de Paris” (Lyonnaise des eaux, AGF, Peugeot) of the year 1997 and French stocks index (1802-1993).

• Caroline Series: Why is there Hyperbolic Geometry in Dynamical Systems?
• Michele Vergne: Convex Polytopes
  We all tried in our youth to work out formulae for sums of the m-th powers of the first N numbers, and to compare them to the corresponding integral This leads to Bernoulli numbers B_n and to the first appearance of the power series

We will then ask ourselves if there are integral formulae computing the number of points with integral coordinates in a convex polytope in Rⁿ given by rational inequalities.

We will see that the solution by Bernoulli, Euler-Mac Laurin,…, Khovanski-Pukhlikhov, … , Brion-Vergne, of this problem is similar to the amazing Riemann-Roch theorem: an integral of characteristic classes resulting in a positive integral number.

We will also indicate a number of very simple open problems on number of magic squares, and a few new results due to Chan-Robbins and Zeilberger, and Baldoni-Vergne, of the number of points on some “concrete polytopes” related to magic squares.

• Asia Weiss: Tessellations and Related Modular Groups
  We shall explain how certain kinds of subgroups of Coxeter groups can be used to derive regular and semi-regular tessellations. In particular, we shall briefly describe the construction of chiral polytopes.Matrices whose entries belong to certain rings of algebraic integers can be associated with discrete groups of transformations of hyperbolic n-space. For small n, these may be Coxeter groups, generated by reflections, or certain subgroups whose generators include direct isometries of the hyperbolic n-space. We shall show how linear fractional transformations over rings of rational and quadratic integers are related to the symmetry groups of regular tessellations of hyperbolic plane or 3-space.

CONTRIBUTED SHORT TALKS

• Barbara Fantechi: Cohomology of sheaves
• Bettina Rehberg: Toeplitz and Hankel Operators on Generalized Bergman-Hardy Spaces
• Konstanze Rietsch: Total positivity, flag varieties and quantum cohomology
• Sabine Schiller: Math-Kit: a multimedia project for teaching
• Rosa Maria Spitaleri: Focus on Women and Science in Italy

PARTICIPANTS AND PHOTOS

There were 65 participants from outside of Malta, and 11 participants from Malta, giving a total of 76 participants coming from 21 countries and 4 continents.

EWM GENERAL MEETING

The EWM General Meeting took place in the afternoon of 26th August. The new Standing Committee was elected, with Ljudmila Bordag as Convenor. Some members of the Organizing Committee were also elected, the remaining vacancies to be filled later once the place for the next meeting in 2003 is decided. Topics for that meeting and also for workshops in the even years were discussed. Regional coordinators were elected. The usual business was successfully conducted.

ACCOMMODATION

Most participants were housed in the Plaza Hotel in Sliema, Malta, where the meeting took place. It is a pleasant hotel with swimming pool by the beach. All rooms have bathroom ensuite.
Prices (Exchange rate at present: 2.6 euro = Lm 1)
Single: Lm 18:50 (limited number)
Twin: Lm 13:50 (3rd and/or 4th adult sharing: 25% less)
Superior Twin: Lm 16:50
One meal: Lm 4:00

Some participants stayed at:
1. Victoria Hotel Lm 35 B&B Tel 00356 334711
2. Diplomat Lm 28 B&B Tel 00356 345361
These are in Sliema near where the conference is taking place.

Some others stayed at the Hibernia Hostel, 5 minutes from the Plaza.

REGISTRATION

There was an EWM registration fee of 30 euros to be paid directly to EWM on arrival. This fee was waived in cases of hardship.

SUPPORT

• The EMS made a small grant to us to enable mathematicians from Eastern Europe to attend the EMS lectures.
• Owing to the skill and diligence of our committee member Emilia Mezzetti and EWM treasurer Cathy Hobbs, our application to the EU was successful. A substantial grant was made to enable us to offer financial support to a good number of participants from countries supported by the EU, and to help in the running costs of the meeting.
• We are waiting for results of our UNESCO application.
• We received material and personnel assistance from the University of Malta. Ms Annabelle Attard from their mathematics department supplied much needed secretarial help.
• World Scientific Publishing Company (Singapore) and Discovery Bookstore (Malta) donated material and offered discount on their books.

TRANSPORT

We invited Air Malta to be our official carrier, who have generously offered a 15% discount to all participants, subject to certain conditions. Quite a number of participants benefited from this offer.

From Luqa airport there are buses to Valletta and then to Sliema. Those accommodated in the Hibernia Hostel generally got free transport from the airport. The Plaza hotel arranged for taxis to pick up those accommodated there.

PROCEEDINGS

Proceedings of the conference are available here.

CONTACT ADDRESS

Prof. Dr. Tsou Sheung Tsun
Mathematical Institute
24-29 St. Giles’
Oxford OX1 3LB
United Kingdom
Fax +44 1865 273583