The CIRM is both a conference center and a hotel. It is located on the campus of Luminy where one can find the Math Department of the Aix-Marseille II University.

Organizing committee

Valérie Berthé (France),
Laura Fainsilber (Sweden,chair),
Tatiana Ivanova (Russia),
Elisabeth Rémy (France),
Irene Sciriha (Malta),
Aviva Szpirglas (France),
Tsou Sheung Tsun (United Kingdom).

Four sessions are planned. All talks are meant for a general public of mathematicians. The idea is that each session can serve as an introduction to the field, and present current research questions for non-experts (which of course can also be of interest for specialists).

1. A pure session devoted to Functional Analysis and Spectral Theory chaired by Karma Dajani, Netherlands Speakers:Svetlana Katok, USALivshitz Theorem for the unitary frame flow and its applications, 50 minutesThe unitary frame flow is defined on a factor of the group of isometries of the complex hyperbolic space by a lattice and is an isometric extension of the geodesic flow. We will present a generalization of the classical Livshitz Theorem to the unitary frame flows and explain how it applies to a construction of spanning sets for cusp forms via new relative Poincare series.Kathy Merrill, USAConstructing Wavelets from Generalized Conjugate Mirror Filters, 50 minutesOver the past ten years, wavelets have gained popularity as bases for transforms used in image and signal processing. This talk will begin with a brief introduction to how wavelets arise naturally in these contexts. We will then show how the tools of abstract harmonic analysis and spectral multiplicity theory can be used to build and classify wavelets. In particular, we present results from joint work with L. Baggett, P. Jorgensen, H. Medina and J. Packer that extends the techniques of Mallat and Meyer to construct wavelets using generalized multi-resolution analyses and generalized conjugate mirror filters.Paola Loreti, ItalyIngham type theorems and applications, 50 minutesWe talk about a well-known theorem due to Ingham and about some of its generalizations. The results are applied to exact controllolability problems. The method consists in considering an observability problem for a dual system governed by partial differential equations. Developing the solution of this homogeneous problem into Fourier series, we are led to establish some non-classical trigonometric inequalities. Ingham’s theorem is very useful when the eigenvalues of the spatial operator associated with the system satisfy a suitable gap condition. However, this crucial gap condition is not always satisfied, so more general theorems are needed in order to solve the corresponding observability and controllability problems. An overview of this topics is given in “Fourier Series in Control Theory”, a book project in collaboration with V. Komornik.Anne Siegel, FranceSpectral theory for dynamical systems arisen by substitutions, 50 minutes

   Symbolic dynamical systems were first introduced to better understand the dynamics of geometric maps; particularly to study dynamical systems for which past and future are disjoint as toral automorphisms or Pseudo-Anosov doffeomorphisms of surfaces. Self-similar systems are defined to be topologically conjugate to their own first return map on a given subset. A basic idea is that, as soon as self-similarity appears, a substitution is hidden behind the original dynamical system. In this talk, we illustrate this idea with concrete examples, and then, try to understand when symbolic codings provide a good representation. The good question finally becomes the following : which substitutive dynamical systems are isomorphic to a rotation on a compact group ? Partial answers have been given by many authors since the early 60’s. Hence, we will see how a spectral analysis problem finally reduces to a combinatorial problem, whose partial answers imply euclidean geometry and even some arithmetics.

   Karma Dajani, Netherlands

   Measures of maximal entropy for random expansions in non-integer bases, 50 minutes

   We consider expansions of real numbers in non-integer bases, and digits generated by means of a random map K. We study the dynamics of K, and show that it has a unique measure of maximal entropy with marginal measure a generalization of the well-known Erds measure. Furthermore, under the measure of maximal entropy the sequence of digits is a uniform Bernoulli process. For certain class of Pisot bases, we show that the measure of maximal entropy is a Markov measure.

   Martine Queffelec, France

   Fourier analysis and continued fractions, 50 minutes

   The set of normal numbers in any base is a big one for it is a set of full Lebesgue measure; on the opposite, numbers with bounded partial quotients are negligible. To precise the localization of these numbers, we prove that there exist infinitely many normal numbers with partial quotients 1 or 2, by using Fourier analysis technics.

    

2. An applied session devoted to Biomathematics chaired by Alessandra Carbone, France Speakers:Natasha Jonoska, USADNA nanotechnology, 45 minutesRecent experiments have shown that arbitrary non-regular graphs can be constructed by DNA self assembly such that junction molecules are used as vertices and duplex DNA molecules are used as edge connections. Such graph assembly has potential use in DNA nano-technology as well as in various models of DNA based computations. Many NP-complete problems such as 3-SAT can be solved by graph self assembly in one biostep (one-pot reaction). However, there are several mathematical problems that arise from these assemblies such as the minimal number of DNA strands needed for construction of the graph. We address this question by considering the DNA strands that make up the graph as boundaries of a compact orientable surface (2-dimensional manifold) such that the graph is topologically embedded in this manifold (as a 1-complex) as a deformation retract. In addition we discuss other mathematical (topological) problems related to DNA self-assembly or DNA based computations.Marie-France Sagot, FranceBioinformatic, 45 minutesPhylogenetic trees are a standard model for representing evolutionary processes, mostly involving biological entities such as species or genes. By a phylogenetic tree, we mean in this talk a rooted unordered tree whose leaves are uniquely labeled with elements of some set S, and whose internal nodes are unlabeled and have exactly two children. The elements of S stand for the contemporary taxa whose evolutionary relationships one intends to model. These taxa correspond to the leaves of the tree, whereas the ancestral taxa correspond to its internal nodes, so that for each ancestral taxon, all of its nearest derived taxa are depicted as its children in the tree. When there has been genetic transfer, that is, exchange of genetic material between the taxa, a taxon may have more than one ancestor. This poses a formidable problem for the reconstruction of a phylogeny from the genetic information present in such taxa: the phylogeny can not anymore be represented by a single tree. It is then important to be able to detect the presence and exact position of all genetic transfers that may have happened between the taxa of interest. This is a difficult problem which contains as sub-problem that of determining how distant two phylogenetic trees are from each other in terms of genetic transfer. In this talk, we shall just mention an initial pragmatic approach to the first problem and concentrate instead on the second sub-problem. Various metrics for measuring a distance between two trees have been defined, among which is SPR for Subtree Prune and Regraft. This was initially thought to be directly related to another way of comparing two trees T and U, which consists in computing their so-called Maximum Agreement Forest (MAF). Informally, the number of components of an agreement forest tells how many edges need to be cut from each of T and U so that the resulting forests agree, after performing some forced edge contractions. The relation between SPR and MAF is not so direct as was initially thought but there is a conjecture that the two are close. Being able to calculate the MAF is therefore an interesting issue for our purposes. This problem is known to be NP-hard. It was introduced by Hein et al. in 1997, who presented an approximation algorithm for it. We show that the performance ratio of Hein’s algorithm is 4 and present three approximation algorithms for this problem whose ratio is 3. All three algorithms are very simple. Obtaining a proof of the ratio for one of them is however tricky. We show that proving it was nevertheless worth the effort as indicated by simulations: the corresponding algorithm presents a ratio that in practice is much better than for the other two 3-approximation algorithms, and is between 1.5 and 2 for trees that present a moderate to high level of rearrangement. The less well performing among the three new approximation algorithms is interesting for indirectly providing a lower bound for the MAF between two trees that is good, specially for trees with a moderate level of rearrangement.Rebecca Wade, GermanyFrom protein structure to drug via the computer?The polypeptide chains of proteins fold to adopt complex three-dimensional structures. These structures can be exploited in “structure-based drug design”, a process that can be considered analogous to finding the right key (drug) for a lock (target protein). Computer-aided structure-based drug design has successfully led to the design of drugs that are now in clinical use, such as those against HIV and influenza. With the current emphasis on high-throughput experimental determination of protein structures, the number of potential protein targets for which structure-based drug design is possible is growing rapidly. Will this new structural information translate into new medicines? I will discuss some of the capabilities of and challenges for structure-based drug design approaches in the light of our current knowledge of protein structure and dynamics and in the context of the emerging systems biology perspective.Susan Holmes, USAUsing distances in Multidimensional Statistics, 45 minutes

   I will present examples of extracting useful information by using distances between non standard objects in computational biology. Visualisation of distances often provides much more information that the simple distributions.

   Examples include :

   – Comparing Phylogenetic trees from different DNA data.

   – Comparing Hierarchical clustering trees on melanoma patiens.

   – Comparing protein interaction networks.

   – Constructing confidence sets for non standard data.

   These all require use of interactive multidimensional visualisation techniques.

    

3. An interdisciplinary session devoted to Numerical Methods chaired by Rosa Maria Spitaleri, ItalySpeakers:Tatyana Kozubskaya, RussiaMathematical Models and Numerical Techniques in Euler Based Computational Aeroacoustics, 40 minutesThe talk represents a review on computational aeroacoustics (CAA) governed by the models derived on the base of complete Euler formulation in gas dynamics. Direct Numerical Simulation (DNS) by the Euler or Navier-Stokes equations, Linearised Euler Equations (LEE) and Non-Linear Disturbance Equations (NLDE) are the basic models of this class.An attention is paid to the specifics of aeroacoustics problems resulting in the necessity in developing specific mathematical models and numerical techniques. New formulations of NLDE model are presented, a few efficient numerical algorithms are considered. The results of their implementation are demonstrated on a set of CAA problems.Michelle Schatzman, FrancePreconditioning and partial differential equations: cross-fertilization of numerical analysis and PDE theory in unusual ways, 40 minutesPreconditioning is one of the most important issue of contemporary numerical analysis, since it is the key to the efficient implementation of numerical methods. If one wishes to solve a linear system Ax=b with so many unknowns (the dimension of the vector x that it is impractical to use direct methods, such as Gauss elimination, one must use iterative methods. But the rate of convergence of the method depends on the condition number of A which is the product of the norm of A by the norm of its inverse. The idea of preconditioning is to find an approximate inverse B and to replace the problem by BAx=Bb or by ABy=b. What is required from B? It should be computationnally friendly, and the condition number of BA or AB should be much smaller than the condition number of A. The perfect choice from the condition number point of view would be to take for B the inverse of A, which is computationnally quite unfriendly, since we are trying precisely to solve a system with matrix A. In fact, B can be understood as the numerical analogue of a parametrix in the theory of partial differential equations: a parametrix for a differential operator L=P(x,?) is a generally pseudo-differential operator M such that ML-1, and LM-1 are smoothing. The construction of a parametrix is an iterative process which resembles the iterative solution of linear systems of equations. Conversely, estimates on preconditioners need detailed information from the theory of partial differential equations. An example will be given, where the stationary phase method gives information on the zeroes of orthogonal polynomials, which in turn enables to prove that a preconditioner for a spectral method is spectrally equivalent to the matrix being preconditioned.Rosa Maria Spitaleri, ItalyGrid generation and partial differential equations: numerical methods and applications, 40 minutesZorica Uzelac, Serbia, 25 minutestatiana_vasmail [dot] ru (Tatiana Vasileyva) Russia

   Historical aspects of numerical methods for ODEs, 25 minutes

   We present a short historical review of numerical methods for ODEs. Euler, Adams, Bashforth, Runge papers started the development of ODEs numerical methods. The modern theory of linear multistep methods, questions of stability, convergents are connected with Dahlquist papers. We finish the review with the modern theory of Runge-Kutta methods (DIRK, SIRK), Bashfort papers and stiff problems for ODES systems.

4. A social-cultural session around the theme of Mentoring, coordinated by lauramath [dot] chalmers [dot] se ( Laura Fainsilber).We will discuss mentoring programs with different forms and ambitions, such as for instance EWM’s web-based mentoring scheme set up since the last meeting.If you have experience of mentoring you would like to mention, within a structured program or in a less formal way, please contact lauramath [dot] chalmers [dot] se ( Laura Fainsilber).

Preliminary program

FAST = Fonctional Analysis and Spectral Theory (40 minutes each)

Kathy MERRILL

Paola LORETI

Martine QUEFFELEC

Svetlana KATOK

Karma DAJANI

Anne SIEGEL

BIO = Biomathematics (45 minutes each)

Natasha JONOSKA

Marie-France SAGOT

Rebecca WADE

Susan HOLMES

NM = Numerical Methods

Tatyana KOZUBSKAYA (40 minutes)

Michelle SCHATZMAN (40 minutes)

Rosa Maria SPITALERI (40 minutes)

Tatyana VASSILIEYVA (25 minutes)

Zorica UZELAC (25 minutes)

D. Boukari (45 minutes)

Monday

09h00 09h30 Welcome

09h30 10h20 FAST 1

10h20 10h45 Pause

10h45 11h30 BIO 1

11h30 12h30 Getting to know each other

Lunch

14h30 15h15 BIO 2

15h15 16h00 Pause

16h00 18h00 Mentoring

18h00 19h30 Posters writing and videos (if you know of any interesting video produced whose topic may be of interest to women in mathematics, please bring a copy and we will try to show it)

20h30 22h00 Poster Session I: biomathematics / applied mathematics

Tuesday

09h30 10h20 FAST 2

10h20 10h50 Pause

10h50 11h 30 NM 1

11h45 12h25 BIO 3

Lunch

14h30 15h15 BIO 4

15h15 16h00 Pause

16h00 18h00 Pre-General Assembly: information and discussion

20h30 22h00 Poster Session II

Wednesday

09h30 10h20 FAST 3

10h20 10h50 Pause

10h50 11h35 NM2

Lunch

Afternoon: excursion (visiting the calanque area, i.e. the cliffs and the coast)

Thursday

09h30 10h10 NM6

10h10 11h30 Pause

10h30 12h30 General Assembly EWM

Lunch

14h00 14h45 NM4

15h30 16h10 FAST 4

16h10 16h30 Pause

16h30 17h00 NM4

17h00 19h00 Mentoring 2

20h30 22h00 Poster session 3

Friday

09h30 10h00 NM 5

10h10 10h50 FAST 5

10h50 11h30 Pause

11h30 12h30 Planinng the next meeting

Lunch

14h30 15h10 FAST 6

15h10 15h30 Pause

15h30 17h30 Mentoring 3

Evaluation of the meeting

The French Organization “Femmes et Mathématiques” organizes on Saturday 8th a special day “Mathématiques au féminin en Méditerranée” in Marseille, Centre Saint Charles, University of Provence. All the participants of the EWM conference are welcome.

Accommodation

Unfortunately, EWM does not have any funding available for participants. It is possible to arrive at Cirm on Saturday 1st and to be housed at Cirm in a special building. There will be no food service except on sunday evening. The price is 38,50 euros. Those interested should give their arrival time so that the guard can let them in and give them the keys. (There are no stores or restaurants on campus, so you should buy some food in Marseille before you take the bus to Luminy.)

A POSTER SESSION will be organized and chaired by itathsun1 [dot] jinr [dot] ru ( Tatiana Ivanova) (Dubna, Russia) with special sections for the themes related to the meeting’s main session, and of course general categories where people from other fields also can present their posters. All participants are encouraged to present their work in this way.

Participants will be housed and will have their meals at CIRM. The cost of accommodation with full board will be 60 euros per person per day for a single room and 52 euros for a shared room. If you want to participate to the conference, please send an e-mail to bertheiml [dot] univ-mrs [dot] fr ( Valérie Berthé) before October 1st, 2003.

Your name will then be communicated to CIRM which will contact you directly.

Badrié Kojok

University Saint-Joseph

P.O.Box 514

Mar Roukos, Beirut, Lebanon

The proceedings of the 11th conference of EWM

The proceedings of the 11th conference of EWM held at Luminy (2003) have appeared in the internationally known CWI Tract series. This enabled us, for the first time, to have EWM Scientific Proceedings, for the first time, automatically reviewed by Zentrablatt and Mathscinet.

Limited number of copies of the proceedings are available for purchase. The cost per copy is 15 euros. If you are interested please send an e-mail to dajanimath [dot] uu [dot] nl (Karma Dajani) with your name and address, and please send the payment to:

Name and Address of the payee: European Women in Mathematics Finland, Koulukatu 18 as 22, 20100 Turku, Finland
IBAN: FI 82 1652 3500 2180 71 (leave no blanks!)
SWIFT/BIC: NDEAFIHH
Message (this is important!): What you pay for.
Name and address of the bank: Nordea Bank Finland Plc, Aleksanterinkatu 36, FI-00020 Nordea, Finland

A copy of the proceeedings will be sent once the payment is confirmed.

Contents

• From the Editors
• Preface
• List of Participants
• Kathy Merril: “Constructing Wavelets from Generalized Filters“
• Anne Siegel: “Spectral theory for dynamical systems arising from substitutions“
• Karma Dajani: “Properties of expansions to non-integer bases: a survey“
• Paola Loreti: “On some gap theorems“
• Martine Queffelec: “Fourier Analysis and Continued Fractions“
• Svetlana Katok and Ilie Ugarcovici: “Arithmetic coding of geodesics on the modular surface via continued fractions“
• Michelle Schatzman: “Preconditioning and partial differential equations“
• Poster Session
• About EWM
• EWM Web-based Mentoring Scheme