Pro ceedings of the seventh EWM meeting EUROPEAN WOMEN IN MATHEMATICS Universidad Complutense de Madrid September Contents Preface Europ ean Women in Mathematics EWM on the Web I History Since Luminy EWM since its fth meeting in Luminy Brief rep ort on the sixth meeting of EWM in Warsaw II MADRID Organization of EWM Decisions taken during the general assembly THE MATHEMATICAL PART The Mathematical part of EWM Meetings III Holomorphic Dynamics A short course organized by Caroline Series Holomorphic dynamical systems in the complex plane An introduction Bo dil Branner The theory of p olynomiallike mappings The imp ortance of quadratic p olynomials N uriaFagella Lo cal prop erties of the Mandelbrot set M Similarities b etween M and Julia sets Tan Lei IV Classication in Algebraic Geometry A Short Course organized by Rosa M MiroRoigand Raquel Mallavibarrena On some notions in algebraic geometry Margarida Mendes Lop es On classication of algebraic space curves liaison and mo dules Mireille MartinDeschamps On classication of pro jective varieties of small co dimension Emilia Mezzetti V Mathematical Physics Session organised by Sylvie Paycha Mirror Symmetry Claire Voisin written by Sylvie Paycha and Alice Rogers Mo delling the randomness in physics Flora Koukiou Sup er mo duli space Alice Rogers Universal measuring coalgebras The p oints of the matter Marjorie Batchelor VI Mo duli Spaces An Interdisciplinary Workshop organized by Sylvie Paycha Mo duli spaces and conformal dynamics Caroline Series Mo duli spaces and path integrals in Quantum Field Theory Sylvie Paycha Notes on mo duli spaces in Algebraic Geometry Rosa M MiroRoig An example of mo duli spaces in number theory Laura Fainsilber VI I Short Talks The multidimensional RiemannHilb ert problem generalized Knizhnik Zamolo dchikov equations and applications Valentina A Golub eva Quadratic and hermitian forms over rings Laura Fainsilber On Sampling plans for insp ection by variables Vera I Pagurova VI I I Evaluation Evaluation of the mathematical asp ects of the meeting OTHER TOPICS In b etween meetings the everyday life of EWM Renormalisation in Mathematics and Physics FemailEmail discussion Mathematical studies at Europ ean universities IX Family versus Career Family versus Career in Women Mathematicians COMMITTEES COORDINATORS AND PARTICIPANTS Committee Members Co ordinators List of Participants in EWM Preface to the printed edition This volume contains records of the mathematical activities and some of the other activities which to ok place during the seventh general meeting of Europ ean Women in Mathematics at Universidad Complutense de Madrid September The meeting was attended by participants from countries Denmark EnglandFinland France Germany Italy Norway Portugal Rumania Russia Spain Sweden and Switzer land The main organizers were by far Capi Corrales Ro driganez and Raquel Mallavibarrena from Madrid They were assisted by an organizing committee consisting of Bo dil Branner Denmark Isab el Lab ouriau Portugal Rosa Maria MiroRoigSpain Marjatta Naatanen Finland Sylvie Paycha France Caroline Series England Laura TedeschiniLalli Italy In organizing the meeting we build on earlier exp eriences In particular the work done by Eva Bayer MicheleAudin and Catherine Goldstein all from France around the fth EWM meeting in Luminy in December has b een a constant source of inspiration We are very grateful for the nancial supp ort we received from the spanish Instituto de la Mujer and the Ministerio de Educacion y Ciencia b oth for the Madrid meeting and for the publication of these Pro ceedings The logo of the EWM meeting and the tshirt pattern shown on the front page was designed by DODOT These Pro ceedings were edited by Bo dil Branner and N uriaFagella We thank Christian Mannes for setting up the TeX style we have used The photos were taken by Marketa Novak We wish to express our thanks to all participants for making the Madrid meeting a success and to all who contributed in writing to this volume Esp ecially we thank Capi and Raquel for making it all p ossible February Bo dil Branner and N uriaFagella Addendum to the electronic edition The original version of these pro ceedings was printed at the Universitat de Barcelona with Dep Legal L Impreso Poblagrac SL Av Estacion sn Pobla de Segur The main dierence b etween the electronic edition and the printed one is that some mis prints have b een corrected and that the logo designed by DODOT the photos and the gures contained in the mathematical pap ers do not app ear here If you wish to get a copy of the printed version please contact your regional co ordinator and ask if some are still available Europ ean Women in Mathematics EWM is an aliation of women b ound by a common interest in the p osition of women in mathematics Our purp oses are To encourage women to take up and continue their studies in mathematics To supp ort women with or desiring careers in research in mathematics or mathematics related elds To provide a meeting place for these women To foster international scientic communication among women and men in the mathemat ical community To co op erate with groups and organizations in Europ e and elsewhere with similar goals Our organization was conceived at the International Congress of Mathematicians in Berke ley August as a result of a panel discussion organized by the Asso ciation for Women in Mathematics in which several Europ ean women mathematicians to ok part There have since b een six Europ ean meetings in Paris in Cop enhagen in Warwick England in Lisb on in Marseilles in Warsaw and in Madrid The next meeting will b e in The place of the meeting will b e announced later At the time of writing there are participating members in the following countries Belgium Czech Republic Denmark Estonia Finland France Germany Greece Italy Latvia Lithuania the Netherlands Norway Poland Portugal Romania Russia Spain Sweden Switzerland Turkey Ukraine and the United Kingdom contacts in Albania as well as with several nonEurop ean countries Activities and publicity within each country are organized by regional coordinators Each country or region is free to form its own regional or national organization taking whatever organizational or legal form is appropriate to the lo cal circumstances Such an organization Femmes et Mathematiques already exists in France Other members are encouraged to consider the p ossibility of forming such lo cal regional or national groups themselves There is also an email network For further information contact The secretary of EWM Riitta Ulmanen Department of Mathematics POBox Yliopistonkatu FIN University of Helsinki Finland email ulmanensophiehel sinki Tel Fax For details of the email network contact sarahreesnewcastleacuk September EWM on the Web EWM now has a page on the Web There are two adresses although b oth contain the same information One in Helsinki httpwwwmathhelsinkiEWM and one in Austria httpwwwriscunilinzacatmiscinfoewmEWMhtml The Web account has b een set up by Olga Caprotti Giovanna Ro da Ileana Tomuta and Daniela Vasaru at RISC Linz Research Institute for Symbolic Computation Johannes Kepler University A Linz Austria They can b e reached at the EWM Web account ewmriscunilinz acat or at their p ersonal accounts FirstNameLastNameriscunilinzacat History Since Luminy EWM since its fth meeting in Luminy Caroline Series University of Warwick England The fth EWM meeting was held in Luminy France December th In the lengthy rep ort which was published of the Luminy meeting I wrote a brief history of the rst ve years of EWM Since this is the rst ma jor EWM rep ort to b e published since that time I have b een asked to write a few words to record what has happ ened in the interim The Sixth General Meeting Warsaw June thth The sixth General EWM Meeting to ok place at the Technical University in Warsaw from June thth The main organiser was Anna Romanowska The meeting was attended by ab out participants from Europ ean countries The conference featured lectures in pure and applied mathematics an interesting session on creativity and several business ses sions There was a rep ort from the Round Table on women in Mathematics at the Europ ean Congress in We learned that the prop ortion of women among do ctorates in mathe matics is highest in eastern Europ ean and Mediterranean countries Greece Italy and Spain were represented at the conference and lowest in Scandinavia the Netherlands the UK and Germany There has b een much sp eculation ab out this somewhat counterintuitive situation but it seems more pro ductive to concentrate on how to get more women into mathematics in the northern countries Mary Gray gave a talk on the history aims and activities of the AWM and also gave helpful advice ab out the draft statutes of EWM Legalisation of EWM and establishment of the Helsinki Oce One of our early failures as an organisation which I mentioned in the rep ort of the Luminy meeting was our lo ose structure in which everything dep ended on just one p erson the inter national co ordinator By the time of the Luminy meeting we had decided that it was time to set in place some more formal organisation and that we wanted EWM to b e a legal b o dy During the Luminy meeting we did a lot of work drafting our basic organisational structure and statutes and a small committee consisting of Marjatta Naatanen Riitta Ulmanen and myself was formed to carry this work further In the course of discussing our statutes