www.womeninmath.net Women of mathematics throughout Europe A gallery of portraits A gallery of portraits A gallery

13 portraits offering an unusual insight into mathematics Europe throughout of mathematics Women

Editors Sylvie Paycha, Magdalena Georgescu and Sara Azzali

Photography Noel Tovia Matoff 4 324 0 14 8398 97

Women of mathematics throughout Europe A gallery of portraits Women of mathematics throughout Europe A gallery of portraits

Editors Sylvie Paycha, Magdalena Georgescu and Sara Azzali Photography Noel Tovia Matoff Content

6 Introduction

Protagonists 10 Nalini Anantharaman 18 Karin Baur 24 Stefka Bouyuklieva 32 Alice Fialowski 40 Frances Kirwan 48 Irina Kmit 56 Margarida Mendes Lopes 64 Kaisa Matomäki 72 Barbara Nelli 80 Dušanka Periši´c 88 Katarzyna (Kasia) Rejzner 96 Katrin Wendland 104 Oksana Yakimova

112 Beyond mathematics 113 Elena Mendoza 119 Matina Matoff

122 Acknowledgements 123 The editors 124 Publishing details 6 7

Introduction Together – and with the help of Sara Azzali – we interviewed and took photographs of thirteen female mathematicians over a little more than a year, during which we set up a ritualised procedure. The interviewed women would first give us an accessible impro- Nowadays, women still find it difficult to embrace a career in the vised presentation on the blackboard of their research work. During mathematical academic world; social pressure and personal doubts these lively mathematical conversations, Noel would make a first may restrain them from doing so. As a result, one observes an em- series of photographs. The interviews would take place either be- barrassing disparity between the proportion of men and women fore or after these portrait sessions. The portrayed mathematician among professional mathematicians. This volume, which aims at would then be asked to pose in front of a formula left on the board drawing the reader’s attention to this issue, presents mathematics for a second series of photographs. She would finally be asked to through women mathematicians’ perspectives and samples of their write down on a piece of paper her preferred mathematical formula, life stories. It invites the reader to share their experience as mathe- that now illustrates in the catalogue the chapter dedicated to her. maticians, offering a human outlook on this discipline often feared This ritual gave us time to pause for explanations, to talk and to for its abstractness and dryness. ­listen, creating spontaneous interactions that are reflected in the This is the catalogue of the touring exhibition “Women of photographs and interviews the reader will find in this volume. ­Mathematics throughout Europe. A gallery of portraits”, inaugu- Noel accompanied me in the world of mathematics, with which rated on the 20th of July 2016 during the 7th European Congress she was not acquainted; the week we spent in a meeting of the of Mathematics (ECM) at the Technische Universität Berlin (TU ­organisation European Women in Mathematics, that took place in Berlin). Like the exhibition, it presents the photographic portraits “Il Palazzone” in the beautiful town of Cortona, served as a rather and interviews of thirteen female mathematicians from different radical immersion! In sharing with me her outlook on this singu- countries throughout Europe. lar world she was entering, Noel influenced the way the project In 2014, in preparation for a talk I had been asked to give at the was conducted. The fact that she recognised the same enthusiasm University of Konstanz on “Women and mathematics”, I wrote to in women mathematicians for their work as that of her sister’s ten female mathematicians I know around the world, asking them – a midwife – for hers, led us to interview and portray her sister to answer a set of questions related to their careers. I assembled ­Matina Matoff. This in turn triggered the idea of portraying another the replies, together with a photograph of each mathematician, in non-mathematician, the composer Elena Mendoza, author of the a hand-made booklet entitled “Women mathematicians around the two musical pieces performed at the exhibition opening in Berlin, world. A gallery of portraits”. The positive response these inter- where she also reported on the situation of women composers. views received from the mathematical community encouraged me One can “do” and discuss mathematics regardless of the circum- to ask Agnes Handwerk, the author of various documentary films, stances and the environment. Mathematics can wait, as it neither radio programmes and articles on mathematicians, whether she was dries, nor does it perish, and little does the weather matter when willing to work with me on a film project based on this document. doing mathematics. In contrast, light and darkness are essential for Agnes suggested to use the booklet as a starting point towards a a photographer portraying mathematicians at work. What weather more ambitious goal, an exhibition at the 7th European Congress could we expect in Turku on Thursday December 17th 2015, when of Mathematics - and thus the project was born. Little did I realise portraying Kaisa? How about in Jena on Thursday October 29th then what an enterprise and adventure this was going to become! 2015, for Oksana's portrait? In Oxford on Monday June 1st 2015 I was very happy when Noel Matoff, a photographer I great- for Frances’s? In Tarnovo on Monday February 22nd 2016 for ly admire for her work on midwives and people suffering from Stefka's? How far would the blackboard be from the window? ­Alzheimer, accepted to accompany me in this adventure, taking The answer to these questions was of decisive importance. The light photographs of the mathematicians we intended to portray. was all the more important for Noel, who took photographs on a 8 9

120 roll film with her medium format camera, a twin lens Rolleiflex, We have learned a lot from overcoming the many obstacles on the­ in addition to using her digital equipment. This way, she could cre- path to its realization, some of them thanks to the generous support ate a certain intimacy between the photographer and the portrayed of colleagues such as Sara Munday, who proofread the interviews. woman. We are also very thankful to Maria Hoffmann-Dartevelle, who Contingency can nevertheless not be totally ignored while translated the interviews into German. doing mathematics, as one can read from Dušanka’s experience of We are immensely grateful to the main protagonists of the ­project, abruptly interrupting a mathematical discussion at the sound of the thirteen portrayed women, Nalini Anantharaman, ­Karin Baur, a siren which brought back threatening memories of the war in Stefka Bouyuklieva, Alice Fialowksi, Frances Kirwan, Irina Kmit, Serbia. Women are generally confronted with contingencies more Margarida Mendes Lopes, Kaisa Matomäki, Barbara Nelli, Dušanka often than men are; as Karin, they might consider reducing their Periši´c , Kasia Rejzner, Oksana Yakimova, and ­Katrin Wendland, workload while their children are young, or as Alice, they might for their readiness to share their experience and dedicate time to the decide to give up a good position to take care of a sick mother. interview and portraying. Let me address my thanks to two further These contingencies, combined with a lack of self-confidence protagonists of this catalogue, Elena Men­doza and Matina Matoff, possibly induced in part by a lack of support from family, friends for their willingness to answer the questions we had asked the thir- or the mathematical community, can make it very tough for young teen mathematicians, only slightly ­adapted to the features of their women to become professional mathematicians. We hope that the respective professions, namely composer and midwife. testimonies given by the thirteen mathematicians in this catalogue We are also thankful for decisive support from Jean-Pierre Bour- will stimulate young women scientists to trust their own strength. guignon, who gave us an essential impulse at a moment of great The fact that all thirteen mathematicians answer negatively as to discouragement due to the lack of funding sources, Jan Erdnüß­ whether they have any regret concerning the choice of their career who, without hesitation, welcomed the exhibit to the Mathematics as a mathematician should serve as a strong incentive! Library premises at Technische Universität Berlin, and actively sup- This exhibition project – which, as well as the photographer ­ ported the project along the way, and Pierre Clavier who patiently Noel Matoff, involved four mathematicians in the planning and put up with our endless lunch-time discussions about the prepara- organisation, Alexandra Antoniouk, Sara Azzali, Magdalena tions for the exhibit, and provided feedback. Georgescu and myself – has been an exhilarating experience, in that My personal thanks go to my colleague Sylvie Roelly for her it has brought us to interact differently from the way we would in ­decisive support in applying for funding, and to Steffanie Rahn, ­ our ordinary mathematical life, with each other as well as with the also from the University of Potsdam, who bravely helped us over- portrayed mathematicians. It has also given us a glimpse into the come various administrative impediments we came across with this artistic world through Noel and Elena. exhibition project, an unusual type of project for a mathematics The difficulties we encountered along the way created further department to run. bonds amongst us organisers, as we also shared the anguish of find- We hope that this catalogue can convey to the reader how math- ing enough financial support for the project. Bringing this ­exhibition ematics and life experiences intertwine, and thereby the joys we project to life turned out to be far more difficult than ­expected, for a mathematicians experience in the daily practice of our craft. Let this project dealing with women issues does not find much support in a catalogue serve as a cordial invitation to the realm of mathematics! mathematical world still very much dominated by men. We were all the more grateful to the Humboldt foundation, which supported the project by granting Alexandra Antoniouk ­the “Humboldt Alumni Sylvie Paycha Award 2015 for Innovative Networking Ini­tiatives”. My warmest thanks go to Alexandra, Magdalena, Noel and Sara, without whom the exhibition and this catalogue would not exist! 10 11

Nalini Anantharaman

Nalini Anantharaman grew up in Orléans. After her studies at the École Normale Supérieure de Paris, she obtained her PhD in 2000 under the supervision of François Ledrappier at the University of Paris 6. She worked at the École Normale Supérieure de Lyon, at the École Polytechnique, and became a full Professor at the Topics of research: University of Paris-Sud, Orsay in 2009. Presently, she is a Profes- – dynamical systems sor at the University of Strasbourg. She was awarded the Henri – semi-classical analysis Poincaré Prize for mathematical physics (2012), the Salem Prize – mathematical physics (2011), and the Grand Prix Jacques Herbrand from the French – spectral theory Academy of Science (2011). – wave equation 12 13

How and when did research specifically around you choose to do physics. mathematics? How did you come to I grew up in Orléans, where I choose mathematics? lived until my A-levels (bacca- At school I always preferred lauréat). After that I studied in scientific topics, so mathemat- Paris where I was admitted to ics, physics and biology. I was the École Normale Supérieure. also very much drawn to mu- After a PhD under the super­ sic, I played the flute and the vision of François Ledrappier piano. For some three or four on probability and ergodic years following my A-levels, theory, I was offered a position I hesitated somewhat whether as lecturer/assistant professor to choose a musical career, but (maître de conferences) at the the lack of information con- École Normale Supérieure in cerning professional openings Lyon, where I worked from in this area led me to finally opt 2001 to 2006. Then and until for mathematics. My parents 2009, I was employed as a re- having encouraged me to take searcher (a CNRS position) at up science rather than music the École Polytechnique for studies, when it came to choos- three years. I have just been ing a specialised curriculum appointed on an Abel chair as a (preparatory classes), I hesitated full professor at the University between biology, mathematics of Strasbourg, which spares me and physics. However an ap- teaching duties for two years. prenticeship in experimental Last year I was given the silver physics convinced me that I CNRS medal, and the year be- should focus on theory and fore that, the Henri Poincaré drew me towards mathematics. prize, which is a distinction in I have nevertheless kept some mathematical physics. interest for physics. Could you call your Were you then encour- field of research mathe- aged by your family, matical physics? friends or other people The Schrödinger equation on around you? which I have been working, My mother being a mathema- and the Laplacian on graphs in tician, I very early had an idea which I am presently interested, of what mathematics could be. are also of interest to physicists. Since she enjoyed her profes- I personally do not insist on sion, she conveyed a very posi- being assigned a “mathemat- tive image of mathematics. My ical physics” title, since I like teachers have always been very changing research area and encouraging to me; the school it is not my aim to focus my teachers I had in primary school 14 15 made me skip a class, in spite of intend to go on working as despite this personal aspect, the my parents’ reticence. However before, when women are ready fruit of my work can be of in- demanding my parents were, to reorganise their schedule and terest to other mathematicians. they always let me find my own to dedicate less time to research. It is a privilege to create beau- way. I recall two occasions on Having received prizes, at the tiful things without having to which I asked them for help: time my children were born, it worry about their applications. in the fourth year of primary was expected that I would get I regret however not being able school when I asked them to back to research straight away. to be directly useful in a world explain division to me, and just However, during my maternity where terrible things happen, after my A-levels, at the begin- leave, topics on which I was not being in a position to repair ning of the specialised curricu- working were the object of re- the evil committed by others. lum (classe préparatoire). Since search, and led to publications I What would you I never had to study much in was not invited to join. ­recommend to a young high school, where I found the In retrospect, are you woman in your coun- syllabus easy, I felt somewhat happy to have chosen try wanting to start a disconcerted when I started mathematics or do you career in mathematics? the specialised curriculum. My have some regrets? For I would recommend that she mother helped me for a while, you, what are the joys of follows her own ambitions and giving me practical hints for mathematics? What are is not influenced by what she how to organise my work. the hardships? hears around her. She should Did you come across I am happy to have done math- not hesitate in being self-de- obstacles in pursuing ematics. I nevertheless find it manding and in setting herself your career as a mathe- difficult not to be able to share ambitious goals, even if neither matician? my interest with my family. her parents nor her professors For a long time, I did not think Were I to choose a career now, I do so. I would like to add that of the difficulties involved in think I would choose medicine. there are various ways of “be- being a woman doing mathe- Medicine incorporates a human ing good” at mathematics; you be as evident as they say it is. I ours. Among the difficulties cepts one meets in meteorolog- matics. Only as I was preparing component which I somewhat do not necessarily need to be would also tell a young woman they are confronted with is the ical phenomena, or in relation my PhD thesis, did I realise miss in mathematics, particu- quick, as one might expect from that the career of a mathemati­ fact that their professors refuse with the stability of the solar how few women there were larly since I like working on the existing encouragement to cian is rather well suited for a to supervise their PhDs if they system. After my thesis I turned at conferences, without being my own. The human aspect of take part in the Olympiads. woman; of course it requires are mothers. to the Schrödinger equation, particularly affected by this teaching provides a little com- Taking the time to understand a lot of work but it provides Could you write a few which arises from quantum fact. Now that I have children, I pensation for this lack. things in depth is also a way to some flexibility, since one can lines describing your mechanics and which permits a wonder more about these issues In my professional activity, I do research. Neither should one organise one’s work. Right now, topics of research in a description of the evolution of a and realise the differences in enjoy the freedom we feel in feel obliged to talk in public, the scarceness of positions pe- manner understandable particle which can be represent- the ways women and men view understanding things. Doing say in a seminar. One should nalises women. I nevertheless to non-experts? ed as a wave in the context of their career. Sharing with my mathematics is a creative work, have enough self-confidence do not see how one can think My thesis concerns ergodic wave-particle duality. It is a par- male colleagues the questions that emanates from my person, to assert one’s own certitudes, that a career as a mathematician theory and dynamical systems, tial differential equation which that come to my mind, such as which another person would not let oneself feel discouraged is not appropriate for women. and specifically chaotic systems, one cannot solve in general and the difficulty to come back to not have done in the same way. or impressed by others, for When I attended a meeting which are dynamical systems whose long term behaviour one mathematics after a maternity In doing mathematics, I ex- example by colleagues who of women mathematicians in sensitive to initial conditions, wants to describe. The theory leave, is difficult, if not impos- press something personal. It is very bluntly claim that a result India, I realised that their prob- whose long time evolution one of chaos applies to particles; sible. After a child’s birth, men a source of joy to know that, is trivial. The result might not lems are rather different from cannot predict. These are con- the issue whether it could be 16 17

applied to waves attracted me ­ concept taken from dynamical my goal, but I did not give up due to the underlying physical systems, to show that solutions and am happy to have kept motivation and also because I of the Schrödinger equations, going, despite discouraging like to confront two different which are waves, cannot localise comments by certain colleagues areas of mathematics. I used at large time in too small a and a referee who claimed I was concepts specific to dynamical region of the manifold. not capable of proving such systems to show that certain Could you describe a result. My own experience waves had a chaotic behaviour. your favourite personal shows the pertinence of long Now, to a mathematician, achievement in mathe- term positions, which allow I would say that the context matics? you to ­dedicate several years to is that of a compact manifold I am rather proud of the result the same problem without im- with negative curvature, which ­I just mentioned, and which mediately finding a result. creates a chaotic situation. was rewarded by various prizes. I used entropy, which is a It took me three years to reach 18 19

Karin Baur

Karin Baur was born in Zurich, where she studied Mathematics, Philosophy and French literature. She got her PhD in Mathematics at the University of Basel in 2002. She was a postdoctoral assis- tant at ETH Zurich, at the University of California at San Diego and Topics of research: at the University of Leicester, UK, where in 2006 she obtained the – cluster algebras University of Leicester achievement bonus. In 2007 she was of- – cluster categories fered an SNSF Professorship which she held at ETH Zurich and – representation theory since 2011 she is Professor at the University of Graz, in Austria. – categorification 20 21

How and when did to have a gap year. I spent some you choose to do time in France and took the mathematics? Cours de Civilisation Française I loved mathematics from the (Sorbonne), which included time I was very small, but did politics and history of art. I did not then actually know what not find standing in front of a it meant. I just liked to play painting for hours very exciting. around with numbers. My Since I was also interested in ­­parents used to make jokes, that medicine, I did an internship in I would become a “Zweistein” a hospital back in Switzerland, because of this. The pleasure of working as a nurse assistant. playing around with numbers This was a requirement to start I seem to have passed on to the medical studies. I enjoyed this next generation; when I once a lot and found it very interest- asked my five year old child ing, since it gave me insight into why he was so quiet, he told me the routine of the internal medi- he had counted up to 600! cine ward, the operating theatre In Switzerland, where I was and access to the patients’ med- brought up, at the age of twelve ical history files. What I did ­not I decided to go to the “Gymna- like was the competitive atmo- sium” to learn more mathemat- sphere among doctors and ics. The neighbourhood I grew nurses. Also, health problems up in was mostly working class, are not well posed, and medi- where most children would end cine, which is not an exact school after nine years and start science, relies on “trial and an apprenticeship, as 75% of error”. Why and how a treat- the pupils in Switzerland actu- ment is efficient is unclear. ally do. In my class I was the Seeing very young people die only girl to go to high school. of serious illnesses, such as can- It was a rather conservative cer, convinced me that I would environment and my teacher rather study mathematics than thought girls did not need to get medicine. Since I did not want further education. to focus on mathematics only, At high school (Gymnasium) I chose to study at the Univer- where one has twelve subjects sity of Zurich where I studied until the last year, I still enjoyed mathematics, philosophy and mathematics, but since my par- French for six years. During ents are not in academics, it was that period, I went back to not clear what I should do. I got Paris as an Erasmus student the “Matura” (A-Levels), which for one semester. gave me access to any subject at any Swiss University. I was hes- itant what to study and decided 22 23

Were you then encour- of the subject. This made me research in mathematics, not so something wrong, even though in Switzerland were working Early in my PhD studies I had aged by your family, aware that I was very good at it. much in teaching it to teenagers. I knew the material very well. in the areas I was interested in my first child. To get a fellow- friends or other people My first mathematics teacher at Did you come across A few months later I passed this (algebraic geometry and alge- ship supporting my PhD stud- around you? high school was a great teacher obstacles in pursuing exam with the top mark, and bra) and went to various places ies and relieving me from teach- My parents encouraged me and the second one was also your career as a mathe- pursued my studies without any in Switzerland (Geneva, Bern, ing duties, I had to go through when I decided to go to the very fond of me. He would matician? prejudice from this unfortunate Basel, Lausanne) in search of a an interview during which I was Gymnasium. They were very have liked me to become a A first obstacle I came across incident. Finding a PhD super- PhD adviser, ending up in Basel asked by the former president open minded concerning my high school teacher and when was when I failed my oral visor took me some time, in where I actually did my PhD. of the Swiss National Science choices: to their eyes education I later came back to work at Vordiplom (part of the exam at part due to the lack of support In retrospect, I think it was a Foundation (SNSF) if I intend- was important, as well as doing that Gymnasium replacing the end of the first year). I did from my Master thesis super- very good thing I did not go on ed to work part time. In Swit- something you enjoy. During a teacher for some time, he not open my mouth when the visor; to my great disappoint- working under the supervision zerland many women take up my school years, I regularly expected me to accept a long examiner asked me a question, ment, he was not willing to take of my Master thesis supervisor, part time when they have chil- ­explained maths to classmates term position there. But I never for I could not quite understand me as a PhD student. So with since we did not get along very dren, so I wanted to switch to and friends, who were im- wanted to become a teacher; the way he had formulated the help of the student advisor, well at the time. a 70% time job so that I could pressed by my understanding I am interested in doing it and was too scared to say I looked up which professors spend 1,5 days a week at home 24 25 with my children. My decision country also meant giving up in mathematics, you can work Could you describe was also influenced by the the arrangements my husband anywhere and on anything your research field to social pressure I felt to spend and I had made for child care. without deadlines. So our job is a lay person? more time with my children; I was giving up the comfort great in that it is very flexible. My research topic lies in al- later, in 2009, neighbors who of having their grandparents I have many collaborators gebra, a very abstract field of were my age and well educated close. In hindsight, I think it I met in various contexts, at mathematics, a part of pure asked me whether I really had was a great experience that I do a reading seminar as a PhD mathematics. You do pure to work with four children at not regret! My post-doc years student, or later on at confer- mathematics for the joy of it home. Even given the context ­ consisted of two years in the ences, and I enjoy doing re- and its abstractness makes it at the time, the female mem- US, two years in England and search with them. difficult to explain. Never- ber of the hiring commission finally four years in Zürich with Starting off in a new topic might theless, in cluster theory, the dissuaded me from choosing a Swiss National Science profes- be difficult and the progress field I am working in, you can to work part time if I wanted sorship, which gave me the op- is very slow. But rarely do I visualise many things using ele- to do serious research. Thanks portunity to build up my own feel lost or discouraged. Maybe mentary geometry, the building to her, I finally opted for 80%, research group. During all these sometimes I do when I attend a blocks there can be interpreted which turned out to be a good years, my husband has been talk I struggle to follow. In such as diagonals of a polygon and option during the preparation flexible enough to travel with us moments, I often start thinking things I could explain to a of my PhD. At the time, my and to take care of the children about my own research ques- child translate to very abstract husband was studying and we when I attended conferences or tions, even with new ideas for mathematics. For example, the were both flexible. I enjoyed visited co-authors. how to tackle them. Pythagoras theorem can be both my work and the kids and All in all, based on my experi- The one thing I do maybe regret translated to cluster theory. I do not think they missed me ence, I think it is harder for a is that I did not get a serious Can you describe your while I was busy working. woman to get a permanent job education in theoretical physics favourite personal During my postdoc years I as a mathematician than it is for and did philosophy instead. achievement in mathe- had some doubts whether to a man, but I cannot prove this And sometimes I struggle com- matics? continue, in great part due to assertion. bining my career in research I am very proud of my first the uncertainty of getting a In retrospect, are you with a family. Often I continue article I wrote after my PhD; it permanent position one day. happy to have chosen working in the evening or on has been valued as a “beautiful My father suggested I should mathematics or do you weekends. It can also be tricky article” by prominent mathema- wait until the age of 45 before have some regrets? For to travel for weeks in a row. ticians. It was published in the opting for another type of job. you, what are the joys of What would you re­ journal “Transformation groups” In Switzerland, there are many mathematics? What are commend to a young and consists of a problem I good options for trained math- the hardships? woman in your coun- posed and completely solved. ematicians outside academia. I I am happy and have no regrets. try wanting to start a your experiences keeps you on Our job is not easy and requires Related open questions turned got my first permanent position Mathematics is a world you can career in mathematics? track. You should not hesitate both courage and endurance. out to be too difficult to solve; as a mathematician at the age of dive into. I like exploring and There is no recipe; you should to ask questions, including on You cannot relax; it is like run- for this reason, the article has 41 and am grateful to my father you can learn every day from just move forward one step people’s life experience. When ning a marathon, with the differ- only had a few citations so far. for his comforting advice. doing research, you can invent at a time, not thinking too far I was a student, I remember ence that you do not know when Recent work I am proud of is My two year postdoc experi- new words, new ideas. Choos- ahead. It is important to follow asking a physics female pro- it ends! You do not choose such the development of dimer alge- ence in the US was interesting ing a problem is like picking out your interest, try things out, fessor whom I knew how she a job to make money; it is a vo- bras and boundary algebras on but difficult: I hesitated whether a chocolate from a chocolate attend conferences, meet peo- combined family and career, cation and a school of thought. surfaces in joint work with my to leave for the US since I had box; you choose it according to ple, do a post-doc. Talking to since this is what I was trying collaborators A. King and R. two kids, and moving out of my your own taste. It is the same people with whom you share to do. Marsh. 26 27

Stefka Bouyuklieva

Stefka Bouyuklieva studied Mathematics at the University of Sofia. She obtained her PhD in Mathematics in the University of Veliko Tarnovo in 1997 under the supervision of Prof. Vassil Yorgov, with a thesis on extremal self-dual codes. From 1999 to 2000 she was a postdoc at Delft University of Technology in the Netherlands. As a Humboldt research fellow she worked at the Magdeburg University in Germany from 2004 to 2005. She joined the Faculty of Mathematics and Informatics at Veliko Tarnovo University in 1992, first as an assistant professor and then as an associate pro- Topics of research: fessor. Since 2003 she is the Head of the Department of Algebra – coding theory and Geometry, and since 2012 she is Professor in Mathematics at – discrete mathematics the University of Veliko Tarnovo. – combinatorics 28 29

How and when did my sister, who enjoyed painting I still keep in touch with my Another person who was sup- you come to choose to and drawing from a very early school fellows; we meet every portive throughout my career do mathematics? age, in doing arts. five years. I am the only one is my husband, whom I met at I came to mathematics at a very My algebra teacher at high- out of the two special classes university, while studying. He early age, since my parents were school, Stefan Dodunekov, of mathematics that year to be has always encouraged me to teachers of mathematics. I was encouraged me to attend the doing research. do research and we’ve actually very good at school and en- national Olympiads. Three This same teacher encouraged also worked together on several joyed mathematics very much. participated from our school me later in my career. I came occasions. We married when I From the age of fourteen to in a team of some fifty children to Veliko Tarnovo, where I am was 21 and I had my first child the age of eighteen, I attended from all over the country, but still working, on his instigation; shortly after. We spent one year a special school in Sofia, some only one out of the three went at the time a satellite of the in Montana, my home town, 100 km away from my home to the international Olympiads. Academy of Science had just where my husband had a posi- town, that trained pupils in To take part in the national opened in Veliko Tarnovo and tion as a school teacher, while mathematics. There I met a re- Olympiads, you first had to he encouraged me to accept a I was taking care of my newly markable teacher, the late Stefan win the school Olympiads, then position there. born second child. Then came Dodunekov, who taught us the city of Sofia Olympiads. the offer for a position at the algebra. We also had classes in geometry and later in analysis, all delivered by excellent teach- ers. All three were assistant professors at the faculty of mathematics of the University of Sofia and one of them, the analysis lecturer, later became head of the school. In my year, for pupils wanting to specialise in mathematics, there were two classes of around 25 pupils each. In mathematics, there were as many girls as boys, but there were only four girls specialising in physics. Were you then encour- aged by your family, friends or by other people around you? My father, who believed every child had some talent and made a point of encouraging the child in developing this talent, spotted my gift for mathemat- ics and encouraged me in that direction. He also encouraged 30 31

Academy of Science in Veliko was not propitious to do a where the proportion of wom- Tarnovo, an offer which we PhD since the situation in the en professors is higher than in were both very happy about. Academic world was unstable. some other European countries. We moved there in 1988, just Only in 1994 did I start a PhD Also child care was provided after I had defended my master which I defended in 1997. De- for our children. However, in thesis. fending my PhD thesis so late our department, out of eight Did you come across actually slowed down my career professors and lecturers (Doz- obstacles in pursuing somewhat. Another obstacle ent) in mathematics, there are your career as a mathe- we came across was the lack of only two women, one professor matician? access to articles; at the time, and one lecturer, both of whom The political situation and par- Prof. Dodunekov would help are active researchers. Among ticularly the “transition period” us by bringing back articles and the men, some two or three (in the 1990s) from a socialist books from his travels. Hav- are doing research. I neverthe- to a capitalist economy, made ing access to articles is still a less observe that in one of the things difficult for us. A cou- problem today; we do not have classes in computer science, we ple of years after we arrived free access to the publications have only two female students (in 1988) at the Academy of of some publishing houses, as at our department for twenty Science in Veliko Tarnovo, the one does in Western European male students, but the two girls institute went through some Universities. are the best in the group. restructuring and a new focus The first years at Veliko Tarno- In retrospect, are you was made on mathematics vo were also difficult since we happy to have chosen applied to computer science. then had two small children. mathematics or do you Whether I could keep my job At that time, accommodations have some regrets? For while continuing to do research were scarce, so that we only had you, what are the joys in pure mathematics was then a one room accommodation of mathematics? What unclear. So in 1992, I decided to during the first eight months. are the hardships? move to the University of Ve- Our children had to stay with I have no regret whatsoever; liko Tarnovo and my husband their grandparents, my daughter what I like about doing mathe- chose to stay at the Academy; with my parents in Montana, in matics is that it is so creative. ­ this way, I could go on with my the Northwest of Bulgaria, and I enjoy meeting other mathema- research in pure mathematics my son with my husband’s par- ticians, discussing and working and the risk of both of us losing ents in Yambol, in the South- with them, even though I also our job simultaneously was east of Bulgaria. So we would enjoy working on my own. avoided. I was first an assistant, travel on week-ends to see our Another feature of mathemat- then senior assistant, then main children, visiting each of them ics I like very much is that it is assistant; I was promoted to a every other week-end. Our common to the whole world, Lecturer (Dozent) in 2000, a parents were very supportive, and insensitive to politics. position I held until 2011 when and also helped us a lot later, It is a universal language. I became a full professor. I did in taking care of the children For me, working on a mathe- not have a PhD degree when when we went to conferences. matical problem is like playing I was at the Academy, where I I do not think that being a a game. I feel happy solving a was appointed with a Master’s woman was an obstacle for me mathematical problem in the degree. The “transition period” as a mathematician in Bulgaria, same way as my mother very 32 33

much enjoys solving Sudoku Could you write a few games. I have fun in solving lines describing your Olympiad problems. Instead topics of research in a of doing a crossword, I like ­ manner understandable to spend time solving an Olym- to non-experts? piad problem. My subject is coding theory. I Mathematics is however a am interested in the structure challenging subject by which of codes, like how to construct we attempt to solve arduous and classify new codes. Some problems. If ever I feel discour­ of these codes are used in prac- aged when faced with a diffi- tice to transmit or store infor- cult problem, I tend to look mation. We build codes that at another problem, which correct errors which can occur sometimes helps me to attack during the storage or the trans- the original one from a different mission. So when you want to angle. So all in all, I do not view transmit 1 or 0 in a binary code, mathematics as a tough subject; let us say you want to transmit it is hard for people who do 1, you actually transmit more not understand it because they information such as repeated lack the basics. ones 1111111. This way, if an What would you error pops up in the form of a recommend to a young zero in the middle of the series woman in your coun- of ones, say 1110111, the receiv- try wanting to start a er seeing that the dominant fig- career in mathematics? ure is a one, will guess that the I would tell her that doing zero is an error and understand mathematics is a fulfilling and that 1 was the figure initially creative occupation. It leaves sent. one a lot of spare time, one can What is your favourite work at home and hardly needs personal achievement any equipment at all. Actually, in mathematics? my recommendation would I am very proud of my Hum- be the same for a woman or boldt fellowship, which I got a man, and I do not think my quite easily after my first ap- colleagues would answer differ- plication. After that I defended ently to a man or a woman my habilitation in Sofia in 2007, either. We prepare a group of encouraged once again by Prof. students for the Olympiads and Dodunekov. I am very proud of out of the five students in the the contents of the habilitation group, most students are girls. thesis; however, being written in Bulgarian and on a special- ised topic, it is not very much read. 34 35

Alice Fialowski

Born in Budapest, Alice Fialowski obtained her PhD in mathe­ matics at the Eötvös Loránd University in harmonic and functio- nal analysis. After her PhD, she spent a couple of years in Moscow as a postdoc (aspirant) working with Prof. Alexander Kirillov. Back ­­­in Hungary, she worked at the Technical University of Buda- pest. She was a Humboldt fellow for two years in Bonn, where she met Prof. Friedrich Hirzebruch, and later spent several months in Geneva working with Prof. André Haefliger. She worked at MIT with Prof. Victor Kac and was hired as a lecturer at the Univer­ Topics of research: sity of Pennsylvania, where she spent two years. She was later – functional analysis ­appointed associate and then full professor at the University – Lie theory of California Davis. Then she returned to Hungary, where she – representation worked at the Eötvös Loránd University in Budapest. She is – cohomology presently working at the University of Pécs. – deformation 36 37

How and when did special math school, so I did to ask for a problem. He told you choose to do not have the background to me to look for a problem my- mathematics? follow those meetings and self. In a seminar I happened My father was an engineer and stopped attending them. to hear of an open problem liked mathematics. I enjoyed all Then I was admitted to the by Victor Kac, which I solved. the subjects taught at elementa- mathematics program at the After that, Kirillov was very ry school and got high grades in Eötvös Loránd University supportive. Having to set and all of them. I did not have any (ELTE) Budapest, where I later solve a problem on my own special preference for mathe- did my PhD thesis in harmonic was very good training, because matics at the time. Later I went and functional analysis. After once back in Hungary, I would to a girls’ high school, where my graduate studies, I wanted be doing research on my own. most of my schoolmates had to study representation theory, In Moscow I also attended the great difficulties with maths, a subject which was not offered Gelfand seminars. They were and my teacher would spend in Budapest. With that in mind very instructive and exciting. his time helping out weaker I decided to go to Moscow for He taught us to explain the students. Since I wanted guid- three years as an aspirant (post- theory using simple examples, ance in learning mathematics, I graduate studies) to learn from forcing the lecturer to do so. needed to find other means of Professor Kirillov. I was admit- He was a great mathematician, learning. Once a week I would ted and very much looking for- very much appreciated by his attend (for free) a special course ward to attending his courses. colleagues like Kirillov, Fuchs, for gifted children, set up by the Once in Moscow, even though Novikov, Arnold. Of course “Society for Scientific Studies”, I had studied Russian in school there were other female mathe- a state organisation. I adored for years (it was a compulsory maticians attending the seminar, solving problems and would sit subject), it took some time be- in fact quite a few (among them at the back of the classroom at fore I dared open my mouth. Vera Serganova). school, solving the problems At that time, mathematicians in Were you then encour- that I had from this special the Soviet Union could not in- aged by your family, course. There, I had heard of vite foreign students freely. Pro- friends or other people a Hungarian “High School fessor Kirillov was not a party around you? Mathematics Journal”, and my member and when asked why Although I got encourage- parents got a subscription for he invited me, he was unable to ments from my family, what me, so I began solving problems answer. When I was asked why I achieved I did on my own. proposed in it. This journal had I had come, I replied I had been My father was the one in my a monthly competition. At the motivated by Kirillov’s book. family who liked to analyse end of each school year the best I had to ask for the help of the problems, a way of thinking problem solvers were presented, Hungarian Embassy, and man- that I have inherited. with their picture. I was always aged to stay, but was assigned a The years in Moscow were very among them. I also performed second adviser who was a party interesting but rather tough, well on the yearly national member. so we Hungarians needed each math competitions. One year Kirillov was a wonderful teacher, other’s support. Daily life was I got an invitation to join the but he was tough. After I had not so simple, for example we training course for the Olym- got acquainted with represen­ had to stand in line for three piads, but my school was not a tation theory, I went up to him hours to buy a kilogram of but- 38 39 ter, which we would then share, time, the papers which I had many international visitors. We proposals, promotions etc. from selling some to friends. We had written in Russian had been enjoy working together, and different countries. breakfast, lunch and dinner in translated into English and I got even though Hungary is a small I went through some difficult the dining hall which we liked invited by Professor V. Kac at country, I do not feel isolated. years, since my husband was a lot. Russian food is good, but MIT, after which I was offered Did you come across not there during the academic any extras like cheese or cook- a one year lecturer position at obstacles in pursuing year. I used to bring my chil- ies were limited. My room in the University of Pennsylvania. your career as a mathe- dren with me to conferences, the dormitory on the 16th floor I was teaching a class of 240 matician? where I got various reactions of Lomonosov University was students, my very first class I believe a good mathematician from the male participants, very nice (there were elevators); in English! It was there I met is valued for his/her results. I some of whom would comment each of us had a room in a two Professor Gerstenhaber, from am grateful for all the support I that the presence of children room unit with a common whom I learned a lot (and there received throughout my career would make the meeting more bathroom and toilet. There was I also met my future husband!). as a mathematician. Last year I human. My children loved trav- a common kitchen at both ends Then I applied for a position was asked to help build up the elling with me, and my older of each floor. at the University of California PhD school at the University daughter, who is now a geolo- Some of my Hungarian peers Davis, where I became a full of Pécs in Southern Hungary, gist, still enjoys travelling in her could not cope with these living professor. My husband still had where I now work. It is the job. But none of my children conditions. But I consider this his job in Philadelphia at Penn, oldest University in Hungary wanted to become a mathema- as a lovely period of my life. I so he began to commute to (650 years old), but a separate tician, having seen how busy made many nice and generous Davis. Our first child was born Institute of Mathematics was set both their parents were with Russian friends, ready to give there. After five years in Davis, up only some fifteen years ago, their jobs. me their last clothing to help me my mother in Hungary had a so this project is a challenge for In retrospect, are you out. This is a mentality I deeply serious accident and needed me. I have already found good happy to have chosen appreciated, so I was somewhat permanent help. I moved back candidates for the new PhD mathematics or do you sad to leave Moscow. to Budapest to take care of school. I also have students at have some regrets? For Once back in Budapest, my first her and my brother, who was the Eötvös University Buda- you, what are the joys trip to the West was to Ober- suffering from a serious brain pest, where I have a nice office of mathematics? What wolfach, followed by a five disease. I began to work at which I use to work with my are the hardships? month stay in Geneva, at the in- the Eötvös Loránd University foreign visitors. I am very happy to have be- vitation of Professor Haefliger. Budapest. My husband was I am grateful that my work is come a successful and respected He and his nice family helped very supportive, and began his also appreciated internationally. mathematician. I enjoy strug- me to get adjusted to the West. regular trips four times a year I am a member of the Scientific gling with new problems, dis- This is where I wrote my first to come to see us in Hungary. Council of the International cussing and implementing new paper in English (the first ones Ever since, he has done his best Banach Center in Warsaw, and ideas with my collaborators. appeared in Russian). After that to spend as much time with us of the Tbilisi International Mathematics offers a common I went to Bonn as a Humboldt as his teaching duties allow him, Center of Mathematics. Since language across borders. Fellow, where Professor Hirze- which amounts to some 5 to 6 2012 I have been a member of It is a real joy. bruch was my supervisor. I met months every year. Our second the Executive Committee of the his whole family, children and daughter was born in Budapest. European Mathematical Soci- grandchildren. The Hirzebruch I also received a lot of support, ety, an endeavour I like a lot. I family was very supportive, appreciation and respect from also enjoy serving on Editorial particularly at a difficult time, colleagues in various countries. Boards of different journals when my father died. By that I am pleased that I have had and book series, and evaluating 40 41

What would you from doing mathematics and recommend to a young from my family; my husband woman in your coun- and two children are essential try wanting to start a to me. career in mathematics? Could you write a few Mathematics is tough, for men lines describing your as well as for women. For topics of research in a someone gifted in mathematics, manner understandable and ready to invest some effort to non-experts? into it, then why not, he/she My main interest is deforma- should try it out. But the aca- tion theory. Can one modify demic job market is very tough. the definition of multiplica- However, the government in tion in an algebraic object in Hungary is encouraging school a meaningful and useful way? teachers to receive a PhD. Due How many different defor- to the lack of positions in aca- mations does an object with demia, teaching at high school is a given structure have? The therefore also an option. In the most fundamental question is past many first class mathema- to determine which objects are ticians used to be high school “rigid” and which can be de- teachers as well. Another pos- formed. These are the type of sibility for a young person is to questions I am interested in. A later work on some really “hot” typical question in the analytic applications in biology, medical setup is how many complex sciences, chemistry, etc. There structures are there on a com- will always be a big need for pact manifold? Deformations such applications. in the algebraic setup are easier Could you describe to compute, as cohomology your favourite personal computations are simpler there. achievement in mathe- There are many applications matics? of this topic in mathematical I am really happy about my physics. results in algebraic deformation theory, being able to understand the notion of miniversal defor- mation and to work out a con- struction method. I have some surprising infinite dimensional Lie algebra examples and re- sults, like the formal rigidity of the Witt and Virasoro algebra. But what I am most proud of is the success and joy I get both 42 43

Frances Kirwan

Frances Kirwan studied at Cambridge University, and went on to graduate work at Oxford, where she obtained her DPhil in 1983 under the supervision of Sir Michael Atiyah. She was a Junior Fellow at Harvard University 1983–1985, and, after returning to the United Kingdom, she became a Junior Research Fellow of Magdalen College, Oxford and then a Tutorial Fellow at Balliol College, Oxford in 1986. She has been a Professor of Mathemat- ics at Oxford University since 1996. She was awarded a Senior Research Fellowship by the Engineering and Physical Sciences Topics of research: Research Council 2005–2010. She was an invited speaker at the – algebraic and symplectic International Congress of Mathematicians in Zurich in 1994 and geometry (as a plenary speaker) in Beijing in 2002. From 2004 to 2006, – moduli spaces she served as President of the London Mathematical Society, – geometric invariant theory the second-youngest president in the society's history. – localisation formulas 44 45

How and when did year I found the maths very dry low, then returned to Oxford have older brothers. However, you choose to do and wondered whether I should for one more year as a post doc I never got the feeling at home mathematics? switch to history. and finally started as a Tutorial or at school that girls were When I was at school, I always As an undergraduate I also Fellow (a permanent position) not expected to excel academ- enjoyed maths. My earliest enjoyed voluntary work with at Balliol College, where I still ically: quite the reverse was mathematical memory is my small children and thought I’d am. I had my first daughter the case. The atmosphere was father explaining to me the the- like to become a primary school two years later and my other a bit different when I was an orem that the three angles in a teacher. I applied to Durham two children in quite short suc- undergraduate at Cambridge, triangle add up to 180 degrees. University to start a teachers’ cession. I didn’t take as much although I did not feel discour- The idea that something could training course. The interview- maternity leave as I might have aged by anyone who taught me; be proved to be always true was ers discouraged me and instead done after the birth of my first I was annoyed that the Mathe- very appealing to me. At school, encouraged me to train as a daughter, but did later take a matics Department insisted on maths was one of the subjects I secondary school maths teacher, term's sabbatical leave, during addressing me as ‘Mr’ F Kirwan enjoyed, but not the only one. so I decided to apply for a PhD which we went to Berkeley. I in all official correspondence. In the UK school ­system, one and then perhaps train as a took more maternity leave after Since I’ve been at Oxford I usually chooses three to five secondary school maths teacher my youngest was born. All in have never felt isolated as a subjects to study (to A-level) afterwards. From that point on all, I had six to seven years with female mathematician, and I between the age of 16 and 18. I I never thought seriously again very small children; during have been fortunate enough to chose maths and further maths, about being anything other than this time my teaching duties have had incredibly supportive history, Latin and Greek. The a mathematician. took higher priority than my colleagues, especially Keith only science I did apart from My mother was a librarian at research. The first time I got an Hannabuss who was my main maths at school after the age Somerville College in Oxford invitation to speak at the ICM, colleague for several decades of 14 was a joint physics and (I was actually born in Ox- the Congress (in Japan) was at Balliol. When I arrived as a chemistry O-level. I was in an ford, in the hospital that used to be when I would have two graduate student in the early all-girls school where science to stand next to the premises children under the age of two, 80’s there were already around was on the whole not as well of the maths building where so I turned down the invitation, ten women who had permanent taught as the humanities sub- I now work). She introduced unable to envisage travelling all positions in the department (as jects, which were very strong. me to Jenny Harrison who had the way to Japan in such cir- a result of the fact that some I enjoyed history, Latin and a Tutorial Fellowship there. cumstances. of the positions at the colleges Greek very much, more than Jenny was very encouraging Were you then encour- were specifically for women), maths at that time, but I never­ and suggested I should try con- aged by your family, so my male colleagues were theless chose to do maths at tacting Michael Atiyah, which I friends or other people used to having women around. university. It seemed to me that did. So I ended up as a graduate around you? By the late 80’s, most colleges otherwise I would not be able student studying with Atiyah I was very much encouraged by had become mixed; now they to maintain my interest in the in Oxford, along with Simon my parents, who were very sup- are all so. My college, Balliol, subject, whereas in history, and Donaldson and my future hus- portive. My father was an aca- was formerly an all-male college to some extent in Latin and band, Michael Penington, and demic in philosophy. I suppose but admitted female students Greek, I could go on reading other good friends. That was a the fact that my two brothers from 1979; the first female about them without studying wonderful time and place to be were younger than me might Tutorial Fellow at Balliol was them at university. As an under- a graduate student! After that possibly have played a role; appointed in 1973. graduate maths student, I did I was lucky enough to get the it seems to be the case that go to history lectures and some opportunity to go to Harvard women mathematicians of my philosophy lectures; in my first for two years as a Junior Fel- generation do not generally 46 47

Did you come across One of the joys for me is teach- and I’ve always been more not be critical of colleagues ­ obstacles in pursuing ing; I really enjoy undergrad- comfortable as a follower than who travel a lot, when I am your career as a mathe- uate teaching and particularly a leader. And I don’t like the benefitting from other people matician? small group teaching. I find it competitive atmosphere at some travelling to come here. Not really; I was just very very enjoyable working with conferences. What would you lucky. For example, right from youngsters. The research too is These days there’s a lot of pres- recommend to a young when I was a graduate student, great fun and I very much enjoy sure on women to take leader- woman in your coun- there have been many women working with graduate students ship roles, and I am not keen on try wanting to start a in the mathematics depart- and postdocs, but I do find it a doing that myself; for example, career in mathematics? ment, some of them with small bit difficult to justify to myself I would hate to be head of de- I would have to ask her about children. The children could getting paid for the research I partment. I don’t like asking or what mathematicians call the turn up at the department with do, whereas teaching under- telling people to do things they two body problem, and wheth- their mothers without anyone graduates to think logically and don’t want to do! I used to feel er she would like to have chil- objecting. So it felt completely understand mathematics seems guilty about saying “no” when dren, since women who want normal to be a female mathema- much more worthwhile. I’m asked to do something, but I am a family are so much affected tician there, and later a mother. very pleased to make progress getting a bit better at it now. by their biology. I was lucky Also when I started working at in my research, but I don’t feel Another aspect of our mathe- enough to get a permanent job Oxford, mathematicians were that the advances I have made matical life I find uncomfort- before I was 30, which is now very autonomous; we were re- are very likely to help human- able is the fact that we travel very rare; these days mathe- quired to do a certain number kind ... though who can be sure! so much. I discovered about maticians are expected to have of teaching duties but we could I’m a little sorry that the hier- a decade ago that a round held several post-doc positions organise the timing of those to archy currently puts research trip to Australia from the UK before getting a permanent suit ourselves, more or less, and so much above teaching and contributes roughly half the position. On the other hand I as far as research was concerned that hiring committees tend to carbon emissions produced was less lucky, in that for many we did not have to answer to concentrate almost exclusively by an average individual in the years (all through the time our anyone. on research. UK during a year (discounting children were small) my hus- In retrospect, are you I have not always found confer- flying but including everything band worked in London while I happy to have chosen ences very helpful, though there else including other forms of worked in Oxford, and we lived mathematics or do you have of course been exceptions. transport), which made me somewhere in between. One have some regrets? For A lot of what one gets out of realise how much we mathema- advantage of a small crowded you, what are the joys being at a conference comes ticians contribute to polluting country like the UK is that of mathematics? What from talking to other mathe- our planet. I do try to travel to there are plenty of cities within are the hardships? maticians, which I sometimes conferences by train whenever commuting distance of each Yes, I am very happy to have find hard to do. This is partly, I possible, but of course that is other, but it is best to avoid chosen mathematics; in fact, think, because I’m a very visual often completely unrealistic. long commutes if at all possible. when I was asked to write person and I find it hard to Collaboration is hugely import- It is very difficult to know how a short general article about follow what people are telling ant in mathematics research, but to time having children with mathematics a number of years me about maths without seeing once you’ve met people face to a career. Some women decide ago, I called it ‘Mathematics: anything written down. For me face, it becomes much easier to to have a family while being a the right choice’. a maths talk is an amplification collaborate by Skype and other ­ graduate student, since many of what is on the board. Also means. However I am well academic clocks start ticking I’m naturally shy, so I’m happi- aware that, working somewhere after completion of a PhD. It er listening than talking myself, with lots of visitors, I should must be tough keeping momen- 48 49 tum going as a graduate student think about those from a math- dowed with a geometric struc- while looking after small chil- ematical viewpoint rather than ture (for example as an algebraic dren. Others have postponed from physics, and the residue variety) which reflects the way having children, but then they formula came out of thinking the objects vary in families run the risk of leaving it too how to redo a bit of Witten’s depending on parameters. late. work in a mathematically Often there is a natural way to An important piece of advice rigorous way. parametrise the objects which would be to get used to saying Could you write a few has some redundancy given no to things and not feeling lines describing your by a linear algebraic group ac- guilty about doing so. On the topics of research in a tion, so that the construction whole I suspect that women manner understandable of a moduli space reduces to tend to feel guiltier about say- to non-experts? the construction of a suitable ing no than men do, though My research over the years can quotient space for an algebraic obviously that tendency varies be split in three periods: work variety by such a group action. greatly within the genders. building on and related to my The aim of geometric invariant Could you describe thesis (pre-family period), my theory, or GIT, (developed by your favourite personal work with Lisa Jeffrey and Mumford for reductive group achievement in mathe- more recently, during the past actions) is to provide conditions matics? 10 years or so, work (joint ­ under which such quotients can I think there are several but one with a lot of other people) on be constructed, and construc- of them is related to my work geometric invariant theory for tions in these cases. with Lisa Jeffrey. Of course non-reductive groups and ap- In my thesis and related work, it was fun to collaborate with plications in algebraic, symplec- I was studying the topology (in a woman. One of the reasons tic and hyperkähler geometry. particular the Betti numbers) why I felt my work with Lisa It is all motivated by the con- of GIT quotients of complex was a particular achievement struction and study (going back projective varieties by using is because it was the first big to Mumford in the 1960s and methods coming from symplec- piece of research I managed ultimately to Riemann a hun- tic geometry and from Morse after having children. Because I dred years earlier) of ‘moduli theory, and applying the results had three children in quick suc- spaces’ in algebraic geometry. to different moduli spaces. cession, I was either pregnant Moduli spaces arise in classi- The residue formula I found or breast-feeding continuously fication problems, when, as is with Lisa provides expressions for about five years, and during typical in algebraic geometry, for intersection pairings of that time it seemed I was always the objects we want to classi- cohomology classes on GIT exhausted and my brain didn’t fy are not determined (up to quotients, and thus on moduli What does mathe- whole corpus of mathematics, On the research side mathe- function in the same way as the equivalence relation we spaces of bundles over compact matics mean to you? the way it was developed his- matics for me means trying to usual! So to prove something are interested in) by discrete Riemann surfaces. Currently I Mathematics is what I do: what torically and the way we are understand some small parts of like the residue formula with invariants, but instead can am interested in extending as I am is a mathematician and building it up on firm founda- the subject as well as I possibly Lisa was nice. It came out of Ed vary depending on continuous many as possible of the meth- what I do is mathematics. Fol- tions – even if this is not quite can, trying to think about them Witten’s papers “Non-abelian parameters. A moduli space is, ods of GIT to non-reductive lowing on from that, mathemat- as feasible as Hilbert, Russell, in different ways and linking localization” and “Two dimen- roughly speaking, given by the group actions, with potential ics means to me a combination Whitehead and others wanted them with other parts of math- sional Yang-Mills theory”; Lisa set of equivalence classes of the applications in a number of of teaching and research. On it to be at the beginning of the ematics. Jeffrey suggested we should objects we want to classify, en- different areas of geometry. the teaching side, I think of the 20th century. 50 51

Irina Kmit

Irina Kmit studied mathematics at the Lviv University in her home city in Ukraine. During her PhD in the theory of partial differential equations, under the supervision of Prof. Sergij Lavrenyuk, she got interested in hyperbolic PDEs. From 1999 to 2001 she worked at the University of Vienna, thanks to an Topics of research: ÖAD fellowship. In 2009 she was awarded a Humboldt fellow- – analysis ship, which enabled her to work at the Humboldt University – hyperbolic differential of Berlin. Later, she held teaching and research positions at equations the Lviv Polytechnic University and the Ukrainian Academy – boundary value problems of Sciences. Currently, she is working at the Department of – bifurcation Mathematics at the Humboldt University of Berlin. – stability analysis 52 53

How and when did differential equations (PDEs), you choose to do but was not too happy with this mathematics? topic. My advisor suggested I I was born in Lviv, Ukraine. should switch to hyperbolic Here, Stefan Banach spent PDEs and later gave me a lot of 25 years of his life (1920–1945). freedom to carry out my work ­He was one of the greatest as I wished. mathematicians of the 20th My father also supported me in century, and his spirit is still doing mathematics. He noticed present in this city with a long that, as a child, I liked to solve mathematical tradition. problems and bought me a I enjoyed mathematics from an well-known book by Perelman early age. I remember asking popularising mathematics. my teacher at school for addi- On the other hand, my mother, tional mathematical problems who was a doctor, tended to en- to solve. Later I participated in courage me to study medicine. mathematics competitions. However, solving mathematical We had a very good secondary problems gave me a unique education with a focus on natu- sensation of freedom that did ral sciences. I had a very strong not depend on what happened mathematics teacher since the around me. I actually think that 8th grade (so I must have been this was the reason why mathe­ 14 then) who was also interest- matics was so strong in the ing as a person. Not only did Soviet Union; in mathematics, he teach us mathematics but he people were able to find the also encouraged us to do sports. freedom they missed in real life. He considered these two dis- Did you come across ciplines most important. I still obstacles in pursuing enjoy sports and professional your career as a mathe- dancing very much, but stopped matician? practicing it on a regular basis Due to economic difficulties after I had my children, now in the nineties, there was a lack 7 and 14 years old. of money for science, which Were you then encour- forced many researchers to aged by your family, switch to purely teaching po- friends or other people sitions. Many of my colleagues around you? were in that situation, teaching The secondary school teacher I sometimes more than 20 hours mentioned, and later my super- per week. I myself spent some visor at university, encouraged years teaching that load at the me to become a mathematician. Polytechnical University. Those As a 3rd year student, I started who remained at the Academy working on parabolic partial of Science had to survive with 54 55

very low salaries. When I had my first child in 2001, I was at home on maternity leave, which I found quite convenient to get back to doing research. I managed to dedicate even more time to research when I had my second child, due to a reduced teaching load. My husband, who is also a mathematician, prepared his habilitation thesis when we had our first child. I prepared my habilitation thesis when we had our second child. So all in all, the time when our children were small proved to be very productive for both of us. I have not experienced any obstacles due to the fact of being a woman. As I already mentioned, my husband is also a scientist; he works in discrete mathematics. So far, we have managed to pursue a dual career. Our home institu- tion belongs to the Ukrainian Academy of Science. Presently my family is based in Berlin, where both my husband and I are guest researchers at Humboldt University, I at the Institute of Mathematics and he at the Institute of Computer Science. In Berlin we benefit from rather good child care and also the school system. Our children seem quite happy here while we are busy solving research problems. 56 57

In retrospect, are you ship for my first stay in Germa- bolic case. I am rather proud of happy to have chosen ny, does not follow this trend, these advances. mathematics or do you and still supports scientists Could you write a few have some regrets? For doing fundamental research. lines describing your you, what are the joys What would you topics of research in a of mathematics? What recommend to a young manner understandable are the hardships? woman in your coun- to non-experts? I am very happy to have try wanting to start a Life is not uniform, it is full of chosen mathematics and have career in mathematics? singularities, with unexpected never envisaged anything else One should feel a drive to do situations arising; it sometimes than working in mathematics. mathematics, and I would not jumps up and then jumps down. Mathematics is a language and recommend mathematics to The hyperbolic partial differ- you can express deep things in someone otherwise. If a young ential equations (PDEs) I am just a few words. I remember woman feels this drive, I would studying describe singularities. how I was charmed by the encourage her to do mathemat- Sometimes the singularities epsilon-delta formalism during ics, and not to hesitate, moving come from outside, sometimes my first course of analysis. on step by step. Time will take from inside, just as in real life! You can communicate very care of the rest, and if you are Hyperbolic PDEs with singu- efficiently in mathematics, patient enough you will get larities is the world in which which is a language without satisfaction from your results. I am working, and it is real borders. Communicating with I would also recommend to her for me even if it looks illusory other mathematicians in this to find some balance between and mysterious for the general language is very exciting and work and family, and to enjoy public. enriches your life (as mathema- both. ticians usually have many other Could you describe interests besides mathematics). your favourite personal Every mathematician has his or achievement in mathe- her own way of working and matics? thinking. I like working with I work on hyperbolic differen- colleagues in Berlin, Vienna and tial equations. In this area we Innsbruck, in Lviv, Kyiv and still lack results on regularity, Novosibirsk. smooth continuation, bifurca- I see mostly positive sides to tion, and stability of solutions, mathematics; the only draw- comparable with the rich theo- back I can think of is that it ries of parabolic, elliptic or is not funded well enough. ordinary differential equations. Applied (or sometimes seem- In the last years, with colleagues, ingly applied) sciences are well we managed to make progress funded, whereas fundamental in this direction, obtaining sciences such as mathematics interesting results on Fredholm lack funding. I appreciate the solvability, bifurcation and sta- fact that the Humboldt founda- bility analysis, and propagation tion, from which I got a fellow- of singularities in the hyper- 58 59

Kaisa Matomäki

Kaisa Matomäki was born in Nakkila, Finland. She first studied Mathematics at the University of Turku, and then at the Univer­- sity of London Royal Holloway, where she obtained her PhD in Mathematics in 2009 under the supervision of Glyn Harman, with a thesis in analytical number theory. Since then she has worked Topics of research: at the University of Turku, where she was appointed as a tenure – number theory track Associate Professor and as an Academy Research Fellow – multiplicative number theory in 2015. She is an invited speaker at the European Congress of – prime numbers Mathematics in Berlin in 2016. – additive combinatorics 60 61

How and when did Were you then encour- Did you come across you choose to do aged by your family, obstacles in pursuing mathematics? friends or other people your career as a mathe- During the last year of elemen- around you? matician? tary school I had an excellent As a child, I learned a lot No, I didn’t experience any ob- teacher who would give me from my brother who was stacles. I was recently appointed extra maths tasks. As well as 4 years older than me, and to an associate professorship maths, as a child, I enjoyed who would tell me about what at the mathematics department writing and reading, but mostly he was learning at school. of Turku, which I will hold I liked mathematics. Then, at He’s now a statistician working after the 5 year long research the age of sixteen, I went to a at the Turku University hos- position I won simultaneously. special mathematically-oriented pital, where he takes care of On the national level, we were school in Valkeakoski, some the statistics for the medical three to get such a research po- 100 km away from my home researchers. sition, amongst whom two were town. I’d heard about someone My parents, who have now women. I obtained this position who had been to that school retired – my mother was an the second time I applied, after and so I wanted to try it out. I elementary school teacher, my one failed attempt. took the entrance exam and was father a farmer – were very I expect to have a second baby accepted among some 20 pupils supportive. On the one hand in February 2016 and will out of the 80 applicants. Nokia they were proud that I could probably be on maternity leave funded our board and lodging attend a special school for gifted for about a year; the period of and we worked part time for children, on the other hand, well-paid leave is 10 months. them. I spent two years at that they missed me, lamenting that During my maternity leave, I school before the matriculation the school was so far from our will also have my 3-year-old exam (which corresponds to home town. But I was happier son at home, since I don’t want A-Levels). During those two at this school than I had been him to be in day care while I am years, we attended extra uni- at my previous school, where at home. I had a lot of time to versity courses delivered by I had suffered from being dif- think about mathematics when advanced university students, ferent from my school mates. I was on maternity leave for both in computer sciences and I enjoyed the atmosphere at that my first child, even though I mathematics. While at that special school, and have kept didn’t have much time devoted school, I first considered the friends from that time, some solely to work. I’m not sure idea of becoming an engineer of whom studied in Helsinki, how it will work out this time but later changed my mind, where they are now working. with two children. However, as opting for mathematics, which Among the 20 pupils in the I have a quite secure position I then studied at Turku Uni- class, only 4 were women; and an official maternity leave, versity. I chose Turku, a middle the proportion has probably I am not really worried even if size town, rather than Helsinki. increased since them. I do not get much mathematics Also, Turku was known for its done for a year, but can happily number theory group, and I devote time for the family. was already interested in num- ber theory. 62 63

What would you recommend to a young woman in your coun- try wanting to start a career in mathematics? I would tell her to just try it out, and not to care too much about other people’s comments. I would encourage her if she showed some enthusiasm and her credentials were good. As a matter of fact, I would tell a man or a woman the same thing. Could you write a few lines describing your topics of research in a manner understandable to non-experts? Among other things, I am in- terested in the distribution of prime numbers; the larger the numbers, the scarcer the prime numbers. However, one still expects that there are infinitely many twin prime numbers, namely pairs of prime num- bers of the form (p,p+2), such as (5,7) and (17,19). This is a major unsolved conjecture in number theory, but for instance one does know that there are In retrospect, are you I have no regrets, since mathe- When I get stuck, I try to leave infinitely many primes p such happy to have chosen matics is what I enjoy doing. I the problem aside for a while that p+2 is either a prime or a mathematics or do you like doing research, having new and to think about something product of two primes. Another have some regrets? ideas, but do not like getting else. I have many collaborators famous unsolved problem in For you, what are the stuck on a problem, which is a who can help me overcome the the area is the Goldbach con the joys of mathe- source of frustration. To have problem. Ideas go back and jecture, stating that each even matics? What are the a new idea is exhilarating, I get forth between me and my integer at least 4 is the sum of hardships excited and can hardly sleep. collaborators, some of whom two primes (e.g. 10 = 3+7 and I am eager to go on thinking may well find a solution to a 16 = 5+11 = 3+13). It is known about it, and sometimes go on problem I couldn’t solve. that every odd integer at least doing so at night. 7 is a sum of three primes. 64 65

Some of my recent research Could you describe result on general multiplicative concerns the combination your favourite personal functions. of these two approximations achievement in mathe- It turned out that the method of the famous conjectures – matics? we developed could give rise to my collaborator Fernando I am proud of work I recently interesting results concerning Xuan­cheng Shao and I showed did with Maksym Radziwiłł. other problems. Other people, that each large enough odd He came up to me after a talk including Terence Tao, have integer is a sum of three primes I gave in Oberwolfach, on since used our approach to

p1 + p2 + p3, where each prime Fourier coefficients of modular establish some of their recent pi is such that pi + 2 has at most forms. Together we managed to results. two prime factors. improve my results and started These are relatively easy ques- to investigate some generalisa- tions to formulate, easy prob- tions. Our first achievements lems to state. I do not know in view of a generalisation were of any practical applications, pretty unsatisfactory results on but there might be some in sign switches of multiplicative cryptography for some related functions, but eventually we problems. ended up proving a very nice 66 67

Margarida Mendes Lopes

Margarida Mendes Lopes was born in Portugal. Shortly after her degree in mathematics, she got a job in Lisbon as an assistant, after which she moved to the UK and got a PhD in Mathematics from the University of Warwick in 1989 under the supervision of Prof. Miles Reid. In 2002 she obtained the Agregação em Matemática and shortly after was appointed lecturer at the Uni- versity of Lisbon. In 2003 she moved to the Department of Math- ematics of the Instituto Superior Técnico as Professora associada com agregação and retired in 2014. Currently she carries on Topics of research: doing research at the Centro de Análise Matemática, Geometria e – algebraic geometry Sistemas Dinâmicos (CAMGSD) of the Instituto Superior Técnico. – classification of Alongside her teaching activity, she has engaged in several ad- projective varieties ministrative duties such as research evaluation, refereeing, and – surfaces of gene­ral type coordinating large scale research projects in algebraic geometry. – bicanonical maps 68 69

Were you then encour- aged by your family, friends or other people around you? My mother was a mathemati- cian, working at the University of Lisbon, but I did not follow her, as she did not talk to me about mathematics. As any teenager would do, I did not talk with her much, whether about mathematics or other things! My mother was mainly involved in teaching. Research in Mathematics was very incip- ient at the time, mostly because of the brain drain caused by the dictatorship in the 1940’s and 1950’s. My father was a Uni- versity professor in anatomy. It was therefore expected that my siblings and myself would take university degrees. My younger sister is also a math- ematician, and very much involved in teaching; my other sister is a veterinarian, now working as a translator for the EEC. My brother became a jurist. How and when did ics, even if I could not choose took the final exams (Maths, you choose to do mathematics as a subject at Descriptive Geometry and mathematics? school. Indeed, if you chose Physics) required to apply for I used to enjoy numbers and to study history at university a degree in mathematics. This geometry at primary school. I as I had done, you had to take way, I could start studying was twelve when I first chose humanities during the last two mathematics at the University to do mathematics. At the age years of high school. I chose to of Lisbon. I still enjoy reading of fifteen, I opted for history switch to science three months history books and historical instead. During the last two before the final exams and the novels, but I do not think I years of high school, I was end of my second year. So I did would have liked working mainly interested in logic and all the subjects in humanities in history as much as I enjoy Latin and so in the final year I I was supposed to do to finish mathematics. decided to turn to mathemat- high school and in addition I 70 71

Did you come across which, combined with a high obstacles in pursuing teaching load, made it difficult your career as a mathe- to finish writing my PhD thesis. matician? During the last stage of writing I never really came across ob- up my thesis, my intention was stacles; I feel that Portuguese to finish as soon as possible and academics offer equal oppor- then try to find a completely tunities to men and women. I different job; but in the process chose to have children; had I of writing I got enthusiastic not had children, I might have again for research. started producing research In retrospect, are you earlier. I am very proud of my happy to have chosen children and do not regret my mathematics or do you choice. I consider myself very have some regrets? For lucky with the career I led. you, what are the joys In the 30’s many Portuguese of mathematics? What mathematicians were forced are the hardships? to leave the country, which I have no regrets at all. In explains in part why in the 60’s ­mathematics, hardships arise the academic environment was when you spend months look- rather poor in Portugal. After ing for a solution which does the end of the dictatorship in not work out. But what you 1974 some of them came back have then achieved can turn out and more opportunities to to be useful for some purpose. study abroad arose. This and Also, finally finding the solu- the increasing investment in tion is a source of pure joy. science in the 80’s created a I have to admit that I was about rich research environment. to give up doing mathematics Portuguese mathematics has when, as a mother of young since then grown very rapidly. children, I was trying to finish Shortly after my degree in my thesis, which finally took mathematics, I got a job in me 8 years to write up. At Lisbon as an assistant. At that that time, I could not dedicate time it was possible, with some enough time to my work and effort, to get a grant to do a felt rather isolated in Lisbon PhD abroad. So in 1980, I chose before the era of internet and to do my PhD in Warwick, Skype. These are some of the where I spent three years and reasons why I started publish- had my first child. Then my ing rather late in my career. husband, who is an engineer, and I returned to Lisbon with the child. I actually had my three children in five years 72 73

What would you rec- ways of characterising them ommend to a young by means of new theorems is woman in your coun- a very creative process, similar try wanting to start a to that of a composer finding career in mathematics? a new melody or, for a photo­ My recommendations would grapher, finding a new interest- be the same for a woman as for ing angle and viewpoint on the a man. You should make sure object to be photographed. that you enjoy mathematics be- What is the personal fore opting for research in that achievement you are discipline. I know people who most proud of? enjoy reading mathematics, but I am particularly proud of the do not aspire at doing research. results in some of my papers, You should not choose to do particularly the one on Burniat mathematics if you want to surfaces which solves a problem make money; your salary as a I suggested studying and which mathematician will never cor- took us (me and my coauthor respond to the amount of time Rita Pardini) some three to four and energy invested in your years to solve. I like the way work. You should be confident, we wrote this and other articles ask questions, try out crazy and I am proud of having pub- ideas and follow your instinct. lished in many journals I used Nowadays, it is not easy to to admire as a student. I am follow an academic career, also proud of having been the but you should keep in mind first active algebraic geometer that you can do many different in Portugal and to have initi- things with mathematics, ated building up a community working at university is not in Portugal around this topic, the unique option. a community which includes Could you explain your rather isolated mathematicians topic of research in a working in small universities manner understandable around the country. to a non-expert? Last but not least, I am very I study shapes of sets, which proud of the way my husband you can think of as doughnuts, and I raised our family! cones, and so on. In mathemat- ical terms, I work on problems in classification of algebraic complex surfaces. I try to under­stand what their differ- ences and similarities are and look for ways to distinguish or to identify them. Finding new 74 75

Barbara Nelli

Barbara Nelli obtained her PhD in Mathematics at the University of Pisa and at the University of Paris 7 under the supervision of Harold Rosenberg. She was a postdoc in Paris, and a Humboldt fellow at the Technische Universität Berlin. In 1997 she became Topics of research: Ricercatore at the University of L'Aquila and in 2005 she was – geometric analysis appointed Professor at the same University. She is a member of – minimal surfaces the Scientific Committee of the Unione Matematica Italiana. She – Dirichlet problem is a regularly invited professor at the University PUC and UFRJ of – geometric maximum Rio de Janeiro, at the Universities of Paris VII, Tours and Granada. principle 76 77

How and when did Were you then encour- you choose to do aged by your family, mathematics? friends or other people At school, I had always been around you? “good at maths” and liked this I was left free by my family subject, even though I also to choose to study whatever enjoyed other subjects, such as I liked. The encouragements I history. Because I liked doing got came from my mother, who mathematics, I then chose to held one’s financial autonomy study mathematics at univer- and independence to be the sity. Another subject I found most important thing. I was tempting was law, and I also confident and had no doubts considered studying physics. about getting a job as a math- I thought law would appeal to ematician, which at the time me because of its internal logic, was objectively feasible. A very but soon found out this was good mathematics and physics not the case. Also, I realised I teacher I had in high school understood mathematics bet- might have had some influence ter than physics, so I decided on my choices. on mathematics. I knew that Did you come across mathematics could be useful to obstacles in pursuing find a job, maybe in a private your career as a mathe- company. I never thought I matician? would do research though; it I started my PhD in Pisa and, was the Master’s thesis (a the- in agreement with my PhD sis work you do in Italy after adviser there, applied for an 4 years’ studying) that triggered Erasmus grant to study in my decision to opt for research. ­Paris. There I worked under the So I applied for a PhD fellow- supervision of Harold Rosen- ship, and simultaneously went berg, at the University of Paris through the hiring procedure VII. After that I applied for for a position at IBM, which jobs in France, but at that time I eventually got. At that time, being Italian made it harder you would receive many offers to find a job in France, more from private companies when so considering that my PhD you had a mathematics degree. adviser was American and not The application for the PhD French. When I came back to fellowship meant taking a com- Italy, I easily found a job as a petitive exam, which I found “Ricercatore” in L’Aquila in much more challenging than the 1997 – where I am still working hiring procedure at IBM; I liked now – on the grounds of the the challenge and declined the quality of my CV. Then I was IBM offer. confronted with the problem of 78 79

getting a promotion. The fact that I wrote my PhD in France and not in Italy has influenced my career, both positively and negatively. Positively, because I work on a rather unusual topic in Italy, which gives me some independence, which I value very much. Negatively, because this very fact might have been one of the reasons why it took a long time for me to get an assis- tant professorship. I passed the “Idoneità” (a competitive exam which enables you to apply for such a position) in 2003 and was actually promoted in 2005. I am still not a full professor although I was selected for “Abilitazione” (habilitation) in 2013. This is a selective procedure, unrelated to a position. Ac- tually, due to the lack of full professor positions in Italy, particularly in geometry, among the fifty odd people who were selected for the “Abilitazione” In retrospect, are you free to think about what you it. When you have found a way at the same time as I was, only happy to have chosen like, to choose a problem and to approach the problem, you five were appointed professors mathematics or do you the way to solve it. I see math- usually still have a long way and two of them are women. have some regrets? For ematics as a creative job, rather to go before actually solving The statistics show that fewer you, what are the joys than a useful job. Mathematics it. It is often much longer than women than expected apply to of mathematics? What is made of layers, the upper you might have anticipated! get the “Abilitazione”, in spite are the hardships? layer cannot exist without the I went through times of dis- of their merits, which speaks I have no regrets, none at all. lower one. But when you reach couragement; a few years after to the fact that women censure Mathematics gave me the the top layer, you do not see my PhD, I was then already themselves, a widespread opportunity to discover the what the bottom layer looks working at l’Aquila, I felt I had phenomenon among women university world, which was like. reached a dead end, I did not due to cultural reasons. completely new to me. Math- Mathematics is a very difficult know what to aim for in terms ematics is very creative; as a subject, not easy at all! The of my research and how to go mathematician, you are very difficulty comes from having to on. I thought of quitting and independent and can organise find a reasonable problem and working for a private company yourself as you wish. You are an appropriate way of solving and actually enquired at an 80 81 insurance company. The little I fact that to be a professor at Could you describe saw of their way of functioning univer­sity, especially in mathe- your research field to a put me off and convinced me matics (viewed as very abstract lay person? that my place was at university. and not useful, no money in- I study soap bubbles, from a I then found a new impulse volved) is not a highly valued mathematical point of view; to work on new directions of job in Italy. So, it is easily left they are constant mean cur- research. to women. vature surfaces. The mean Working with other people I What would you rec- curvature you can imagine as enjoy a lot, because sharing an ommend to a young the pressure and a soap bubble idea is the best part of having an woman in your country with constant mean curvature idea. I share with someone who wanting to start a career is like one at rest. I have to con- in turn shares with me. Work- in mathematics? fess that I am not interested in ing with young people is also A student in Italy who has a applications, so not in the soap very nice; as a senior mathema- degree in mathematics, I would bubble itself but rather in the tician, you have many things encourage to go abroad, help- mathematics inside it. to tell them and in the best of ing out by suggesting places. Can you describe cases, you get unexpected feed- This for two reasons, because your favourite personal back from them; you give them I believe that living and work- achievement in mathe- something and get a lot back ing abroad is very useful both matics? from them. mathematically and on a human A personal achievement I For a long time, I did not see level, and also because there are ­vividly recall, despite the fact myself as a woman working hardly any prospects for him that it is very simple, is some- in mathematics, but simply or her in Italy. I would encour- thing that happened while I as a mathematician. Only age a woman or a man in the was in France for my PhD. I relatively recently did I real- same way, for I believe that the had come to work with Harold ise, at a conference in Bonn, difficulties one encounters as Rosenberg, and had told him so that there were only men in a woman in mathematics are when I first met him. During the room. It is difficult to tell the same as in any job, and not one of the classes I took with whether I never experienced specific to mathematics. him, he asked me to solve the any discrimination in being a My job is not to tell a young following problem: “Show that woman, or whether I just did woman mathematician about the solution of a positive Gauss not see it as a discrimination. the difficulties she is to expect, curvature equation on a punc- I do not think I experienced it is rather to make her path as tured disc extends continuously any discrimination as a woman a mathematician easier. It might to the disc”, which I indeed in mathematics, although there be better for a young woman solved. This, I think, was what are hardly any women working mathematician not to be aware triggered his decision to super- in my area of research. How­ of the many obstacles she might vise my PhD thesis. ever, interestingly, in Italy there encounter; she could not do Long after my PhD he told me is a higher proportion of wom- much about it anyway. I had been the first female PhD en in mathematics than there student he had had. is on average in Europe, even if not at the top positions. I believe that this is due to the 82 83

Dušanka Perišić

Dušanka Perišić was born in Novi Sad (Serbia), where she studied Mathematics and obtained her PhD in Mathematics in 1992 under the supervision of Stevan Pilipovic, with a thesis on integral transforms and generalised functions theory. In 1993 she was appointed Assistant Professor at the University of Novi Sad, and in 1997 she became an Associate Professor. Since 2003 she is a full professor and Vice Dean of the Faculty of Natural Sciences and Mathematics since 2006. She is an active member Topics of research: of the European Women in Mathematics (EWM) organisation: in – functional analysis 2009 she was the main organiser of the EWM meeting in Novi Sad. – generalised function theories 84 85

How and when did you choose to do mathematics? As far back as I can remember, I enjoyed solving problems and liked mathematics as a child. In high school, I knew that I wanted to continue studying, but was not sure what to study. After the end of high school, I chose to have some time off during the holiday instead of spending the summer prepar- ing an entrance examination for university. Since sciences required no entrance exams, I opted for mathematics! In hindsight, this was a very good choice, since the courses I took during my first year at univer- sity gave me an idea of what mathematics was really about. It was rather different from what I had been taught at school! I found the material taught to us at university amazing; it was a revelation for me! I enjoyed the abstract point of view and going my mathematics teacher reacted They were somewhat surprised thirties, and finally the war our to the essence of the problems, very well, supporting and en- that I chose mathematics but country went through. They and I knew that I wanted to be couraging me, and I remember they supported me, and were had a great impact on my life a mathematician. I still do. her telling me “You will become proud to have a mathematician and career. Were you then encour- a mathematician!” I myself in the family. I had a scholarship to spend aged by your family, was sure that I would succeed, Did you come across a semester in Austria after friends or other people but not that I would become a obstacles in pursuing my Master’s degree, and my around you? mathematician! your career as a mathe- wish was to do a PhD in the During the second year of high I was indeed good at school and matician? US. I applied for a Fullbright school, I was seriously injured both my parents expected me to The biggest obstacles I met scholarship, not realising how in a car accident, lost my sense study, so did my older brother. were the long period of eco- prestigious and difficult it was of balance for two months and My father was a professor in nomic and scientific sanctions to get, but it turned out that I had to miss three months of the Faculty of Law, my mother imposed on my country, was indeed selected and there- school. In contrast to the other was a high ranked company subsequently hyperinflation, fore offered the scholarship. teachers who were worried I lawyer, and my brother had just comparable to the one which I was waiting for the official would repeat the school year, become a solicitor, at the time. happened in Germany in the confirmation to leave for the 86 87

A year after the war was over, I realised I was still trauma- tised; as I was working one day with a colleague, I reacted with anguish to the sound of sirens. I suddenly felt the urge to stop working and run to my family, as I would have done a year before. I relaxed when my colleague told me it was only a radio programme commemorat- ing the first year anniversary of the end of the bombing! Fortunately this difficult period came to an end. We were grad- ually going back to a normal daily and scientific life. A few years later we got access to international journals online. To me, this felt like a miracle; I was glad to be part of the world once again. The difficulties I just described are not specific to women. However, I do have to say that it took me more time than ex- pected to become a professor. US when I received a letter The only way to find out what of children, preparing papers I was lucky enough that one (which I have kept) informing was going on in science was to for publication … But the war colleague of mine, with a rather me that, due to the economic ask colleagues from abroad to came right to our doorstep. My independent mindset, helped and scientific sanctions in that send photocopies of the newly family and my neighbourhood avoid slowing down the promo- part of former Yugoslavia (this published papers by mail. For- survived 72 days of bombing tion procedure unnecessarily. was in 1991), my scholarship tunately people were ready to and from ten to twelve hours In retrospect, are you had been ­“suspended”. So in- help, and it was possible to do every day without water and happy to have chosen stead I did a PhD in Novi Sad mathematics. My first child was electricity. My second child was mathematics or do you which I defended in 1992. This born in 1993, so she was raised then very small, some 5 months have some regrets? was possible since I had already at a time of hyperinflation. We old, and I got his nappies on What are for you the published some papers on my had to learn how to survive in the black market. In such cir- joys of mathematics? own, a requirement to start a spite of the difficult economic cumstances, you do not have I do not have regrets! “Je ne PhD at my university. Because situation. The war came very time to think, you just strive for regrette rien!” I am now very of the so-called scientific sanc- close to my university, but we sur­vival. Today, I can hardly be- confident and feel less pressure. tions, the access to scientific went on living almost normal- lieve all that ever happened. I have decided not to worry journals, books etc was limited. ly. I was teaching, taking care any longer and to simply enjoy 88 89

myself. My past could have of which I am very proud. It been easier but I coped with brought to Novi Sad the “rock it the best I could. The many stars” of mathematics, Michele obstacles forced me to slow Vergne a member of the French down and sometimes to stop, Academy of Science, Ingrid which is maybe a good thing to Daubechies who later became do now and then. I am thankful the president of the IMU, Marta for this project, because it gave Sanz-Solé who later became me the opportunity to think president of the EMS, Barbara back. Rarely do I do that, and Lee Keyfitz then vice-president in retrospect, I consider myself of the ICIAM, Nalini Anan- lucky: I had the opportunity to tharaman who won many pres- teach, to have children, to be tigious prizes in mathematics, successful. Cheryl Praeger and Ragni Piene What would you both members of the Abel com- recommend to a young mittee, Frances Kirwan then woman in your coun- convenor of EWM and who try wanting to start a was later knighted. They were career in mathematics? ready to help and advise young I would advise her to jump into participants. the water and give it a try. It is I am also proud of being a important to be confident, but good teacher and enjoy my this does not mean you should job, which I do as honestly as know everything. Just do your possible. best, try to have a network of Could you write a few people who can help you. It is lines describing your good to have an adviser you topics of research in a trust. Through all these experi- manner understandable ences, I have learned to be open, to non-experts? to stay in touch with other I am working in a field of people, and to be ready to give ­mathematics called functional to people without expecting analysis. The functions as we anything back. learn to draw them at school, Could you describe the smooth ones, do not de- your favourite personal scribe many of the natural or achievement in mathe- human made phenomena. To matics? describe nature we need wilder Through Sylvie Paycha I got functions, jump and discon­ in touch with EWM (European tinuous functions and their Women in Mathematics) where derivatives, such functions we I met many interesting people. consider in functional analysis. I organised an EWM meeting in 2009 in Novi Sad, an event 90 91

Katarzyna (Kasia) Rejzner

Kasia Rejzner was born in Cracow and entered the Natural Sciences course at the Jagiellonian University of Cracow in 2004. She is interested in mathematical structures underlying Quantum Field Theory, an interest triggered by a term spent in Göttingen ­­in 2008, where she first learnt about Algebraic Quantum Field Theory (AQFT). In June 2009 she finished her undergraduate education with distinction and started a PhD in Hamburg, in mathematical physics, under the supervision of Prof. Klaus Fredenhagen. She Topics of research: defended her thesis two years later in 2011, after which she did – mathematical physics a one year postdoc at the Mathematics Department in Hamburg. – operator algebras She spent a year in Rome “Tor Vergata” as an INdAM (Marie Curie – algebraic quantum Actions) postdoc fellow, and then in 2013 was appointed lecturer field theory at the University of York (UK). – renormalization 92 93

Were you then encour- aged by your family, friends or other people around you? Both my parents are architects and they expected me to go into arts, following my artistic inclinations. They were very surprised to hear that I wanted to do maths and physics, but supported me in my choice, as they had always encouraged my natural curiosity. During the first years of my studies, my friends were in artistic circles and I still enjoy artistic activi- ties very much. I see analogies between doing maths and art, which I also enjoy doing; in both you are confronted with a problem for which you need to work out a solution in an imaginative way. With time, my parents also realised that doing maths is a very creative activity and supported me all the more, as they had always wanted to stimulate my creativity. Did you come across How and when did Krakow University (which taking courses in functional obstacles in pursuing you choose to do included maths and physics) analysis and operator algebras, your career as a mathe- mathematics? and found myself drifting more which I enjoyed very much, in matician? It was a long process; as a and more towards maths. The the maths department. During There are obstacles that every child I was naturally curious. decisive moment was my stay my stay in Göttingen, I started mathematician meets; searching My first fascination was for in Göttingen as an Erasmus working on research problems for a job after one’s PhD was physics; I had a good physics student during the summer in mathematical physics, which a difficult time for me. During teacher at primary school, I ­semester of 2008. I found the confirmed my taste for making this job hunting process, women was then some thirteen years atmosphere in Göttingen with statements in physics precise, do not get much support from old (7th grade). In high school the coexistence of mathemat- figuring out why this or that society, which in Poland, the I was lucky to have a good ics and physics fantastic. I equation holds true. In 2009 country where I come from, is maths teacher, who drove me was hosted by the algebraic I went to Hamburg to start a rather conservative. Women are into ­doing maths. I later chose quantum field theory group at PhD thesis in this research field. not expected to set job-hunting to study natural sciences at the physics deparment, whilst around Europe as their primary 94 95

goal at that stage in life, it should sure: searching for funding, What would you rec- come only after building up a being an excellent teacher, and ommend to a young family and raising children. For an excellent researcher puts a woman in your coun- this reason I still feel somewhat lot of pressure. Even more so try wanting to start a guilty/uncomfortable because when you are a perfectionist as career in mathematics? of my life choices. I am and want to do everything When you start studying math- I wish the atmosphere at perfectly, which is impossible. ematics as a subject, you should Polish universities were more I suffered from not being able start looking for opportunities relaxed; I would not want to to do research during the first to go abroad for at least a few work in Polish academia, since year of my present job, but I months. Even though most of I have heard that some “old believe I have now reached a my country-fellow colleagues school” professors still tend to balance which enables me to might want to go back to Po- look down on young women do research. There are ups and land later, having benefitted colleagues. Also, one is freer downs in my job, moments of from some international expe- to pursue one’s own research dark depression and others of rience is very important. But interests and develop one’s exhilarating euphoria. Difficult most important is not to let own ideas in the UK and in times of doubts when you get other people discourage you Western Europe in general. stuck on a problem contrast from doing mathematics. At Nevertheless, things are chang- with the good moments when school, both in Poland where ing in Poland, so I do not ex- you find the answer to a prob- I come from, and in England clude going back to my native lem, a source of much joy and where I work, girls are some- country completely. fulfillment. These ups and times told they are not expected In retrospect, are you downs also may be part of my to be “good at maths” since happy to have chosen personality. The good sides of “maths is hard”. I think a slo- mathematics or do you my job are the flexibility of our gan could be: “Mathematics is have some regrets? For working hours, the freedom not hard, it’s just different!” you, what are the joys you have to choose the topics It is a somewhat different way of mathematics? What you work on, the exposure to of thinking, that’s all! Another are the hardships? new ideas it offers, the possibil- important advice is: “Don’t be I am very happy to be doing ities it gives you to meet very afraid of being wrong!” Mak- mathematics, which is what I interesting people. I particularly ing a mistake should not be a really wanted to do and I do enjoy the creative process we go reason for getting discouraged. not regret not choosing arts, through together when doing You need to explore many which I still do as a hobby. I research with colleagues and things before finding a good paint, do graphics and design, friends. idea. In mathematics, there is a depending on my time con- clear cut between what is right straints of course, but I still or wrong, and it is easy to make hold on to these hobbies. a mistake, so do not fear mak- I like my job very much! Of ing a mistake in front of your course there are good and colleagues. Keep in mind that bad sides to it; it can be a very it is easier to be wrong than to stressful job. As a faculty be correct. You have to learn member, I feel a lot of pres- to defend your ideas and not 96 97 feel personally attacked when main interests are in functional they are criticised. This I found analysis, homological algebra, difficult when I started, but my and some aspects of geometry. PhD advisor told me I should I adopt an (operator) algebraic not take it personally and use point of view in my work and the criticism in a constructive the general research field I am way. He gave me lot of support working in is called algebraic and advice at the beginning of quantum field theory AQFT( ). my career and keeps on doing I sometimes use analytic tools, so. I would like to pass on the but cannot describe myself as a same advice for other young hard analyst. women starting their career in What is your personal mathematics. I used to fear I achievement in math- was not made for mathematics ematics you are most and would look for people to proud of? tell me I was on the right track. What I am most proud of is You need to develop a personal a result I got in my PhD conviction that you “are a thesis, namely how gauge mathe­matician”, and that what theory and gravity fits into you are doing makes sense. the Epstein-Glaser approach However, I feel the most diffi- to renormalization, a simple cult issue for women is the lack formulation I reached after of permanent positions. Many reading many complicated women quit after their PhD, physics articles I found diffi- one of the reasons being that in cult to make mathematically our society it is less common precise. for a man to follow his wife than conversely. Could you describe your topic of research in a manner understandable to non-experts? I am working on mathematics applied to the physics of very small constituents of matter, so on mathematics underlying particle physics. In physics, this branch is called quantum field theory, and its precise mathematical structure and formulation is still unclear. Many topics of mathematics are involved in this area and my 98 99

Katrin Wendland

Katrin Wendland studied at the University of Bonn, where she obtained her diploma in Mathematics in the group of Prof. Werner Müller, and her PhD in Theoretical Physics in the group of Prof. Werner Nahm. She was a postdoc at UNC Chapel Hill and became Lecturer at the Mathematics Institute of the University of Warwick in 2002. In 2006, she was appointed Professor (Chair for Analysis and Geometry) at the University of Augsburg, and since 2011 she is Professor for Mathematics at the University of Freiburg. In 2008, she was awarded a Starting Independent Researcher Grant in Topics of research: Mathematics by the European Research Council. In 2010, she was – geometry and quantum an invited sectional speaker in Mathematical Physics at the Inter- field theory national Congress of Mathematicians 2010 in Hyderabad, India. In – Calabi-Yau manifolds 2013, she was elected full member of the Akademie der Wissen- – conformal and topological schaften und der Literatur Mainz. quantum field theory 100 101

How and when did fered to organise a one week you choose to do internship at a radio-telescope mathematics? near Bonn for me. I went from I chose mathematics and phys- one research or technician's ics after secondary school. I also group to another, which gave liked other subjects, such as me a glimpse into the tech- German; I used to like reading niques they used, that all looked and writing, and still do. I was very exciting. But seeing them also intrigued by history of arts staring at their screens in the and architecture, but did not evenings looked much less ap- think I was creative enough for pealing. I did not like this part those subjects. Philosophy and of their work and decided I en- ancient Greek also attracted me. joyed mathematics much more! But most of all, I loved math- Then during my study, after a ematics and physics. I found talk I gave at a representation mathematics easy and physics theory seminar led by a physics somewhat difficult, succeeding professor who had a very math- all the same. My father is a ematical approach to physics, mathematician, which actually I was lucky enough to be ap- made me hesitate whether or proached by him, offering to not to follow his path. take me under his supervision I then decided that I should go for a PhD. I thought this was for the subjects I liked most, a good opportunity to become but I was not sure whether to bilingual in mathematics and choose mathematics or physics physics and therefore decided and followed his advice to do to do my PhD in theoretical both, but to concentrate first physics. on one of the two. He thought Mathematics requires a lot that learning abstract topics is of creativity. I will not judge easier while you are young, and whether or not I am creative, he suggested to leave the more but I definitely have a lot of applied ones for later on. This ­curiosity. This is similar to the is why I first focused on math- enjoyment that I feel when I ematics but kept on studying travel to new places, exploring physics. them and then, too, experienc- I actually dreamt of becoming ing the thrill of being lost in a an astronomer, and attended city I do not know. courses at the planetarium at Were you then encour- the age of 16. At the University, aged by your family, I took physics and mathematics friends or other people courses, attending astronomy around you? classes as well. A PhD student Yes, absolutely, I was always in astronomy that I knew of- encouraged by my parents to 102 103

do what I liked doing, they let In retrospect, are you me follow my intuition. Know- happy to have chosen ing that I had support from my mathematics or do you family helped me. However, have some regrets? For seeing my father work non-stop you, what are the joys throughout my childhood made of mathematics? What me think I was not going to do are the hardships? the same type of job, but I later I do not have any regrets, as a changed my mind. principle, not only in mathe- Did you come across matics; you never know how obstacles in pursuing things might have turned out, your career as a mathe- had you made other choices. I matician? enjoy being surprised by math- In Germany, there is social ematics and its intrinsic diffi- pressure which can be discour- culty. The moment I enjoy best aging for women wanting to is when the pieces of the puzzle become professional mathe- fall into one coherent whole. maticians. I personally did not Understanding or solving a experience such obstacles, prob- problem is a real source of joy. ably because my family taught I do not mind working alone, me not to care too much what which can be a hardship for other people think. I believe some. But I love discussing this helped me to steer through mathematics with others, for it situations where only much lat- gives you other viewpoints on er I understood that they were things. Teaching is also a very supposed to be obstacles. I used nice part of my job. I enjoy to have many doubts about helping students out when they myself, particularly when be- get stuck on a problem. The tween my Masters and my PhD. many different aspects of math- With time I learned to gain in ematics make it a very appealing patience, and doubt less. I now subject. realise from my experience as Frustration sometimes gets a mentor for young women in the way. I can get very mathematicians, that women angry with myself when I have more doubts about them- make mistakes, but with time selves than men do. During the and experience, I have learned rough time I had between my that it is a good thing to ex- Masters and my PhD, I kept plain a mistake – even in front myself going by thinking that, of students: They will not since I had the privilege over question your expertise for a many others to have gone that mistake you have made. far, it was my duty to keep going. 104 105

field theory, inspired by string theory, which is supposed to describe our universe. A moti- vation for string theory is the description of particles and their interactions. String theory is built on the idea that instead of point-like objects which evolve along curves, you should consider extended string- like objects that evolve along surfaces, which in turn can be placed within complicated geo- metric objects. These strings can ­vibrate – their “sound” so to speak encodes their properties – but the quantum behaviour of such strings is mathematically difficult to describe. We know now that string theory is not a completely satisfactory model, so there are new paths and many related geometric ques- tions to explore. Could you describe your favourite personal achieve- ment in mathematics? I am very proud whenever I What would you rec- If doubts emerge later on in her the right choice for her. It is can cross boundaries between ommend to a young career, such as thinking that she important to love the subject, subjects, finding myself at the woman in your coun- is not “good enough”, I would because one should expect to interface of different fields of try wanting to start a ask her why and tell her to trust come across difficulties. research. Such a position is a career in mathematics? her own abilities. Such doubts In any case, I would recom- source of great pleasure even if A young woman who has just often arise from a mere lack mend that she asks for advice it might feel rather uncomfort- finished school I would advise of self-confidence. It is a good from her peers and her seniors, Could you say a few tries, patterns you find in very able at times. The difficult but to give it a try, and be honest thing to be self-critical, but you maybe in the form of mento- words on your research ­diverse forms and everywhere challenging part is explaining with herself as to whether she should not put yourself down! ring, and that she shares the topic in a manner un- around you. The type of geo­ my work to people in other enjoys mathematics or not. I I personally proceeded step by problems she might encounter derstandable to non-ex- metry I am interested in is fields, a very rewarding exer- would recommend that she be step, not allowing myself to with people she trusts. There perts, describing your inspired by physics and my cise. I often feel like an outsider patient, and to keep on trying plan too far ahead. are lots of mentoring programs, topics of research? ­research work lies between at conferences, but conveying when an obstacle comes in the This said, if this young woman but talking to people is a first I am a geometer, and geometry mathematics and physics. my work to a community I way. does not “burn for mathe- and very useful step. is everywhere in this world. I work on very abstract phys- do not belong to is a source of matics”, then it might not be I am fascinated by symme- ical models such as conformal great pride. 106 107 a

Oksana Yakimova

Oksana Yakimova was born in Moscow. She studied Mathematics at the Moscow State University and obtained a PhD in Mathematics under the supervision of Prof. Ernest Winberg both in Moscow ­ Topics of research: and at the Rheinische Friedrich-Wilhelms-Universität in Bonn, – algebraic groups and where she moved to in 2005. In her thesis, she classified Gelfand Lie algebras pairs. She was later a postdoc at the University of Köln and at the – Poisson structures Friedrich-­Alexander University of Erlangen-Nürnberg. In 2011 she – harmonic analysis on was appointed Juniorprofessor at the University of Jena. Gelfand pairs 108 109

How and when did matics than we had at school, you come to choose to involving combinatorics, the do mathematics? induction principle for example. I come from Moscow, and In the eighth grade, I was then as a child I would spend my 13 years old, I took part in some summers at my grandparents', competitions in which I did in a village in Ukraine some surprisingly well. At the age 24 hours away from Moscow ­ of 16, I went to China in order by train. They were school-­ to take part in the mathematical teachers (my grandmother Olympic games for school chil- passed away and my grand­ dren as a member of the Rus- father retired long ago) and I sian team; six of us from Kazan, used to enjoy doing embroidery Moscow, and Saint Petersburg, with my grandmother. went to Tian Jin in this Olym- My grandfather had many pic exchange program. None books. I must have been some of us got the first prize, as far as 8 or 9 years old when amongst I remember. them I found a big book with At the age of 13, I changed mathematical quizzes such as schools for the third time to this one, which I still recall: attended a special class for How do you take a wolf, a goat children gifted in mathematics and a cabbage across a river to and physics, then a year later, I the other bank, without any of changed to one of the best spe- them disappearing, knowing cial schools in Moscow where I that the wolf eats the goat and remained from September 1993 the goat eats the cabbage but to May 1996. There were four the wolf does not eat the girls in the class of 19, which cabbage? later dropped down to 15 since I adored this book and solved some people left and one was the problem; I recall you needed expelled because he was not to cross the river quite a few ­doing well enough. I enjoyed times! In the 7th or 8th grade this school a lot; we had very (I must have been around 12 intensive teaching, six days a or 13 years old), my parents, week with six lessons a day, both chemists working at comprising algebra (4 lessons ­research institutes in Moscow, a week), geometry (2 lessons a seeing that I was so interested week) and analysis (3 lessons in mathematics, would take a week). At that time I had no me on Saturday afternoons to doubts I wanted to do mathe- classes delivered at Moscow matics, but now with the uncer- State University for school tainty of my professional future children. There, we would see­ in mind, I am not as self-confi- more sophisticated mathe- dent anymore. 110 111

Were you then encour- Did you come across I do not see the fact of being In retrospect, are you aged by your family, obstacles in pursuing a woman as a problem in my happy to have chosen friends or by other your career as a mathe- career. But I do have a vivid mathematics or do you people around you? matician? recollection of a train trip in have some regrets? For My parents had me enrolled at The special school I went to, 1995 with a group of some you, what are the joys the special school for mathe- school number 57, tends to twenty 9th, 10th and 11th grade of mathematics? What matics and took me to the classes produce “intellectual snobs”, as pupils (I myself was in the 10th are the hardships? at university when I was still one may be tempted to call us. grade) on our way to Saratov, I do not regret, not at all; a school girl, but they would And definitely this is how we quite far from Moscow, for a things I do regret lie outside have rather I studied chemistry, were looked upon as students at mathematical Olympic game. mathematics. I still enjoy their subject. My mother has the Moscow State University. It I recall the astonishment on solving mathematical puzzles a PhD in chemistry and has was a shock for me to be treated the (female) ticket officer’s face and in a way I am the same written various research articles. by the administration of the when she came up to me, the small girl with the big quiz She recently lost her job at the university in a very soviet man- only girl in the wagon since book. I like to find out as much research institute where she was ner. For example, they would the students who were accom- about a mathematical object as working, and is now working address us with the familiar panying us were also male. possible, just as you might want for a private clinic. My father “ty” form instead of the more I then realised that I indeed was to understand a person as well has a diploma in chemistry and formal “Vy” form we had been the only girl! as possible. Collaborating with is still working at a research used to in the special school. I In Germany, there are few other people is part of the fun; institute in Moscow. Chemistry did not feel as respected as I had women mathematician pro- I myself collaborate with people is different from mathematics, been as a school pupil. I took fessors; in Jena out of some from Italy, England and Hun­ in that it essentially relies on two diploma exams in parallel 10 members of our algebra gary. I enjoy inviting people, experiments. (in 2001), one at Lomonosov group, only one PhD student visiting them, going to con- At my first school, I must have University and one at the In- and myself are women. In Jena, ferences. But not yet having a been around ten years old, a dependent University, both of among seventeen full profes- permanent position is a source female teacher spotted me and which required writing a small sors in mathematics (including of worry and an unpleasant was pleased when I answered thesis. At the end of the second stochastics) there used to be ­situation for me. I cannot her questions. She herself was year, when you are supposed one woman, who has recently pro­ject myself into the future, frustrated to be working as a to find an advisor, I went to retired. to buy a flat for example is school teacher, since she had a Vinberg. There was not much Even though I enjoy collaborat- something I cannot do in my diploma in mathematics from choice then, for people like ing with women, I find it more situation. I do not think that the Lomonosov University in Gelfand and Kirillov had left. I difficult than with men, since the fact of being a woman is Moscow. She could therefore liked Vinberg and attended his we start talking about other the source of the problem, even not provide a very positive an- course intended for third year things; starting from mathemat- though it is true that usually a swer to my question, “what can students. I liked him as a person ics, we can end up talking about man gets the position in spite one do with mathematics”? and appreciated his style. He flowers! Men are much more of the fact that a woman was was very well organised, taught focused, no flowers with them! invited for an interview. Being in an interesting way, and was a Russian woman, which is always formally dressed. He what I officially am even if I looked the way a professor actually feel Ukrainian, is a should look! I am still in touch handicap. with him and gave a talk at his I do not enjoy teaching too seminar three weeks ago. much, maybe not at all! 112 113

Teaching students seems like Could you write a What is your favourite a hopeless task to me! Teaching few lines, in a manner personal achievement becomes enjoyable when you understandable to non- in mathematics? have students who understand experts, describing your In my PhD thesis – which I the material, but this is rare topics of research? defended at the Max Planck since students do not like to Take any object, and forget institute in Bonn in 2005 with think nowadays. When I was its colour. Take this cup for an MPIM fellowship – I clas- young, I thought you had to example; I can rotate it and see sified Gelfand pairs, which is think to become a mathemati- the same object; it is the same probably the best result I ever cian, until I met some PhD object after rotation. This is a got. Particularly flattering is the students at the Max Planck manifestation of a symmetry. fact that Joe Wolf included it in Institute in Bonn who told A ball has a lot of symmetries, his book “Harmonic analysis me the opposite; a comput- an infinite number, the cup has on commutative spaces”. er program, they claimed, is fewer. Different objects have I had to consider many special enough to generate an article. different symmetries. You can cases, and when I finished the But I believe that everyone combine two symmetries, im- classification, I spent a lot of needs to think, otherwise life plementing two rotations one time looking for an appropriate is too boring! after the other for example. formulation of the results. What would you One says that symmetries form More recently, I found a coun- recommend to a young a group. I am trying to under- terexample to a conjecture of woman in your coun- stand all the symmetries of a Joseph’s concerning symmetric try wanting to start a given object and conversely, to semi-invariants of biparabolics. career in mathematics? recognise an object from the I was actually trying to prove If she seemed to be hesitant, group of its symmetries. The Premet’s conjecture when I I would advise her to leave platonic solid I have in my realised that it was not true. mathematics, to do something hands for example, has many By a coincidence, the counter­ else! If you have doubts, just symmetries, but not infinitely example disproves Joseph's give up; finding a position later many. Using these symmetries conjecture as well! is too hard to be worth trying you can reconstruct the solid out mathematics if you are not from one of its vertices. Some fully convinced from the start. quantities, such as the length Fighting your way up is too of an edge, are preserved under tough if you do not love mathe- some symmetries, such as a matics. For a Russian woman, it rotation. They do not vary and is especially hard. The situation are called invariants. Using the in Russia is somewhat difficult distance as an invariant, you can and many mathematicians have put the solid inside a sphere. already left; the job market Symmetries are used in physics abroad is saturated. to describe fundamental parti- cles, which are characterised by their symmetry group. 114 115

Beyond mathematics Why and when did you decide to become a composer? I come from a culturally privileged family. My father is an architect, my mother a curator. I was very creative, as a child I would draw and write. Then I learnt to play the We present two more professions, the practitioners of which piano and was naturally drawn manifest the same enthusiasm for their work as the portrayed to composition, since I always mathematicians. The interviews with Elena Mendoza, a com- tended to be creative. Why I poser, and Matina Matoff, a midwife, contain certain already opted for music and not for encountered themes. another artistic discipline, I Like a musician, a mathematician needs to hone her craft. am not sure. Probably because Creatively speaking, she is somewhere between an interpreter music was less present at home and a composer. Only once she has mastered the necessary than other forms of art. Or skills, can she compose new concepts and techniques, which in perhaps this was a youngster’s turn have to be communicated to the wider community. After a reaction to her father, who had slow maturation process, a mathematician develops an intuition dreamt she would become an about specific topics in mathematics. In explaining a concept, architect. After a few years of she brings to life for the audience ideas already tangible in her piano studies, I realised that I mind. Similarly, a musical composition is the fruit of a long wanted to become a composer. germination, which is then conveyed by an interpreter. Elena Composition was the best way Mendoza speaks of "moments of total freedom" when compos- for me to express myself artisti- ing, an echo of Irina Kmit’s assertion that mathematics served cally. I actually started studying as a refuge for people lacking freedom in the Soviet Union. composition when I was twenty Creating and sharing, whether it is mathematics or music, is a three. Age tends to have a posi- source of intense joy. tive incidence on composition; Matina Matoff conveys the same contagious enthusiasm when a certain degree of maturity she recounts her experiences of assisting women in giving helps to study composition – birth. Hers is a risky profession, as a mistake would have Elena Mendoza in contrast to instrumentalists, drastic consequences, more so than a mathematician’s or a composer for whom starting very young composer’s. Matina is proud to play a role in a different kind is an asset. of creation process, but she had to give up a lot on a personal Were you encouraged level for her very demanding job. Some of the sacrifices and by your family, friends compromises which needed to be made by the portrayed or other people? mathematicians are evident from the interviews, and what they Sevilla, where I was brought surely share with Matina is a dogged pursuit of their goals, and up, lies on the edge of Europe dedication to their work. We invite the reader to find other and I was born during Spain’s surprising and striking analogies between such a priori differ- transition to democracy. After a ent occupations as that of a mathematician and a midwife. long period of isolation, many Spanish people felt the need 116 117 to open up to other cultures. will be played. For anybody, In retrospect, are you I need quite a lot of time to gives you a certain status. power driven authority, on the When I was a child, my parents, whether man or woman, assert- happy to have chosen write and consider myself to The big asset of a professorship contrary, we should protect it who wanted me to get an open ing oneself is a lot of work. this profession or do be slow. My feeling is that each is that one does not need to with pugnacity. minded education, sent me to There are fewer role models for you have some regrets? musical piece should be a new worry about making one’s Could you describe the German school in Sevilla. women. To be taken seriously For you, what are the project and lead to new ques- living. Usually a composer finds the main features of That is how I learned to speak in the first place is generally ­ joys of composition? tions; this is why I need time. it difficult to live from his or your profession as a German very early in life. more difficult for women What are the hardships? From a market-economy point her work. Since in my case, the composer to someone I studied music at the conser- than it is for men. Usually a Having a creative job fulfills of view, one could say it is material aspect is secured, I who is not acquainted vatory in Sevilla, which at the woman needs to achieve more a deep personal need. Had ­ ineffective. However, you can- can dedicate myself to artistic with it? time offered a rather low level than a man to become at all I not chosen composition, I not judge experimentation and projects that really interest me “Pure sound-impure music“, tuition. Thanks to a German visible. Luckily, the situation would surely have opted for artistic discoveries according and just take the time to carry the title of my opening concert female schoolmate, a flutist, has improved in recent years, another creative activity. The to efficiency criteria … and we them out. I do not need to pro- on the February 13th at the whom I had met during a sum- but we are still very far from pleasure of composing lies in should fight to defend this. duce music on a canning line, UdK, could serve as a motto for mer music course, I came to a genuine normality. A survey the time that you spend with Since I was appointed a year nor to earn my living by that. my composition. I consider the Germany at the age of twenty. led by Klangzeitort, our insti- yourself. These are moments of ago at the University of the What advice would sound as a complex phenome- I landed in Augsburg, where tute for contemporary music, total sense of freedom. Writing Arts [UdK in Berlin], I try to you give a young non, which is not a sheer super- this friend was also studying. In showed that the proportion of music makes me feel free, in keep a balance between my woman wanting to position of parameters such as Augsburg I studied the ­piano women represented in contem- that I can determine my own duties as a professor and a become a composer? pitch, duration, and so on. and later composition. The porary music festivals is only reality and not be determined mental freedom for creativity, My advice would be the same I wish to deal with sound the composition teacher, John Van 13%. Women are also really by the outside reality. Such between teaching, preparing for for a woman or a man. One same way one works with Buren, strongly supported me underrepresented amongst moments have a therapeutical seminars and projects, building should only try it out when stones of various textures, the and encouraged me to carry on professors of composition. In effect, without them I would up a musical ensemble. I occupy one feels it is a necessity. One way a carver would chisel a along that path. This is how I German-speaking European probably fall ill. Composition a 2/3 part time position in order should be highly motivated sculpture. arrived in Düsseldorf for the countries, I only know of five; helps me to come to terms to have a little more time left and this motivation is only pos- On the other hand, maybe due summer semester in 1996, to Isabel Mundry at the School with life. for the artistic work, which sible when it comes from to my upbringing, I am very study with Manfred Trojahn. of Advanced Studies in The- Another very gratifying aspect means that an invited professor a strong personal drive. open to other artistic fields such He also generously supported ater and Music in Munich, is working together with other takes over the remaining third I would advise a woman to as theater and literature and my me, even when I started explor- Carola Bauckholt at the Anton musicians or stage directors and of my teaching load. Since a full follow her path with her own music is narrative and full of ing other musical directions Brückner Private University in other artists, to reach the magi- teaching load corresponds to means, not trying to mimic references outside music. This is than his. I will always remain Linz, Rebecca Saunders at the cal point during rehearsals. This 18 hours a week this leaves me male role models. Composing why I like to speak of “impure grateful to him for that. I came School for Advanced Studies type of cooperation towards a with “only” twelve hours teach- and directing do not just hap- music”. to Berlin as a postgraduate in Music, Theater and Media in common goal makes one believe ing a week. Composition and pen to be typical male fields What are you particu- student, and studied here for Hannover, Cathy van Eck at the in a Utopia of peaceful and academic work can complement – they are positions of power larly proud of? another two years with Hans- University of the Arts in Bern productive communities. each other wonderfully, as long inside the world of music! We I am very proud of my musical peter Kyburz. and Iris Ter Schiphorst at the For me, the difficult aspects as a good ratio is maintained. women usually are less driven theater work. I have a strong Did you come across University of Music and Per- of the job are its technical and Otherwise, they tend to com- by an interest for power than collaboration with the Berlin obstacles in pursuing formance Arts in Vienna. One logistic sides, producing the pete and to tear you apart. One men are. On the contrary, stage director Matthias Reb- your career as a com- could add a few teachers in the material for the representa- should therefore make sure that women are usually outstanding stock. We have created two poser? theory of music and electronic tion, the never ending revision the ratio remains constructive. team workers and have a better works/pieces together; the sec- To survive as a composer is in composition. process for the scores. And of However, the academic and talent to communicate. These ond of these pieces, La ciudad itself difficult, namely making course, surviving concretely on artistic scene differ; in the artis- qualities typically lead to suc- de las mentiras, based on four sure that you get contracts, and a daily basis is the tricky part tic scene, a professorship does cess in music, and we should short stories by Juan Carlos that the pieces you compose for any composer. not help much, even though it not let music be subjected to a Onetti, will premiere at the 118 119

Teatro Real in February 2017 in Why and when did Madrid. The first piece, Niebla, you decide to become a which premiered in Dresden midwife? Hellerau in 2007, is based on ­ I was thirteen, lying on my bed a novel with the same title by bored stiff, when I came across Miguel de Unanumo. this profession while gazing We have developed an uncon- over a brochure. In spite of the ventional working method. fact that I then didn’t know the In traditional opera, first the word “midwife”, I immediately libretto is written and only then felt that this was a job I could does the composer start work- do and, moreover, anywhere in ing. At the very end comes the world. I was interested in the stage director, whom most medicine but since studying was often the composer did not not my cup of tea, I didn’t want know before. We proceed the to study medicine: so to be a other way around. midwife was the perfect choice The staging concept emerges for me. In my family, one was at the very beginning of our expected to take A-levels, so I reflections, and from there we applied for a training college derive and develop together at the age of nineteen, after the text and the composition. my A-levels. I had to wait for At a very preliminary stage, we five years before I was finally organise pre-rehearsals with accepted in Mainz. That was the interpreters, so as to test exactly what I wanted. our material and to develop it Were you encouraged further in form of improvisa- by your family, friends tions. The stage and costume or other people? designers are also involved at a I was definitely not encouraged very early stage of the process. by my family. Traditionally, a This way we can react to each woman in my family would get other and allow for a genuine further education after A-levels. interaction between the artistic Matina Matoff My mother was indifferent to disciplines to take place. midwife my decision to become a mid- wife. My father found this de- cision “very silly”, because the training that went with it didn’t involve academic studies and had nothing to do with arts. At the time, I felt I had disappoint- ed him; in his view, midwife was not an enviable profession. Only some twenty years later, when he realised how happy 120 121

I was in my job, did he admit you will be working; it changes each birth is unique. To experi- and another six months with a with empathy, help the family that it had indeed been the right all the time, which makes it ence a delivery is very moving, freelance midwife. She should to find its own way. The baby is choice for me to make. really difficult. I can never have it puts you in a good mood. learn through experience that the mother’s, the couple’s; even I did get support from my a glass of wine in the evening It is remarkable that I am just this job has a lot to do with if they change the baby’s nappy husband; he encouraged me since I can never know whether as enthusiastic every time. serving and with banalities. clumsily, you shouldn’t inter- to go on applying until I was I will be called for a delivery But I am also exhausted, both Midwives should not impose fere. You should ask the parents admitted. He was very proud during the night. Only on holi- mentally and physically. their viewpoints and values on how they imagine themselves of me. He gave up a position at day can I grant myself this plea- When you come across difficul- young parents. with the child, and let them the theater in Essen to move out sure. One’s social life suffers ties, you can feel very helpless, She should also know that follow their path. A midwife is with me to Frankfurt, where from this job and this is a draw- a feeling which can hang on to midwives are not doctors and not a psychologist, she should he became freelance. At the back. It once happened that I you for weeks. If a child dies, that she will be subjected to know her limitations, and when time, I was commuting between had invited people to my home the whole team is there to help a strong medical hierarchy. to refer patients to other col- Frankfurt and Mainz, where my for New Year's Eve, and didn’t you; this has happened to me a Midwives take care of physio­ leagues. training college was located. In turn up because I’d been called few times. However advanced lo­gical issues, doctors of patho­ When brothers or sisters are 1986, after our first child was for a delivery. This year I did the medicine, whatever high- logies. Only through experi- born, I sometimes see children ­ born, I interrupted the training go to my grandson’s birthday tech device is used, there will ence, which is very valuable, do a few years after I first met for a whole year. After that, I and missed out on three deliv- always be mothers who won’t you gain recognition. Young them when they were born went through “sheer stress”: eries. I often find myself letting survive or children who won’t midwives turn to experienced and realised how much of their alongside 40 hours shiftwork down friends, missing training make it. This won’t change, it ones for advice, and I have personality was already there a week, I had to study for the sessions, music and theater per- will always remain a fact. It is now reached such a status. from the beginning. As mid- exams, plus a child at home formances. Actually, the divorce a very emotional profession; You need to collect a lot of wives, we can encourage the and a mother suffering from rate amongst midwives is high. I sometimes need to cry. But experience, learn a lot of mate- parents to accept their child’s dementia to take care of. With- In retrospect, are you you shouldn’t suffer with the rial which you cannot find in personality as it is from the out my older sister’s support happy to have chosen mother; she is giving birth, books. You even need to learn very start, and not to twist it during that time, I could never this profession or not you. to smell, to recognise symp­toms according to their own views. have become a midwife. The do you have some What advice would from their smell. By simply What are you particu- training team of midwives were regrets? For you, what you give a young listening, touching, feeling, larly proud of? impressed by my enthusiasm in are the joys of being a woman wanting to observing, I can sometimes set People always look forward to the delivery room and did their midwife? What are the become a midwife? a diagnosis without examining seeing me, whether for a home best to share their experience hardships? First of all, that a midwife be a the patient. Watching carefully visit or in a maternity hospital. with me. With the experienced I would do it again, anytime! woman is essential for me; there is essential to gain experience. I’m proud to convey trust. It is midwives watching over me, I Each birth is different; what is a male midwife in Frankfurt, Could you describe the a lovely feeling to know peo- was allowed to help out with happens during a birth is but I am strongly against this. I main features of your ple enjoy my sheer presence. the deliveries in a rather auton- incredible and difficult to de- don’t mean that a man does not job to someone who is It happens every day and it is omous way, which was some- scribe. Every time I feel an im- have empathy, but I consider not acquainted with it? a luxurious feature of my job. what unusual. mense joy; it is a gift from God. this to be a job for women. A The skill in my job is to know People do not fear me. Often, Did you come across It is different for each child, the delivery is something intimate, a lot but to do very little. You families want to make friends obstacles in pursuing way children open their eyes or where (apart from the partner) achieve a lot by watching, by with me; that’s when I offend your career as a mid- hold them closed, the way they men are not especially welcome. an empathic presence. Sitting “my women”, since I always wife? shout changes from one child I would strongly recommend to and watching, doing nothing, decline their invitation. I never Combining the job as a midwife to another. Also, the parents’ a young woman who wants to giving time, not pushing, mo- go out for coffee or lunch with with family life is difficult. You tears of joy. I have brought become a midwife to spend six tivating, trusting people. Also, them. They’re “my women” never know when and how long some 2500 babies to life, but months in a maternity hospital for home visits you should, but they’re not my friends. 122 123

Acknowledgements Editors Photography Team of mathematicians

Sylvie Paycha Noel Tovia Matoff is a photo­ Alexandra Antoniouk, Magdalena Georgescu grapher who has always been Senior scientist in the Sara Azzali passionately interested in Department of Nonlinear The exhibition on which this catalogue is based was made portraying people. She feels Analysis at the Institute of possible thanks to the financial support of various institutions: challenged to present her own Mathematics of the Nation- Alexander von Humboldt Stiftung (“Humboldt Alumni Award personal view, approaching ­ al Academy of Sciences of 2015 for Innovative Networking Initiatives”), Bosch Stiftung, each individual on an eye to Ukraine. London Mathematical Society, Berlin Mathematical School, eye level and thereby creating University of Potsdam and Maecenia Frankfurt. an intimate relationship. She Sara Azzali, postdoc in the enjoys portraying people of mathematics department of For their decisive support, we are also very grateful to: different social and cultural the University of Potsdam, European Women in Mathematics, European Mathematical strata, as well as accompanying Germany. Society and Technische Universität Berlin. actors and artists during their work. Another focal point Magdalena Georgescu, visiting is portraying health-related researcher at the University topics, such as people taking of Potsdam in Germany. In care of relatives with Alzheimer October 2016 she is starting a disease and midwives helping postdoc in Israel. women give birth. Sylvie Paycha, Professor in For being very supportive, the mathematics department Noel Tovia Matoff wishes to of the University of Potsdam, acknowledge Albrecht Ecke, Germany, on leave from the Gesine Krüger, Stefan Krug, Blaise Pascal University in Wenke Neunast, Jost Schilgen Clermont-Ferrand, France. and Nika Schneider. Additionally, she offers many Project website: thanks to all the helping friends www.womeninmath.net and family members. E-mail: [email protected] 124

Publishing details

Bibliografische Information Der Deutschen Nationalbibliothek Die Deutsche National­ bibliothek verzeichnet diese Publikation in der Deutschen Nationalbibliografie; detaillierte bibliografische Daten sind im Internet über http: //dnb.d-nb.de abrufbar.

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Project website: www.womeninmath.net E-mail: [email protected]

Photography © Noel Tovia Matoff, www.matoff.de Interviews © the authors

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ISBN 978-3-9814032-4-4 1st edition 2016