European women in mathematics : proceedings of the 13th General Meeting, University of Cambridge, UK, 3-6 September 2007

European women in mathematics (Proceedings of the 13th General Meeting, University of Cambridge, UK, 3-6 September 2007) This volume offers a unique collection of outstanding contributions from renowned women mathematicians who met in Cambridge for a conference under the auspices of European Women in Mathematics (EWM). These contributions serve as excellent surveys of their subject areas, including symplectic topology, combinatorics and number theory. The volume moreover sheds light on prominent women mathematicians who worked in Cambridge in the late 19th and early 20th centuries by providing an insightful historical introduction at the beginning of the volume. The volume concludes with short contributions from women mathematicians from across Europe working in various areas of mathematics ranging from group theory to magnetic fields. CONTENTS 10 Preface 6 Organizing Committees 8 Part A Invited Talks 12 Deformation Quantisation and Connections S. Gutt 14 1. Quantization 14 2. Basic definitions 16 3. Symplectic case: star products and symplectic connections 19 3.1. Fedosov’s construction 22 4. Star products on Poisson manifolds 26 4.1. Star products on Poisson manifolds and formality 26 4.2. Kontsevich’s formality for Rd 33 4.3. Universal star product and universal formality 37 Universal star product 39 Universal formality 40 References 42 What is Symplectic Geometry? D. McDu 44 1. First notions 44 2. Symplectomorphisms 48 3. Almost complex structures and J-holomorphic curves 54 3.1. Sketch proof of the nonsqueezing theorem 61 Acknowledgements 63 References 63 Regular Permutation Groups and Cayley Graphs C. E. Praeger 66 1. Introduction 66 1.1. Permutation groups and regularity 66 1.2. Cayley graphs 67 2. A recognition problem for Cayley graphs 69 3. Cayley graphs and B-groups 72 4. A fascinating density result 73 5. Exact factorisations of groups 74 6. Primitive Cayley graphs for various groups G 75 7. Types of finite primitive groups 77 8. Exact factorisations of finite classical groups 78 References 79 Arithmetic of Elliptic Curves through the Ages R. Sujatha 82 1. Introduction 82 2. Elliptic curves and number theory 83 3. Iwasawa theory 86 4. Iwasawa algebras 88 5. Main conjectures 91 6. Applications and examples 95 References 98 Part B Contributed Short Talks 102 Tricritical Points and Liquid-Solid Critical Lines A. Aitta 104 1. Introduction 104 2. Landau theory 105 3. Experimental evidence for iron 109 4. Conclusions 111 References 112 Elastic Waves in Rods of Rectangular Cross Section A. A. Bondarenko 114 1. Introduction 114 2. Formulation of the problem 115 3. Method of solution 116 4. Results and discussion 119 5. Conclusion 122 Acknowledgement 122 References 122 Natural Extensions for the Golden Mean K. Dajani & C. Kalle 124 1. Introduction 124 2. Expansions and fundamental intervals 126 3. Two rows of rectangles 128 4. Towering the orbits 132 References 133 An Equivariant Tietze Extension Theorem for Proper Actions of Locally Compact Groups A. Feragen 136 1. Introduction 136 2. Prerequisites 137 3. The equivariant Tietze extension theorem 138 References 140 On Uniform Tangential Approximation by Lacunary Power Series G. Harutyunyan 142 Notation and Introduction 142 1. Uniform and tangential approximation by holomorphic functions 143 2. Lacunary approximation 145 2.1. Uniform approximation by lacunary polynomials 145 2.2. Auxiliary Proposition 146 2.3. The main result 150 References 153 Cyclic Division Algebras in Space-Time Coding: A Brief Overview C. Hollanti 154 1. Space-time coding: Idea and design criteria 154 2. Cyclic division algebras and orders 157 3. The discriminant bound 160 References 163 Part C Women in Mathematics 164 And What Became of the Women? C. Series 166 Introduction 167 At Cambridge 167 What did these three women do afterwards? 171 Postscript 173 Sources 173 References 173 Three Great Girton Mathematicians R. M. Williams 176 Dame Mary Cartwright, F.R.S. 176 Bertha Swirles, Lady Je reys 179 Olga Taussky-Todd 181 Conclusion 184 Acknowledgment 185 References 185 What About the Women Now? R. M. Williams 186 Introduction 186 Women in DAMTP report 187 Women and the Mathematical Tripos: Myth and Reality; the Salter Report 190 Indicators of Academic Performance 192 Conclusions 197 Acknowledgment 199 References 199 Mathematics in Society (Taking into Account Gender- Aspects) — A One-Semester Course (BSc) C. Scharlach 200 1. Introduction 200 2. Studying math at German universities - the current situation 201 3. The one-semester course at HU Berlin 202 3.1. Mathematics as a profession 202 3.2. Interviews with mathematicians 204 3.3. History and philosophy of mathematics 205 3.4. Gender meets Mathematics 206 3.5. The scientific community in mathematics 207 3.6. What is mathematics? 208 References 209 CONTENTS......Page 10 Preface......Page 6 Organizing Committees......Page 8 Part A Invited Talks......Page 12 1. Quantization......Page 14 2. Basic definitions......Page 16 3. Symplectic case: star products and symplectic connections......Page 19 3.1. Fedosov’s construction......Page 22 4.1. Star products on Poisson manifolds and formality......Page 26 4.2. Kontsevich’s formality for Rd......Page 33 4.3. Universal star product and universal formality......Page 37 Universal star product......Page 39 Universal formality......Page 40 References......Page 42 1. First notions......Page 44 2. Symplectomorphisms......Page 48 3. Almost complex structures and J-holomorphic curves......Page 54 3.1. Sketch proof of the nonsqueezing theorem......Page 61 References......Page 63 1.1. Permutation groups and regularity......Page 66 1.2. Cayley graphs......Page 67 2. A recognition problem for Cayley graphs......Page 69 3. Cayley graphs and B-groups......Page 72 4. A fascinating density result......Page 73 5. Exact factorisations of groups......Page 74 6. Primitive Cayley graphs for various groups G......Page 75 7. Types of finite primitive groups......Page 77 8. Exact factorisations of finite classical groups......Page 78 References......Page 79 1. Introduction......Page 82 2. Elliptic curves and number theory......Page 83 3. Iwasawa theory......Page 86 4. Iwasawa algebras......Page 88 5. Main conjectures......Page 91 6. Applications and examples......Page 95 References......Page 98 Part B Contributed Short Talks......Page 102 1. Introduction......Page 104 2. Landau theory......Page 105 3. Experimental evidence for iron......Page 109 4. Conclusions......Page 111 References......Page 112 1. Introduction......Page 114 2. Formulation of the problem......Page 115 3. Method of solution......Page 116 4. Results and discussion......Page 119 References......Page 122 1. Introduction......Page 124 2. Expansions and fundamental intervals......Page 126 3. Two rows of rectangles......Page 128 4. Towering the orbits......Page 132 References......Page 133 1. Introduction......Page 136 2. Prerequisites......Page 137 3. The equivariant Tietze extension theorem......Page 138 References......Page 140 Notation and Introduction......Page 142 1. Uniform and tangential approximation by holomorphic functions......Page 143 2.1. Uniform approximation by lacunary polynomials......Page 145 2.2. Auxiliary Proposition......Page 146 2.3. The main result......Page 150 References......Page 153 1. Space-time coding: Idea and design criteria......Page 154 2. Cyclic division algebras and orders......Page 157 3. The discriminant bound......Page 160 References......Page 163 Part C Women in Mathematics......Page 164 And What Became of the Women? C. Series......Page 166 At Cambridge......Page 167 What did these three women do afterwards?......Page 171 References......Page 173 Dame Mary Cartwright, F.R.S.......Page 176 Bertha Swirles, Lady Je reys......Page 179 Olga Taussky-Todd......Page 181 Conclusion......Page 184 References......Page 185 Introduction......Page 186 Women in DAMTP report......Page 187 Women and the Mathematical Tripos: Myth and Reality; the Salter Report......Page 190 Indicators of Academic Performance......Page 192 Conclusions......Page 197 References......Page 199 1. Introduction......Page 200 2. Studying math at German universities - the current situation......Page 201 3.1. Mathematics as a profession......Page 202 3.2. Interviews with mathematicians......Page 204 3.3. History and philosophy of mathematics......Page 205 3.4. Gender meets Mathematics......Page 206 3.5. The scientific community in mathematics......Page 207 3.6. What is mathematics?......Page 208 References......Page 209