European Women in Mathematics
Total Page：16
File Type：pdf, Size：1020Kb
Load more
Recommended publications
-
Of the American Mathematical Society August 2017 Volume 64, Number 7
ISSN 0002-9920 (print) ISSN 1088-9477 (online) of the American Mathematical Society August 2017 Volume 64, Number 7 The Mathematics of Gravitational Waves: A Two-Part Feature page 684 The Travel Ban: Affected Mathematicians Tell Their Stories page 678 The Global Math Project: Uplifting Mathematics for All page 712 2015–2016 Doctoral Degrees Conferred page 727 Gravitational waves are produced by black holes spiraling inward (see page 674). American Mathematical Society LEARNING ® MEDIA MATHSCINET ONLINE RESOURCES MATHEMATICS WASHINGTON, DC CONFERENCES MATHEMATICAL INCLUSION REVIEWS STUDENTS MENTORING PROFESSION GRAD PUBLISHING STUDENTS OUTREACH TOOLS EMPLOYMENT MATH VISUALIZATIONS EXCLUSION TEACHING CAREERS MATH STEM ART REVIEWS MEETINGS FUNDING WORKSHOPS BOOKS EDUCATION MATH ADVOCACY NETWORKING DIVERSITY blogs.ams.org Notices of the American Mathematical Society August 2017 FEATURED 684684 718 26 678 Gravitational Waves The Graduate Student The Travel Ban: Affected Introduction Section Mathematicians Tell Their by Christina Sormani Karen E. Smith Interview Stories How the Green Light was Given for by Laure Flapan Gravitational Wave Research by Alexander Diaz-Lopez, Allyn by C. Denson Hill and Paweł Nurowski WHAT IS...a CR Submanifold? Jackson, and Stephen Kennedy by Phillip S. Harrington and Andrew Gravitational Waves and Their Raich Mathematics by Lydia Bieri, David Garfinkle, and Nicolás Yunes This season of the Perseid meteor shower August 12 and the third sighting in June make our cover feature on the discovery of gravitational waves -
Properties of High Rank Subvarieties of Affine Spaces 3
PROPERTIES OF HIGH RANK SUBVARIETIES OF AFFINE SPACES DAVID KAZHDAN AND TAMAR ZIEGLER Abstract. We use tools of additive combinatorics for the study of subvarieties defined by high rank families of polynomials in high dimensional Fq-vector spaces. In the first, analytic part of the paper we prove a number properties of high rank systems of polynomials. In the second, we use these properties to deduce results in Algebraic Geometry , such as an effective Stillman conjecture over algebraically closed fields, an analogue of Nullstellensatz for varieties over finite fields, and a strengthening of a recent result of [5]. We also show that for k-varieties X ⊂ An of high rank any weakly polynomial function on a set X(k) ⊂ kn extends to a polynomial. 1. Introduction Let k be a field. For an algebraic k-variety X we write X(k) := X(k). To simplify notations we often write X instead of X(k). In particular we write V := V(k) when V is a vector space and write kN for AN (k). For a k-vector space V we denote by Pd(V) the algebraic variety of polynomials on V of degree ≤ d and by Pd(V ) the set of polynomials functions P : V → k of degree ≤ d. We always assume that d< |k|, so the restriction map Pd(V)(k) → Pd(V ) is a bijection. For a family P¯ = {Pi} of polynomials on V we denote by X V P¯ ⊂ the subscheme defined by the ideal generated by {Pi} and by XP¯ the set XP (k) ⊂ V . We will not distinguish between the set of affine k-subspaces of V and the set of affine subspaces of V since for an affine k-subspace W ⊂ V, the map W → W(k) is a bijection. -
![Arxiv:2007.03981V1 [Math.FA] 8 Jul 2020](https://docslib.b-cdn.net/cover/3082/arxiv-2007-03981v1-math-fa-8-jul-2020-243082.webp)
Arxiv:2007.03981V1 [Math.FA] 8 Jul 2020
FOURIER UNIQUENESS IN R4 ANDREW BAKAN, HAAKAN HEDENMALM, ALFONSO MONTES-RODRÍGUEZ, DANYLO RADCHENKO, AND MARYNA VIAZOVSKA Abstract. We show an interrelation between the uniqueness aspect of the recent Fourier interpolation formula of Radchenko and Viazovska and the Heisenberg uniqueness for the Klein-Gordon equation and the lattice- cross of critical density, studied by Hedenmalm and Montes-Rodríguez. This has been known since 2017. 1. Introduction 1.1. Basic notation in the plane. We write Z for the integers, Z+ for the positive integers, R for the real line, and C for the complex plane. We write H for the upper half-plane {τ ∈ C : Im τ> 0}. Moreover, we d let h·, ·id denote the Euclidean inner product of R . 1.2. The Fourier transform of radial functions. For a function f ∈ L1(Rd), we consider its Fourier transform (with x = (x1,..., xd) and y = (y1,..., yd)) −i2πhx,yid fˆ(y):= e f (x)dvold(x), dvold(x):= dx1 ··· dxd. ZRd If f is radial, then fˆis radial too. A particular example of a radial function is the Gaussian iπτ|x|2 (1.2.1) Gτ(x):= e , which decays nicely provided that Im τ> 0, that is, when τ ∈ H. The Fourier transform of a Gaussian is another Gaussian, in this case −d/2 −d/2 τ −iπ|y|2/τ τ (1.2.2) Gˆ τ(y):= e = G−1/τ(y), i i Here, it is important that τ 7→ −1/τ preserves hyperbolic space H. In the sense of distribution theory, the above relationship extends to boundary points τ ∈ R as well. -
Twenty Female Mathematicians Hollis Williams
Twenty Female Mathematicians Hollis Williams Acknowledgements The author would like to thank Alba Carballo González for support and encouragement. 1 Table of Contents Sofia Kovalevskaya ................................................................................................................................. 4 Emmy Noether ..................................................................................................................................... 16 Mary Cartwright ................................................................................................................................... 26 Julia Robinson ....................................................................................................................................... 36 Olga Ladyzhenskaya ............................................................................................................................. 46 Yvonne Choquet-Bruhat ....................................................................................................................... 56 Olga Oleinik .......................................................................................................................................... 67 Charlotte Fischer .................................................................................................................................. 77 Karen Uhlenbeck .................................................................................................................................. 87 Krystyna Kuperberg ............................................................................................................................. -
Maryna Viazovska (HU Berlin)
s well as BMS Friday Colloquium Friday 4 November 2016 at 14:15 Tea & Cookies starting at 13:00 BMS Loft, Urania, An der Urania 17, 10787 Berlin Maryna Viazovska (HU Berlin) Solving packing problems by linear programming How much of Euclidean space can be filled with pairwise non-over- lapping congruent copies of a given convex body K? We call this the body packing problem. Problems of this kind are solved comple- tely only in rare cases. One powerful method to attack these geome- tric questions is linear programming. This approach was developed by Philippe Delsarte in the early seventies. Based on inequalities for © Maryna Viazovska the distance distribution of point configurations, this method was successfully applied to the “kissing number problem“ in dimensions 8 and 24. The original Delsarte method was applied to the optimization on compact spaces. In 2003, Cohn and Elkies generalized this method to Euclidean space. In particular, they improved existent upper bounds for the maximum density of sphere packings in dimensions 4,...,36. Recently, Viazovska and her coauthors proved that linear pro- gramming provides tight bounds for sphere packing in dimensions 8 and 24. In her talk, Viazovska will explain the linear programming method and demonstrate how it works on various examples. Born in the Ukraine, Maryna Viazovska completed her PhD at MPIM in Bonn in 2013 under the supervision of Don Zagier. Her research interests include number theory and discrete geometry. In October 2013, she became a visiting researcher at the IHÉS in France. In August 2014, she took up the two-year position of BMS Dirichlet Postdoctoral Fellow based at HU Berlin, during which time she solved the hyper- sphere packing problem for dimension 8. -
Notices of the AMS 595 Mathematics People NEWS
NEWS Mathematics People contrast electrical impedance Takeda Awarded 2017–2018 tomography, as well as model Centennial Fellowship reduction techniques for para- bolic and hyperbolic partial The AMS has awarded its Cen- differential equations.” tennial Fellowship for 2017– Borcea received her PhD 2018 to Shuichiro Takeda. from Stanford University and Takeda’s research focuses on has since spent time at the Cal- automorphic forms and rep- ifornia Institute of Technology, resentations of p-adic groups, Rice University, the Mathemati- especially from the point of Liliana Borcea cal Sciences Research Institute, view of the Langlands program. Stanford University, and the He will use the Centennial Fel- École Normale Supérieure, Paris. Currently Peter Field lowship to visit the National Collegiate Professor of Mathematics at Michigan, she is Shuichiro Takeda University of Singapore and deeply involved in service to the applied and computa- work with Wee Teck Gan dur- tional mathematics community, in particular on editorial ing the academic year 2017–2018. boards and as an elected member of the SIAM Council. Takeda obtained a bachelor's degree in mechanical The Sonia Kovalevsky Lectureship honors significant engineering from Tokyo University of Science, master's de- contributions by women to applied or computational grees in philosophy and mathematics from San Francisco mathematics. State University, and a PhD in 2006 from the University —From an AWM announcement of Pennsylvania. After postdoctoral positions at the Uni- versity of California at San Diego, Ben-Gurion University in Israel, and Purdue University, since 2011 he has been Pardon Receives Waterman assistant and now associate professor at the University of Missouri at Columbia. -
![Arxiv:1910.04675V1 [Math.DS] 10 Oct 2019 UNIAIEDSONNS FNILFLOWS of DISJOINTNESS QUANTITATIVE Ekts,Cmie Ihtesrcua Hoesfrnlosby Ziegler](https://docslib.b-cdn.net/cover/4293/arxiv-1910-04675v1-math-ds-10-oct-2019-uniaiedsonns-fnilflows-of-disjointness-quantitative-ekts-cmie-ihtesrcua-hoesfrnlosby-ziegler-1214293.webp)
Arxiv:1910.04675V1 [Math.DS] 10 Oct 2019 UNIAIEDSONNS FNILFLOWS of DISJOINTNESS QUANTITATIVE Ekts,Cmie Ihtesrcua Hoesfrnlosby Ziegler
QUANTITATIVE DISJOINTNESS OF NILFLOWS FROM HOROSPHERICAL FLOWS ASAF KATZ Abstract. We prove a quantitative variant of a disjointness the- orem of nilflows from horospherical flows following a technique of Venkatesh, combined with the structural theorems for nilflows by Green, Tao and Ziegler. arXiv:1910.04675v1 [math.DS] 10 Oct 2019 1 2 1. Introduction In a landmark paper [10], H. Furstenberg introduced the notion of joinings of two dynamical systems and the concept of disjoint dynam- ical systems. Ever since, this property has played a major role in the field of dynamics, leading to many fundamental results. In his paper, Furstenberg proved the following characterization of a weakly-mixing dynamical system: 1.1. Theorem (Furstenberg [10], Theorem 1.4). A dynamical system (X,β,µ,T ) is weakly-mixing if and only if (X, T ) is disjoint from any Kronecker system. Namely, given any compact abelian group A, equipped with the ac- tion of A on itself by left-translation Ra, the only joining between (X, T ) and (A, Ra) is the trivial joining given by the product mea- sure on the product dynamical system (X A, T R ). The Wiener- × × a Wintner ergodic theorem readily follows from Furstenberg’s theorem. In [2], J. Bourgain derived a strengthening of Furstenberg’s disjoint- ness theorem, which amounts to the uniform Wiener-Wintner theorem. The proof is along the lines of Furstenberg’s but utilizing the Van-der- Corput trick to show uniformity over various Kronecker systems. In a recent work [41], A. Venkatesh gave a quantitative statement of the uniform Wiener-Wintner theorem for the case of the horocyclic flow on compact homogeneous spaces of SL2(R) (and in principal, his proof works also for non-compact spaces as well, by allowing the decay rate to depend on Diophantine properties of the origin point of the orbit). -
![Arxiv:1006.0205V4 [Math.NT]](https://docslib.b-cdn.net/cover/9173/arxiv-1006-0205v4-math-nt-1449173.webp)
Arxiv:1006.0205V4 [Math.NT]
AN INVERSE THEOREM FOR THE GOWERS U s+1[N]-NORM BEN GREEN, TERENCE TAO, AND TAMAR ZIEGLER Abstract. This is an announcement of the proof of the inverse conjecture for the Gowers U s+1[N]-norm for all s > 3; this is new for s > 4, the cases s = 1, 2, 3 having been previously established. More precisely we outline a proof that if f : [N] → [−1, 1] is a function with kfkUs+1[N] > δ then there is a bounded-complexity s-step nilsequence F (g(n)Γ) which correlates with f, where the bounds on the complexity and correlation depend only on s and δ. From previous results, this conjecture implies the Hardy-Littlewood prime tuples conjecture for any linear system of finite complexity. In particular, one obtains an asymptotic formula for the number of k-term arithmetic progres- sions p1 <p2 < ··· <pk 6 N of primes, for every k > 3. 1. Introduction This is an announcement and summary of our much longer paper [20], the pur- pose of which is to establish the general case of the Inverse Conjecture for the Gowers norms, conjectured by the first two authors in [15, Conjecture 8.3]. If N is a (typically large) positive integer then we write [N] := {1,...,N}. Throughout the paper we write D = {z ∈ C : |z| 6 1}. For each integer s > 1 the inverse conjec- ture GI(s), whose statement we recall shortly, describes the structure of functions st f :[N] → D whose (s + 1) Gowers norm kfkU s+1[N] is large. -
Jakub M. Konieczny Curriculum Vitae
Jakub M. Konieczny Curriculum Vitae E-mail: [email protected] CONTACT Einstein Institute of Mathematics Webpages: INFORMATION Edmond J. Safra Campus The Hebrew University of Jerusalem mathematics.huji.ac.il/people/jakub-konieczny Givat Ram. Jerusalem, 9190401, Israel jakubmichalkonieczny.wordpress.com RESEARCH Ergodic theory and dynamical systems. Applications to combinatorial number theory. Sym- INTERESTS bolic dynamics. Fourier analysis. Higher order Fourier analysis. Dynamics on nilmani- folds. Generalised polynomials. Automatic sequences. q-multiplicative sequences. Ultrafil- ters. Ramsey theory. Extremal combinatorics. CURRENT Postdoctoral Fellow, October 2017 to present ACADEMIC Einstein Institute of Mathematics, The Hebrew University of Jerusalem APPOINTMENTS under ERC grant: Ergodic Theory and Additive Combinatorics Advisor: Tamar Ziegler EDUCATION University of Oxford Doctor of Philosophy in Mathematics, 1 August 2017 • Supervisor: Ben Green • Area of study: Ergodic theory/Additive combinatorics • Thesis title: On combinatorial properties of nil-Bohr sets of integers and related problems Jagiellonian University, Kraków and Vrije Universiteit, Amsterdam (joint degree) Master of Science in Mathematics, 18 July 2013 (UJ) | 30 August 2013 (VU) • Supervisor: P. Niemiec (UJ) and T. Eisner-Lobova (VU) and A. J. Homburg (VU) • Area of study: Ergodic theory/Combinatorial number theory • Thesis title: Applications of ultrafilters in ergodic theory and combinatorial number theory Jagiellonian University, Kraków Bachelor of Science in Mathematics, 15 July 2011 • Individualised Studies in Mathematics and Natural Sciences (SMP) programme • Extended curriculum incorporating material from Computer Science and Physics JOURNAL PAPERS [1] J. Byszewski, J. Konieczny, and E. Krawczyk. Substitutive systems and a finitary version (PUBLISHED OR of Cobham’s theorem. To appear in Combinatorica, available at arXiv: 1908.11244 ACCEPTED FOR [math.CO] PUBLICATION) [2] J. -
Issue 118 ISSN 1027-488X
NEWSLETTER OF THE EUROPEAN MATHEMATICAL SOCIETY S E European M M Mathematical E S Society December 2020 Issue 118 ISSN 1027-488X Obituary Sir Vaughan Jones Interviews Hillel Furstenberg Gregory Margulis Discussion Women in Editorial Boards Books published by the Individual members of the EMS, member S societies or societies with a reciprocity agree- E European ment (such as the American, Australian and M M Mathematical Canadian Mathematical Societies) are entitled to a discount of 20% on any book purchases, if E S Society ordered directly at the EMS Publishing House. Recent books in the EMS Monographs in Mathematics series Massimiliano Berti (SISSA, Trieste, Italy) and Philippe Bolle (Avignon Université, France) Quasi-Periodic Solutions of Nonlinear Wave Equations on the d-Dimensional Torus 978-3-03719-211-5. 2020. 374 pages. Hardcover. 16.5 x 23.5 cm. 69.00 Euro Many partial differential equations (PDEs) arising in physics, such as the nonlinear wave equation and the Schrödinger equation, can be viewed as infinite-dimensional Hamiltonian systems. In the last thirty years, several existence results of time quasi-periodic solutions have been proved adopting a “dynamical systems” point of view. Most of them deal with equations in one space dimension, whereas for multidimensional PDEs a satisfactory picture is still under construction. An updated introduction to the now rich subject of KAM theory for PDEs is provided in the first part of this research monograph. We then focus on the nonlinear wave equation, endowed with periodic boundary conditions. The main result of the monograph proves the bifurcation of small amplitude finite-dimensional invariant tori for this equation, in any space dimension. -
Additive and Analytic Combinatorics
IMA Workshops September 29-October 3, 2014 Additive and Analytic Combinatorics ORGANIZERS SPEAKERS David Conlon, University of Oxford Tim Austin, Courant Institute of Mathematical Sciences Ernie Croot, Georgia Institute of Technology Vitaly Bergelson, The Ohio State Van Vu, Yale University University Tamar Ziegler, Hebrew University Emmanuel Breuillard, Université de Paris XI (Paris-Sud) Boris Bukh, Carnegie Mellon University Mei-Chu Chang, University of California, Additive combinatorics is the theory of counting Riverside additive structures in sets. This theory has seen David Conlon, University of Oxford exciting developments and dramatic changes in Ernie Croot, Georgia Institute of direction in recent years thanks to its connections Technology with areas such as harmonic analysis, ergodic Jacob Fox, Massachusetts Institute of Technology theory, and representation theory. As it turns out, Bob Guralnick, University of Southern many combinatorial ideas that have existed in the California combinatorics community for quite some time can Akos Magyar, University of British be used to attack notorious problems in other areas Columbia of mathematics. A typical example is the Green- Hamed Hatami, McGill University Tao theorem on the existence of long arithmetic Frederick Manners, University of Oxford progressions in primes, which uses a famous Lilian Matthiesen, Institut de theorem of Szemerédi on arithmetic progressions Mathematiques de Jussieu in dense sets as a key component. The field is also Jozsef Solymosi, University of British of great interest to computer scientists; a number of Columbia the techniques and theorems have seen application Terence Tao, University of California, Los Angeles in, for example, communication complexity, Van Vu, Yale University property testing, and the design of randomness Melanie Wood, University of Wisconsin, extractors. -
An Inverse Theorem for the Gowers U4-Norm
Glasgow Math. J. 53 (2011) 1–50. C Glasgow Mathematical Journal Trust 2010. doi:10.1017/S0017089510000546. AN INVERSE THEOREM FOR THE GOWERS U4-NORM BEN GREEN Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, UK e-mail: [email protected] TERENCE TAO UCLA Department of Mathematics, Los Angeles, CA 90095-1555, USA e-mail: [email protected] and TAMAR ZIEGLER Department of Mathematics, Technion - Israel Institute of Technology, Haifa 32000, Israel e-mail: [email protected] (Received 30 November 2009; accepted 18 June 2010; first published online 25 August 2010) Abstract. We prove the so-called inverse conjecture for the Gowers U s+1-norm in the case s = 3 (the cases s < 3 being established in previous literature). That is, we show that if f :[N] → ރ is a function with |f (n)| 1 for all n and f U4 δ then there is a bounded complexity 3-step nilsequence F(g(n)) which correlates with f . The approach seems to generalise so as to prove the inverse conjecture for s 4as well, and a longer paper will follow concerning this. By combining the main result of the present paper with several previous results of the first two authors one obtains the generalised Hardy–Littlewood prime-tuples conjecture for any linear system of complexity at most 3. In particular, we have an asymptotic for the number of 5-term arithmetic progressions p1 < p2 < p3 < p4 < p5 N of primes. 2010 Mathematics Subject Classification. Primary: 11B30; Secondary: 37A17. NOTATION . By a 1-bounded function on a set X we mean a function f : X → ރ with |f (x)| 1 for all x∈ X.