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BERNOULLI NEWS, Vol 24 No 1 (2017)
Vol. 24 (1), May 2017 Published twice per year by the Bernoulli Society ISSN 1360–6727 CONTENTS News from the Bernoulli Society p. 1 Awards and Prizes p. 2 New Executive Members A VIEW FROM THE PRESIDENT in the Bernoulli Society Dear Members of the Bernoulli Society, p. 3 As we all seem to agree, the role and image of statistics has changed dramatically. Still, it takes ones breath when realizing the huge challenges ahead. Articles and Letters Statistics has not always been considered as being very necessary. In 1848 the Dutch On Bayesian Measures of Ministry of Home Affairs established an ofŮice of statistics. And then, thirty years later Uncertainty in Large or InŮinite minister Kappeyne van de Coppelo abolishes the “superŮluous” ofŮice. The ofŮice was Dimensional Models p. 4 quite rightly put back in place in 1899, as “Centraal Bureau voor de Statistiek” (CBS). Statistics at the CBS has evolved from “simple” counting to an art requiring a broad range On the Probability of Co-primality of competences. Of course counting remains important. For example the CBS reports in of two Natural Numbers Chosen February 2017 that almost 1 out of 4 people entitled to vote in the Netherlands is over the at Random p. 7 age of 65. But clearly, knowing this generates questions. What is the inŮluence of this on the outcome of the elections? This calls for more data. Demographic data are combined with survey data and nowadays also with data from other sources, in part to release the “survey pressure” that Ůirms and individuals are facing. -
Contemporary Mathematics 78
CONTEMPORARY MATHEMATICS 78 Braids Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Artin's Braid Group held July 13-26. 1986 at the University of California, Santa Cruz, California Joan S. Birman Anatoly Libgober Editors http://dx.doi.org/10.1090/conm/078 Recent Titles in This Series 120 Robert S. Doran, Editor, Selfadjoint and nonselfadjoint operator algebras and operator theory, 1991 119 Robert A. Melter, Azriel Rosenfeld, and Prabir Bhattacharya, Editors, Vision geometry, 1991 118 Yan Shi-Jian, Wang Jiagang, and Yang Chung-chun, Editors, Probability theory and its applications in China, 1991 117 Morton Brown, Editor, Continuum theory and dynamical systems, 1991 116 Brian Harboume and Robert Speiser, Editors, Algebraic geometry: Sundance 1988, 1991 115 Nancy Flournoy an'il Robert K. Tsutakawa, Editors, Statistical multiple integration, 1991 114 Jeffrey C. Lagarias and Michael J. Todd, Editors, Mathematical developments arising from linear programming, 1990 113 Eric Grinberg and Eric Todd Quinto, Editors, Integral geometry and tomography, 1990 112 Philip J. Brown and Wayne A. Fuller, Editors, Statistical analysis of measurement error models and applications, 1990 Ill Earl S. Kramer and Spyros S. Magliveras, Editors, Finite geometries and combinatorial designs, I 990 II 0 Georgia Benkart and J. Marshall Osborn, Editors, Lie algebras and related topics, 1990 109 Benjamin Fine, Anthony Gaglione, and Francis C. Y. Tang, Editors, Combinatorial group theory, 1990 108 Melvyn S. Berger, Editor, Mathematics of nonlinear science, 1990 107 Mario Milman and Tomas Schonbek, Editors, Harmonic analysis and partial differential equations, 1990 I 06 Wilfried Sieg, Editor, Logic and computation, 1990 I 05 Jerome Kaminker, Editor, Geometric and topological invariants of elliptic operators, 1990 I 04 Michael Makkai and Robert Pare, Accessible categories: The foundations of categorical model theory, 1989 I 03 Steve Fisk, Coloring theories, 1989 I 02 Stephen McAdam, Primes associated to an ideal, 1989 101 S.-Y. -
07 26Microsoft 2022
PRESS RELEASE August 27, 2021 Jennifer Balakrishnan Awarded the 2022 AWM-Microsoft Research Prize The 2022 AWM-Microsoft Balakrishnan’s research exhibits Research Prize in Algebra and extraordinary depth as well as Number Theory will be presented breadth. In joint work with Besser, to Jennifer Balakrishnan in Çiperiani, Dogra, Müller, Stein recognition of outstanding and others, she has worked contributions to explicit methods extensively on computing p-adic in number theory, particularly her height pairings for hyperelliptic advances in computing rational curves. Applications of this points on algebraic curves over research include the formulation, number fields. along with numerical evidence, of a p-adic analogue of the Professor Balakrishnan is celebrated Birch and internationally recognized as a leader in Swinnerton-Dyer conjecture, some new explicit computational number theory. Her doctoral examples in Iwasawa theory, and more. With dissertation presents the first general technique Ho, Kaplan, Spicer, Stein and Weigandt, for computing iterated p-adic Coleman integrals Balakrishnan has assembled the most extensive on hyperelliptic curves. In the course of her computational evidence to date on the collaboration with Minhyong Kim at Oxford, distribution of ranks and Selmer groups of Balakrishnan helped realize the substantial elliptic curves over the rational numbers, thereby practical potential of Kim’s non-abelian providing the most convincing evidence thus far Chabauty method, and with her collaborators, in support of the widely believed conjecture that turned it into a powerful tool for identifying the average rank of a rational elliptic curve is ½. integral and rational points on curves that are entirely beyond reach using the traditional After receiving her doctorate from the Chabauty approach. -
Quadratic Chabauty for Atkin-Lehner Quotients of Modular Curves
Quadratic Chabauty for Atkin-Lehner Quotients of Modular Curves of Prime Level and Genus 4, 5, 6 Nikola Adˇzaga1, Vishal Arul2, Lea Beneish3, Mingjie Chen4, Shiva Chidambaram5, Timo Keller6, and Boya Wen7 1Department of Mathematics, Faculty of Civil Engineering, University of Zagreb∗ 2Department of Mathematics, University College London† 3Department of Mathematics and Statistics, McGill University‡ 4Department of Mathematics, University of California at San Diego§ 5Department of Mathematics, University of Chicago¶ 6Department of Mathematics, Universit¨at Bayreuth‖ 7Department of Mathematics, Princeton University∗∗ May 12, 2021 Abstract + We use the method of quadratic Chabauty on the quotients X0 (N) of modular curves X0(N) by their Fricke involutions to provably compute all the rational points of these curves for prime levels N of genus four, five, and six. We find that the only such curves with exceptional rational points are of levels 137 and 311. In particular there are no exceptional rational points on those curves of genus five and six. More precisely, we determine the rational + points on the curves X0 (N) for N = 137, 173, 199, 251, 311, 157, 181, 227, 263, 163, 197, 211, 223, 269, 271, 359. Keywords: Rational points; Curves of arbitrary genus or genus =6 1 over global fields; arithmetic aspects of modular and Shimura varieties 2020 Mathematics subject classification: 14G05 (primary); 11G30; 11G18 1 Introduction + The curve X0 (N) is a quotient of the modular curve X0(N) by the Atkin-Lehner involution wN (also called the Fricke + involution). The non-cuspidal points of X0 (N) classify unordered pairs of elliptic curves together with a cyclic isogeny + of degree N between them, where the Atkin-Lehner involution wN sends an isogeny to its dual. -