Analytic Methods In Arithmetic Geometry
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Analytic Methods In Arithmetic Geometry
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Author : Alina Bucur
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-11-22
Analytic Methods In Arithmetic Geometry written by Alina Bucur and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-22 with Education categories.
In the last decade or so, analytic methods have had great success in answering questions in arithmetic geometry and number theory. The School provided a unique opportunity to introduce graduate students to analytic methods in arithmetic geometry. The book contains four articles. Alina C. Cojocaru's article introduces sieving techniques to study the group structure of points of the reduction of an elliptic curve modulo a rational prime via its division fields. Harald A. Helfgott's article provides an introduction to the study of growth in groups of Lie type, with SL2(Fq) and some of its subgroups as the key examples. The article by Étienne Fouvry, Emmanuel Kowalski, Philippe Michel, and Will Sawin describes how a systematic use of the deep methods from ℓ-adic cohomology pioneered by Grothendieck and Deligne and further developed by Katz and Laumon help make progress on various classical questions from analytic number theory. The last article, by Andrew V. Sutherland, introduces Sato-Tate groups and explores their relationship with Galois representations, motivic L-functions, and Mumford-Tate groups.
Analytic Methods In Arithmetic Geometry
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Author : David Zureick-Brown
language : en
Publisher:
Release Date : 2019
Analytic Methods In Arithmetic Geometry written by David Zureick-Brown and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Arithmetical algebraic geometry categories.
This volume contains the proceedings of the Arizona Winter School 2016, which was held from March 12-16, 2016, at The University of Arizona, Tucson, AZ. In the last decade or so, analytic methods have had great success in answering questions in arithmetic geometry and number theory. The School provided a unique opportunity to introduce graduate students to analytic methods in arithmetic geometry. The book contains four articles. Alina C. Cojocaru's article introduces sieving techniques to study the group structure of points of the reduction of an elliptic curve modulo a rational prime via its division fields. Harald A. Helfgott's article provides an introduction to the study of growth in groups of Lie type, with \mathrmSL}_2(\mathbb{F}_q) and some of its subgroups as the key examples. The article by Étienne Fouvry, Emmanuel Kowalski, Philippe Michel, and Will Sawin describes how a systematic use of the deep methods from \ell-adic cohomology pioneered by Grothendieck and Deligne and further developed by Katz and Laumon help make progress on various classical questions from analytic number theory. The last article, by Andrew V. Sutherland, introduces Sato-Tate groups and explores their relationship with Galois representations, motivic L-functions, and Mumford-Tate groups.
New Complex Analytic Methods In The Study Of Non Orientable Minimal Surfaces In Rn
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Author : Antonio Alarcón
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-05-13
New Complex Analytic Methods In The Study Of Non Orientable Minimal Surfaces In Rn written by Antonio Alarcón and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-13 with Education categories.
All the new tools mentioned above apply to non-orientable minimal surfaces endowed with a fixed choice of a conformal structure. This enables the authors to obtain significant new applications to the global theory of non-orientable minimal surfaces. In particular, they construct proper non-orientable conformal minimal surfaces in Rn with any given conformal structure, complete non-orientable minimal surfaces in Rn with arbitrary conformal type whose generalized Gauss map is nondegenerate and omits n hyperplanes of CPn−1 in general position, complete non-orientable minimal surfaces bounded by Jordan curves, and complete proper non-orientable minimal surfaces normalized by bordered surfaces in p-convex domains of Rn.
Arithmetic Geometry And Number Theory
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Author : Lin Weng
language : en
Publisher: World Scientific
Release Date : 2006-06-02
Arithmetic Geometry And Number Theory written by Lin Weng and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-02 with Mathematics categories.
Mathematics is very much a part of our culture; and this invaluable collection serves the purpose of developing the branches involved, popularizing the existing theories and guiding our future explorations.More precisely, the goal is to bring the reader to the frontier of current developments in arithmetic geometry and number theory through the works of Deninger-Werner in vector bundles on curves over p-adic fields; of Jiang on local gamma factors in automorphic representations; of Weng on Deligne pairings and Takhtajan-Zograf metrics; of Yoshida on CM-periods; of Yu on transcendence of special values of zetas over finite fields. In addition, the lecture notes presented by Weng at the University of Toronto from October to November 2005 explain basic ideas and the reasons (not just the language and conclusions) behind Langlands' fundamental, yet notably difficult, works on the Eisenstein series and spectral decompositions.And finally, a brand new concept by Weng called the Geometric Arithmetic program that uses algebraic and/or analytic methods, based on geometric considerations, to develop the promising and yet to be cultivated land of global arithmetic that includes non-abelian Class Field Theory, Riemann Hypothesis and non-abelian Zeta and L Functions, etc.
Arithmetic Geometry Of Logarithmic Pairs And Hyperbolicity Of Moduli Spaces
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Author : Marc-Hubert Nicole
language : en
Publisher: Springer Nature
Release Date : 2020-10-31
Arithmetic Geometry Of Logarithmic Pairs And Hyperbolicity Of Moduli Spaces written by Marc-Hubert Nicole and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-31 with Mathematics categories.
This textbook introduces exciting new developments and cutting-edge results on the theme of hyperbolicity. Written by leading experts in their respective fields, the chapters stem from mini-courses given alongside three workshops that took place in Montréal between 2018 and 2019. Each chapter is self-contained, including an overview of preliminaries for each respective topic. This approach captures the spirit of the original lectures, which prepared graduate students and those new to the field for the technical talks in the program. The four chapters turn the spotlight on the following pivotal themes: The basic notions of o-minimal geometry, which build to the proof of the Ax–Schanuel conjecture for variations of Hodge structures; A broad introduction to the theory of orbifold pairs and Campana's conjectures, with a special emphasis on the arithmetic perspective; A systematic presentation and comparison between different notions of hyperbolicity, as an introduction to the Lang–Vojta conjectures in the projective case; An exploration of hyperbolicity and the Lang–Vojta conjectures in the general case of quasi-projective varieties. Arithmetic Geometry of Logarithmic Pairs and Hyperbolicity of Moduli Spaces is an ideal resource for graduate students and researchers in number theory, complex algebraic geometry, and arithmetic geometry. A basic course in algebraic geometry is assumed, along with some familiarity with the vocabulary of algebraic number theory.
Analytical Methods Of Optimization
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Author : D. F. Lawden
language : en
Publisher: Courier Corporation
Release Date : 2006-05-05
Analytical Methods Of Optimization written by D. F. Lawden and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-05 with Mathematics categories.
Suitable for advanced undergraduates and graduate students, this text surveys the classical theory of the calculus of variations. It takes the approach most appropriate for applications to problems of optimizing the behavior of engineering systems. Two of these problem areas have strongly influenced this presentation: the design of the control systems and the choice of rocket trajectories to be followed by terrestrial and extraterrestrial vehicles. Topics include static systems, control systems, additional constraints, the Hamilton-Jacobi equation, and the accessory optimization problem. Prerequisites include a course in the analysis of functions of many real variables and a familiarity with the elementary theory of ordinary differential equations, especially linear equations. Emphasis throughout the text is placed upon methods and principles, which are illustrated by worked problems and sets of exercises. Solutions to the exercises are available from the publisher upon request.
Arithmetic Geometry Number Theory And Computation
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Author : Jennifer S. Balakrishnan
language : en
Publisher: Springer Nature
Release Date : 2022-03-15
Arithmetic Geometry Number Theory And Computation written by Jennifer S. Balakrishnan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-15 with Mathematics categories.
This volume contains articles related to the work of the Simons Collaboration “Arithmetic Geometry, Number Theory, and Computation.” The papers present mathematical results and algorithms necessary for the development of large-scale databases like the L-functions and Modular Forms Database (LMFDB). The authors aim to develop systematic tools for analyzing Diophantine properties of curves, surfaces, and abelian varieties over number fields and finite fields. The articles also explore examples important for future research. Specific topics include● algebraic varieties over finite fields● the Chabauty-Coleman method● modular forms● rational points on curves of small genus● S-unit equations and integral points.
Analytic Trends In Mathematical Physics
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Author : Houssam Abdul-Rahman
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-01-06
Analytic Trends In Mathematical Physics written by Houssam Abdul-Rahman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-06 with Education categories.
This volume contains the proceedings of the Arizona School of Analysis and Mathematical Physics, held from March 5–9, 2018, at the University of Arizona, Tucson, Arizona. A main goal of this school was to introduce graduate students and postdocs to exciting topics of current research that are both influenced by physical intuition and require the use of cutting-edge mathematics. The articles in this volume reflect recent progress and innovative techniques developed within mathematical physics. Two works investigate spectral gaps of quantum spin systems. Specifically, Abdul-Rahman, Lemm, Lucia, Nachtergaele, and Young consider decorated AKLT models, and Lemm demonstrates a finite-size criterion for D D-dimensional models. Bachmann, De Roeck, and Fraas summarize a recent proof of the adiabatic theorem, while Bachmann, Bols, De Roeck, and Fraas discuss linear response for interacting Hall insulators. Models on general graphs are the topic of the articles by Fischbacher, on higher spin XXZ, and by Latushkin and Sukhtaiev, on an index theorem for Schrödinger operators. Probabilistic applications are the focus of the articles by DeMuse and Yin, on exponential random graphs, by Saenz, on KPZ universality, and by Stolz, on disordered quantum spin chains. In all, the diversity represented here is a testament to the enthusiasm this rich field of mathematical physics generates.
Analytic Methods In Algebraic Geometry
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Author : Jean-Pierre Demailly
language : en
Publisher:
Release Date : 2010
Analytic Methods In Algebraic Geometry written by Jean-Pierre Demailly and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with categories.
Arithmetic Geometry
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Author : Clay Mathematics Institute. Summer School
language : en
Publisher: American Mathematical Soc.
Release Date : 2009
Arithmetic Geometry written by Clay Mathematics Institute. Summer School and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
Based on survey lectures given at the 2006 Clay Summer School on Arithmetic Geometry at the Mathematics Institute of the University of Gottingen, this tile is intended for graduate students and recent PhD's. It introduces readers to modern techniques and conjectures at the interface of number theory and algebraic geometry.