Softcover ISBN:  9781470437848 
Product Code:  CONM/740 
List Price:  $117.00 
MAA Member Price:  $105.30 
AMS Member Price:  $93.60 
Electronic ISBN:  9781470456290 
Product Code:  CONM/740.E 
List Price:  $117.00 
MAA Member Price:  $105.30 
AMS Member Price:  $93.60 

Book DetailsContemporary MathematicsVolume: 740; 2019; 248 ppMSC: Primary 11; 20; 05; 19; 14;
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 \(\mathrm{SL}_2(\mathbb{F}_q)\) 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 SatoTate groups and explores their relationship with Galois representations, motivic \(L\)functions, and MumfordTate groups.ReadershipGraduate students and research mathematicians interested in arithmetic and algebraic geometry and analytic number theory.

Table of Contents

Articles

Alina Carmen Cojocaru  Primes, elliptic curves and cyclic groups

Harald Andrés Helfgott  Growth and expansion in algebraic groups over finite fields

Étienne Fouvry, Emmanuel Kowalski, Philippe Michel and Will Sawin  Lectures on applied $\ell $adic cohomology

Andrew V. Sutherland  SatoTate distributions


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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 \(\mathrm{SL}_2(\mathbb{F}_q)\) 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 SatoTate groups and explores their relationship with Galois representations, motivic \(L\)functions, and MumfordTate groups.
Graduate students and research mathematicians interested in arithmetic and algebraic geometry and analytic number theory.

Articles

Alina Carmen Cojocaru  Primes, elliptic curves and cyclic groups

Harald Andrés Helfgott  Growth and expansion in algebraic groups over finite fields

Étienne Fouvry, Emmanuel Kowalski, Philippe Michel and Will Sawin  Lectures on applied $\ell $adic cohomology

Andrew V. Sutherland  SatoTate distributions