Proceedings of Symposia in Pure Mathematics,Volume: 101
2019; 450 pp; Hardcover
MSC: Primary 11; 20; 22;
Print ISBN: 978-1-4704-4284-2
This volume contains the proceedings of the Conference on Representation Theory and Algebraic Geometry, held in honor of Joseph Bernstein, from June 11-16, 2017, at the Weizmann Institute of Science and The Hebrew University of Jerusalem.
The topics reflect the decisive and diverse impact of Bernstein on representation theory in its broadest scope. The themes include representations of pp-adic groups and Hecke algebras in all characteristics, representations of real groups and supergroups, theta correspondence, and automorphic forms.
Graduate students and researchers interested in representation theory and automorphic forms.
Mathematical Surveys and Monographs, Volume: 237
2019; 300 pp; Hardcover
MSC: Primary 53; 58; 57;
Print ISBN: 978-1-4704-5014-4
The method of using the moduli space of pseudo-holomorphic curves on a symplectic manifold was introduced by Mikhail Gromov in 1985. From the appearance of Gromov's original paper until today this approach has been the most important tool in global symplectic geometry. To produce numerical invariants of these manifolds using this method requires constructing a fundamental cycle associated with moduli spaces.
This volume brings together three approaches to constructing the gvirtualh fundamental cycle for the moduli space of pseudo-holomorphic curves. All approaches are based on the idea of local Kuranishi charts for the moduli space. Workers in the field will get a comprehensive understanding of the details of these constructions and the assumptions under which they can be made. These techniques and results will be essential in further applications of this approach to producing invariants of symplectic manifolds.
Graduate students and researchers interested in recent developments in symplectic topology and moduli spaces.
Pure and Applied Undergraduate Texts, Volume: 35
2019; 488 pp; Hardcover
MSC: Primary 11; 14;
Print ISBN: 978-1-4704-5016-8
Geometry and the theory of numbers are as old as some of the oldest historical records of humanity. Ever since antiquity, mathematicians have discovered many beautiful interactions between the two subjects and recorded them in such classical texts as Euclid's Elements and Diophantus's Arithmetica. Nowadays, the field of mathematics that studies the interactions between number theory and algebraic geometry is known as arithmetic geometry. This book is an introduction to number theory and arithmetic geometry, and the goal of the text is to use geometry as the motivation to prove the main theorems in the book. For example, the fundamental theorem of arithmetic is a consequence of the tools we develop in order to find all the integral points on a line in the plane. Similarly, Gauss's law of quadratic reciprocity and the theory of continued fractions naturally arise when we attempt to determine the integral points on a curve in the plane given by a quadratic polynomial equation. After an introduction to the theory of diophantine equations, the rest of the book is structured in three acts that correspond to the study of the integral and rational solutions of linear, quadratic, and cubic curves, respectively.
This book describes many applications including modern applications in cryptography; it also presents some recent results in arithmetic geometry. With many exercises, this book can be used as a text for a first course in number theory or for a subsequent course on arithmetic (or diophantine) geometry at the junior-senior level.
Undergraduate and graduate students interested in learning and teaching.
Contemporary Mathematics,Volume: 725
2019; 275 pp; Softcover
MSC: Primary 35; 37; 47; 58; 76; 93;
Print ISBN: 978-1-4704-4109-8
This volume contains the proceedings of the AMS Special Session on Spectral Calculus and Quasilinear Partial Differential Equations and the AMS Special Session on PDE Analysis on Fluid Flows, which were held in January 2017 in Atlanta, Georgia. These two sessions shared the underlying theme of the analysis aspect of evolutionary PDEs and mathematical physics.
The articles address the latest trends and perspectives in the area of nonlinear dispersive equations and fluid flows. The topics mainly focus on using state-of-the-art methods and techniques to investigate problems of depth and richness arising in quantum mechanics, general relativity, and fluid dynamics.
Graduate students and research mathematicians interested in analysis, PDEs, and fluid dynamics.
A co-publication of the AMS and Bar-Ilan University
Contemporary Mathematics, Volume: 726
2019; 224 pp; Softcover
MSC: Primary 03; 08; 20; 16; 17; 18;
Print ISBN: 978-1-4704-3713-8
This volume contains the proceedings of the Research Workshop of the Israel Science Foundation on Groups, Algebras and Identities, held from March 20?24, 2016, at Bar-Ilan University and the Hebrew University of Jerusalem, Israel, in honor of Boris Plotkin's 90th birthday.
The papers in this volume cover various topics of universal algebra, universal algebraic geometry, logic geometry, and algebraic logic, as well as applications of universal algebra to computer science, geometric ring theory, small cancellation theory, and Boolean algebras.
Graduate students and research mathematicians interested in universal algebra, algebraic geometry, group theory, ring theory, and category theory.