Edited by: Stephane Ballet, Aix-Marseille University, France, Marc Perret, Universite de Toulouse II Le Mirail, France, and Alexey Zaytsev, Immanuel Kant Baltic Federal University, Kaliningrad, Russia

Algorithmic Arithmetic, Geometry, and Coding Theory

Contemporary Mathematics, Volume: 637
2015; 306 pp; softcover
ISBN-13: 978-1-4704-1461-0
Expected publication date is May 27, 2015.

This volume contains the proceedings of the 14th International Conference on Arithmetic, Geometry, Cryptography, and Coding Theory (AGCT), held June 3-7, 2013, at CIRM, Marseille, France.

These international conferences, held every two years, have been a major event in the area of algorithmic and applied arithmetic geometry for more than 20 years.

This volume contains 13 original research articles covering geometric error correcting codes, and algorithmic and explicit arithmetic geometry of curves and higher dimensional varieties. Tools used in these articles include classical algebraic geometry of curves, varieties and Jacobians, Suslin homology, Monsky-Washnitzer cohomology, and L-functions of modular forms.

Readership

Graduate students and research mathematicians interested in algebraic geometry and related topics of coding theory.

Table of Contents

Edited by: Javad Mashreghi, Laval University, Quebec, Canada, Emmanuel Fricain, Universite Lille 1, Villeneuve d'Ascq, France, and William Ross, University of Richmond, VA

Invariant Subspaces of the Shift Operator

Contemporary Mathematics, Volume: 638
2015; 317 pp; softcover
ISBN-13: 978-1-4704-1045-2
Expected publication date is May 27, 2015.

This volume contains the proceedings of the CRM Workshop on Invariant Subspaces of the Shift Operator, held August 26-30, 2013, at the Centre de Recherches Mathematiques, Universite de Montreal, Montreal, Quebec, Canada.

The main theme of this volume is the invariant subspaces of the shift operator (or its adjoint) on certain function spaces, in particular, the Hardy space, Dirichlet space, and de Branges-Rovnyak spaces.

These spaces, and the action of the shift operator on them, have turned out to be a precious tool in various questions in analysis such as function theory (Bieberbach conjecture, rigid functions, Schwarz-Pick inequalities), operator theory (invariant subspace problem, composition operator), and systems and control theory.

Of particular interest is the Dirichlet space, which is one of the classical Hilbert spaces of holomorphic functions on the unit disk. From many points of view, the Dirichlet space is an interesting and challenging example of a function space. Though much is known about it, several important open problems remain, most notably the characterization of its zero sets and of its shift-invariant subspaces.

Readership

Graduate students and research mathematicians interested in operator theory and function spaces.

Table of Contents

Edited by: C. S. Aravinda, TIFR, Bangalore, India, William M. Goldman, University of Maryland, College Park, MD, Krishnendu Gongopadhyay, Indian Institute of Science Education and Research, Punjab, India, Alexander Lubotzky, Hebrew University of Jerusalem, Israel, Mahan Mj, RKM Vivekanada University, Howrah, India, and Anthony Weaver, Bronx Community College, CUNY, New York, NY

Geometry, Groups and Dynamics

Contemporary Mathematics, Volume: 639
2015; 369 pp; softcover
ISBN-13: 978-0-8218-9882-6
Expected publication date is May 27, 2015.

This volume contains the proceedings of the ICTS Program: Groups, Geometry and Dynamics, held December 3-16, 2012, at CEMS, Almora, India. The activity was an academic tribute to Ravi S. Kulkarni on his turning seventy.

Articles included in this volume, both introductory and advanced surveys, represent the broad area of geometry that encompasses a large portion of group theory (finite or otherwise) and dynamics in its proximity. These areas have been influenced by Kulkarni's ideas and are closely related to his work and contribution.

Readership

Graduate students and research mathematicians interested in geometry group theory and related areas.

Table of Contents

Shiri Artstein-Avidan, Tel Aviv University, Israel, Apostolos Giannopoulos, University of Athens, Greece, and Vitali D. Milman, Tel Aviv University, Israel

Asymptotic Geometric Analysis, Part I

Mathematical Surveys and Monographs, Volume: 202
2015; 451 pp; hardcover
ISBN-13: 978-1-4704-2193-9
Expected publication date is June 22, 2015.

The authors present the theory of asymptotic geometric analysis, a field which lies on the border between geometry and functional analysis. In this field, isometric problems that are typical for geometry in low dimensions are substituted by an "isomorphic" point of view, and an asymptotic approach (as dimension tends to infinity) is introduced. Geometry and analysis meet here in a non-trivial way. Basic examples of geometric inequalities in isomorphic form which are encountered in the book are the "isomorphic isoperimetric inequalities" which led to the discovery of the "concentration phenomenon", one of the most powerful tools of the theory, responsible for many counterintuitive results.

A central theme in this book is the interaction of randomness and pattern. At first glance, life in high dimension seems to mean the existence of multiple "possibilities", so one may expect an increase in the diversity and complexity as dimension increases. However, the concentration of measure and effects caused by convexity show that this diversity is compensated and order and patterns are created for arbitrary convex bodies in the mixture caused by high dimensionality.

The book is intended for graduate students and researchers who want to learn about this exciting subject. Among the topics covered in the book are convexity, concentration phenomena, covering numbers, Dvoretzky-type theorems, volume distribution in convex bodies, and more.

Readership

Graduate students and research mathematicians interested in geometric functional analysis and applications.

Table of Contents

Olli Lehto, University of Helsinki, Finland
Translated by William Hellberg

Lars Ahlfors -- At the Summit of Mathematics

2015; 125 pp; softcover
ISBN-13: 978-1-4704-1846-5
Expected publication date is July 13, 2015.

This book tells the story of the Finnish-American mathematician Lars Ahlfors (1907-1996). He was educated at the University of Helsinki as a student of Ernst Lindelof and Rolf Nevanlinna and later became a professor there. He left Finland permanently in 1944 and was professor and emeritus at Harvard University for more than fifty years.

Already at the age of twenty-one Ahlfors became a well-known mathematician having solved Denjoy's conjecture, and in 1936 he established his world renown when he was awarded the Fields Medal, the "Nobel Prize in mathematics". In this book the description of his mathematics avoids technical details and concentrates on his contributions to the general development of complex analysis.

Besides mathematics there is also a lot to tell about Ahlfors. World War II marked his life, and he was a colorful personality, with many interesting stories about him.

Olli Lehto, the author of the book, first met Lars Ahlfors and his family as a young doctor at Harvard in 1950. Numerous meetings after that in various parts of the world led to a close friendship between them.

Readership

Undergraduate and graduate students and research mathematicians interested in the history of mathematics.

Table of Contents

Family background
Exceptional talent emerges
Mathematical renown secured
To America and back again
War years in Finland
In Sweden and Switzerland
Professorship at Harvard University
The legacy of Riemann and Teichmuller
New research and return to the old
Distinctions
Additions to the portrait
Epilogue in Finland
Sources
Index