ISBN: 978-0-8218-7281-9
Series, Volume: CRM Proceedings & Lecture Notes, Volume 53
Published: 16 September 2011 Pages: 426; Softcover
Logic and Foundations
Algebra and Algebraic Geometry
Graduate students and research mathematicians interested in model theory, logic, and higher-dimensional category theory.
This book deals with the main themes in Mihaly Makkai’s research career: traditional model theory, categorical model theory and logics, and higher-dimensional category theory. Included are both research papers and survey papers, giving useful material for experts and students in these fields. Particularly valuable are papers that show how the techniques and understanding in one field can be productively applied to another; examples are the paper by Harnik, which explains how Shelah’s T e q construction (in model theory) is the same as the categorical notion of pretopos completion; the paper by Kamensky, which gives category-theoretic treatments of sophisticated notions from stability theory; and the paper by Prest relating categorical logic and the model theory of modules. These and other papers in this volume should make this a valuable resource for any mathematician interested in classical or categorical model theory or higher dimensional category theory.
ISBN: 978-2-85629-311-9
Series, Memoires de la Societe Mathematique de France, Number 124
Published: 15 July 2011; Copyright Year: 2011; Pages: 194; Softcover;
Algebra and Algebraic Geometry
Graduate students and research mathematicians interested in algebra and algebraic geometry.
Let E /F be a finite cyclic extension of local or global fields, of degree d . The theory of base change from GLn (F ) to GLn (E ) and the theory of automorphic induction from GLm (E ) to GLm d (F ) are two instances of Langlands’ functoriality principle: when F is local, they correspond respectively to restriction to E of representations of the Weil-Deligne group of F , and induction to F of representations of the Weil-Deligne group of E . If F is a finite extension of a p -adic field Qp , these theories were established long ago (Arthur-Clozel, Henniart-Herb).
In this memoir the authors extend them to the case where F is a non-Archimedean locally compact field of positive characteristic. They also prove, for a global functions field F , that these two local theories are compatible with the global maps of base change and automorphic induction deduced, via the Langlands correspondence proved by Lafforgue, from restriction and induction of global Galois representations.
ISBN: 978-0-8218-6906-2
Series, Volume: MSRI Mathematical Circles Library, Volume 7
Published: 8 October 2011; Copyright Year: 2011; Pages: 176; Softcover
High school and undergraduate students interested in problem solving and mathematical circles.
The Moscow Mathematical Olympiad has been challenging high-school students with stimulating, original problems of different degrees of difficulty for over 75 years. The problems are nonstandard; solving them takes wit, thinking outside the box, and, sometimes, hours of contemplation. Some are within the reach of most mathematically competent high-school students, while others are difficult even for a mathematics professor. Many mathematically inclined students have found that tackling these problems, or even just reading their solutions, is a great way to develop mathematical insight.
In 2006 the Moscow Center for Continuous Mathematical Education began publishing a collection of problems from the Moscow Mathematical Olympiads, providing for each an answer (and sometimes a hint) as well as one or more detailed solutions. This volume represents the years 2000-2005.
The problems and the accompanying material are well suited for math circles. They are also appropriate for problem-solving classes and practice for regional and national mathematics competitions.
Information for our distributors: Titles in this series are co-published with the Mathematical Sciences
ISBN: 978-0-8218-5320-7
Series, Volume: IAS/Park City Mathematics Series, Volume 18
Published: 27 October 2011; Copyright Year: 2011; Pages: 501; Hardcover
Number Theory
Graduate students and research mathematicians interested in number theory and L-functions.
The overall theme of the 2009 IAS/PCMI Graduate Summer School was connections between special values of L-functions and arithmetic, especially the Birch and Swinnerton-Dyer Conjecture and Stark’s Conjecture. These conjectures are introduced and discussed in depth, and progress made over the last 30 years is described. This volume contains the written versions of the graduate courses delivered at the summer school. It would be a suitable text for advanced graduate topics courses on the Birch and Swinnerton-Dyer Conjecture and/or Stark’s Conjecture. The book will also serve as a reference volume for experts in the field.
ISBN: 978-0-8218-7286-4
Series, Volume: Courant Lecture Notes, Volume 22
Published: 23 October 2011; Copyright Year: 2011; Pages: 149; Softcover;
Graduate students and research mathematicians intrested in mathematical biology, population biology, system biology, computational biology, and epidemiology.
Complex diseases involve most aspects of population biology, including genetics, demographics, epidemiology, and ecology. Mathematical methods, including differential, difference, and integral equations, numerical analysis, and random processes, have been used effectively in all of these areas. The aim of this book is to provide sufficient background in such mathematical and computational methods to enable the reader to better understand complex systems in biology, medicine, and the life sciences. It introduces concepts in mathematics to study population phenomena with the goal of describing complicated aspects of a disease, such as malaria, involving several species.
The book is based on a graduate course in computational biology and applied mathematics taught at the Courant Institute of Mathematical Sciences in fall 2010. The mathematical level is kept to essentially advanced undergraduate mathematics, and the results in the book are intended to provide readers with tools for performing more in-depth analysis of population phenomena.
Information for our distributors: Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.