This volume contains the proceedings of the First Mathematical Congress of the Americas, held from August 5?9, 2013, in Guanajuato, Mexico. With the participation of close to 1,000 researchers from more than 40 countries, the meeting set a benchmark for mathematics in the two continents.
The papers, written by some of the plenary and invited speakers, as well as winners of MCA awards, cover new developments in classic topics such as Hopf fibrations, minimal surfaces, and Markov processes, and provide recent insights on combinatorics and geometry, isospectral spherical space forms, homogenization on manifolds, and Lagrangian cobordism, as well as applications to physics and biology.
Contemporary Mathematics
Volume: 656 2016 201 pp; Softcover
Print ISBN: 978-1-4704-2310-0
This volume contains the proceedings of the First Workshop gMatematicos Mexicanos Jovenes en el Mundoh, held from August 22?24, 2012, at Centro de Investigacion en Matematicas (CIMAT) in Guanajuato, Mexico.
One of the main goals of this meeting was to present different research directions being pursued by young Mexican mathematicians based in other countries, such as Brazil, Canada, Colombia, Estonia, Germany, Spain and the United States, showcasing research lines currently underrepresented in Mexico.
Featured are survey and research articles in six areas: algebra, analysis, applied mathematics, geometry, probability and topology. Their topics range from current developments related to well-known open problems to novel interactions between pure mathematics and computer science. Most of the articles provide a panoramic view of the fields and problems the authors work on, making the book accessible to advanced graduate students and researchers in mathematics from different fields.
This book is published in cooperation with Sociedad Matematica Mexicana
Contemporary Mathematics
Volume: 657 2016 237 pp; Softcover
Print ISBN: 978-1-4704-2192-2
This volume includes expanded versions of the lectures delivered in the Graduate Minicourse portion of the 2013 Park City Mathematics Institute session on Geometric Analysis. The papers give excellent high-level introductions, suitable for graduate students wishing to enter the field and experienced researchers alike, to a range of the most important areas of geometric analysis. These include: the general issue of geometric evolution, with more detailed lectures on Ricci flow and Kahler-Ricci flow, new progress on the analytic aspects of the Willmore equation as well as an introduction to the recent proof of the Willmore conjecture and new directions in min-max theory for geometric variational problems, the current state of the art regarding minimal surfaces in R3
AS/Park City Mathematics Series
Volume: 22 2016
Print ISBN: 978-1-4704-2313-1
This book is an introduction to the theory of algebraic spaces and stacks intended for graduate students and researchers familiar with algebraic geometry at the level of a first-year graduate course. The first several chapters are devoted to background material including chapters on Grothendieck topologies, descent, and fibered categories. Following this, the theory of algebraic spaces and stacks is developed. The last three chapters discuss more advanced topics including the Keel-Mori theorem on the existence of coarse moduli spaces, gerbes and Brauer groups, and various moduli stacks of curves. Numerous exercises are included in each chapter ranging from routine verifications to more difficult problems, and a glossary of necessary category theory is included as an appendix.
It is splendid to have a self-contained treatment of stacks, written by a leading practitioner. Finally we have a reference where one can find careful statements and proofs of many of the foundational facts in this important subject. Researchers and students at all levels will be grateful to Olsson for writing this book.
Graduate students and research mathematicians interested in algebraic spaces and stacks.
Colloquium Publications
Volume: 62
Print ISBN: 978-1-4704-2798-6
This book brings a reader to the cutting edge of several important directions of the contemporary probability theory, which in many cases are strongly motivated by problems in statistical physics. The authors of these articles are leading experts in the field and the reader will get an exceptional panorama of the field from the point of view of scientists who played, and continue to play, a pivotal role in the development of the new methods and ideas, interlinking it with geometry, complex analysis, conformal field theory, etc., making modern probability one of the most vibrant areas in mathematics.
Graduate students and research mathematicians interested in recent developments in probability and statistical physics and random structures in mathematics.
Proceedings of Symposia in Pure Mathematics
Volume: 91 2016 471 pp; Softcover
Print ISBN: 978-1-4704-2248-6
The subject of this book is the theory of operads and colored operads, sometimes called symmetric multicategories. A (colored) operad is an abstract object which encodes operations with multiple inputs and one output and relations between such operations. The theory originated in the early 1970s in homotopy theory and quickly became very important in algebraic topology, algebra, algebraic geometry, and even theoretical physics (string theory). Topics covered include basic graph theory, basic category theory, colored operads, and algebras over colored operads. Free colored operads are discussed in complete detail and in full generality.
The intended audience of this book includes students and researchers in mathematics and other sciences where operads and colored operads are used. The prerequisite for this book is minimal. Every major concept is thoroughly motivated. There are many graphical illustrations and about 150 exercises. This book can be used in a graduate course and for independent study.
Graduate Studies in Mathematics
Volume: 170 2016 428 pp; Softcover
Print ISBN: 978-1-4704-2723-8
Graduate students and research mathematicians interested in the use of operads in various areas of mathematics.