Clay Mathematics Proceedings
Each volume in the Clay Mathematics Institute Proceedings Series is developed from lectures given at the annual CMI summer schools or other conference/workshops organzied by the Clay Mathematics Institute. The aim is to give clear, accessible introductions to areas of current research.
Evolution Equations
Editors: David Ellwood, Igor Rodnianski, Gigliola Staffilani and Jared Wunsch
This volume is a collection of notes from lectures given at the 2008 CMI Summer School in Zürich, Switzerland. The main focus of the program was on recent progress in the theory of evolution equations. Such equations lie at the heart of many areas of mathematical physics and arise not only in situations with a manifest time evolution but also in the high energy of semi-classical limits of elliptic problems.
Topics in Noncommutative Geometry
Editor: Guillermo Cortiñas
This volume contains the proceedings of the third Luis Santaló Winter School held at FCEN in 2010. Topics included in this volume concern noncommutative geometry in a broad sense, encompassing various mathematical and physical theories that incorporate geometric ideas to the study of noncommutative phenomena. It explores connections with several areas, including algebra, analysis, geometry, topology and mathematical physics.
Probability and Statistical Physics in Two and More Dimensions
Editors: David Ellwood, Charles Newman,Vladas Sidoravicius and Wendelin Werner
This volume is a collection of lecture notes for six of the ten courses given in Búzios, Brazil by prominent probabilists at the 2010 CMI Summer Schoool, "Probability and Statistical Physics in Two and More Dimesions" and at the XIV Brazilian School of Probability.
Grassmannians, Moduli Spaces and Vector Bundles
Editors: David Ellwood and Emma Previato
This collection of cutting-edge articles on vector bundles and related topics originated from a CMI workshop, held in October 2006, that brought together a community indebted to the pioneering work of P. E. Newstead, visiting the United States for the first time since the 1960s.
On Certain L-Functions
Editors: James Arthur, James W. Cogdell, Steve Gelbart, David Goldberg, Dinakar Ramakrishnan, Jiu-Kang Yu
This volume constitutes the proceedings of a conference, "On certain L-functions", held July 23-27, 2007, at Purdue University, West Lafayette, Indiana. The conference was organized in honor of the 60th birthday of Freydoon Shahidi, widely recognized as having made groundbreaking contributions to the Langlands program.
Motives, Quantum Field Theory, and Pseudodifferential Operators
Editors: Alan Carey, David Ellwood, Sylvie Paycha and Steven Rosenberg
This volume contains articles related to the conference "Motives, Quantum Field Theory, and Pseudodifferential Operators" held at Boston University in June 2008, with partial support from the Clay Mathematics Institute, Boston Uiversity, and the National Science Foundation.
Quanta of Maths
Editors: Étienne Blanchard, David Ellwood, Masoud Khalkhali, Matilde Marcolli, Henri Moscovici and Sorin Popa
The work of Alain Connes has cut a wide swath across several areas of mathematics and physics. Reflecting its broad spectrum and profound impact on the contemporary mathematical landscape, this collection of articles covers a wealth of topics at the forefront of research in operator algebras, analysis, noncommutative geometry, topology, number theory and physics.
Homogeneous Flows, Moduli Spaces and Arithmetic
Editors: Manfred Leopold Einsiedler, David Alexandre Ellwood, Alex Eskin, Dmirty Kleinbock, Elon Lindenstrauss, Gregory Margulis, Stefano Marmi and Jean-Christophe Yoccoz.
This book contains a wealth of material concerning two very active and interconnected directions of current research at the interface of dynamics, number theory and geometry. Examples of the dynamics considered are the action of subgroups of SL(n,R) on the space of unit volume lattices in Rn and the action of SL (2, R) or its subgroups on moduli spaces of flat structures with prescribed singularities on a surface of genus >= 2.
The Geometry of Algebraic Cycles
Editors: Reza Akhtar, Patrick Brosnan and Roy Joshua
The subject of algebraic cycles has its roots in the study of divisors, extending as far back as the nineteenth century. Since then, and in particular in recent years, algebraic cycles have made a significant impact on many fields of mathematics, among them number theory, algebraic geometry, and mathematical physics. The present volume contains articles on all of the above aspects of algebraic cycles. It also contains a mixture of both research papers and expository articles, so that it would be of interest to both experts and beginners in the field.
Arithmetic Geometry
Editors: Henri Darmon, David Alexandre Ellwood, Brendan Hassett and Yuri Tschinkel
This book is based on survey lectures given at the 2006 Clay Summer School on Arithmetic Geometry at the Mathematics Institute of the University of Göttingen. Intended for graduate students and recent Ph.D.'s, this volume will introduce readers to modern techniques and outstanding conjectures at the interface of number theory and algebraic geometry.
Analytic Number Theory: A Tribute to Gauss and Dirichlet
Editors: William Duke and Yuri Tschinkel
Articles in this volume are based on talks given at the Gauss-Dirichlet Conference held in Göttingen on June 20-24, 2005. The conference commemorated the 150th anniversary of the death of C.-F. Gauss and the 200th anniversary of the birth of J.-L. Dirichlet.
Surveys in Noncommutative Geometry
Editors: Nigel Higson and John Roe
In June 2000, the Clay Mathematics Institute organized an Instructional Symposium on Noncommutative Geometry in conjunction with the AMS-IMS-SIAM Joint Summer Research Conference. These events were held at Mount Holyoke College in Massachusetts from June 18 to 29, 2000. The Instructional Symposium consisted of several series of expository lectures which were intended to introduce key topics in noncommutative geometry to mathematicians unfamiliar with the subject. Those expository lectures have been edited and are reproduced in this volume.
Floer Homology, Gauge Theory, and Low Dimensional
Topology
Editors: David Ellwood, Peter Ozsváth, András Stipsicz and Zoltán Szabó
This volume is based on lecture courses and advanced seminars given at the 2004 Clay Mathematics Institute at the Alfréd Rényi Institute of Mathematics in Budapest, Hungary. Several of the authors have added a considerable amount of additional material to that presented at the school, and the resulting volume provides a state-of-the-art introduction to current research, covering material from Heegaard Floer homology, contact geometry, smooth four—manifold topology, and symplectic four—manifolds.
Harmonic Analysis, The Trace Formula,
And Shimura Varieties
Editors: James Arthur, David Ellwood and Robert Kottwitz
The modern theory of automorphic forms, embodied in what has come to be known as the Langlands program, is an extraordinary unifying force in mathematics. It proposes fundamental relations that tie arithmetic information from number theory and algebraic geometry with analytic information from harmonic analysis and group representations. These "reciprocity laws", conjectured by Langlands, are still largely unproved. However, their capacity to unite large areas of mathematics insures that they will be a central area of study for years to come.The goal of this volume is to provide an entry point into this exciting and challenging field.
Global Theory of Minimal Surfaces
Editor: David Hoffman
In the Summer of 2001, the Mathematical Sciences Research Institute (MSRI) hosted the Clay Mathematics Institute Summer School on the Global Theory of Minimal Surfaces. During that time, MSRI became the world center for the study of minimal surfaces: 150 mathematicians--undergraduates, post-doctoral students, young researchers, and world experts--participated in the most extensive meeting ever held on the subject in its 250-year history. The unusual nature of the meeting made it possible to put together this collection of expository lectures and specialized reports, giving a panoramic view of a vital subject presented by leading researchers in the field.
Strings and Geometry
Editors: Michael Douglas, Jerome Gauntlett and Mark Gross
This volume is the proceedings of the 2002 Clay Mathematics Institute School on Geometry and String Theory. This month-long program was held at the Isaac Newton Institute for Mathematical Sciences in Cambridge, England, and was organized by both mathematicians and physicists: A. Corti, R. Dijkgraaf, M. Douglas, J. Gauntlett, M. Gross, C. Hull, A. Jaffe and M. Reid. The early part of the school had many lectures that introduced various concepts of algebraic geometry and string theory with a focus on improving communication between these two fields. During the latter part of the program there were also a number of research level talks.
Strings 2001
Editors: Atish Dabholkar, Sunil Mukhi and Spenta Wadia
String theory, sometimes called the "Theory of Everything", has the potential to provide answers to key questions involving quantum gravity, black holes, supersymmetry, cosmology, singularities and the symmetries of nature. This multi-authored book summarizes the latest results across all areas of string theory from the perspective of world-renowned experts, including Michael Green, David Gross, Stephen Hawking, John Schwarz, Edward Witten and others.
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