Clay Mathematics Institute

Dedicated to increasing and disseminating mathematical knowledge

Online Library

Books, lecture notes and articles in pdf form are available below. Please click on the title to download. Books are published in printed form and available for purchase through the AMS bookstore with 20% Student Discount.

Special Editions

The Millennium Prize Problems
James Carlson, Arthur Jaffe, Andrew Wiles
PDF file (1.1 MB) • PDF file with cover (4.8 MB)
Print version at the AMS Bookstore

Monographs

The Geometrization Conjecture
John Morgan and Gang Tian
PDF file (1.5 MB) • PDF file with cover (2.5 MB) 
Print version at the AMS bookstore

Dirichlet Branes and Mirror Symmetry
Michael Douglas and Mark Gross
PDF file (5.0 MB) • PDF file with cover (5.1 MB)
Print version at the AMS bookstore

Ricci Flow and the Poincaré Conjecture
John Morgan and Gang Tian
PDF file (3.6 MB)PDF file with cover (4.2 MB)
Print version at the AMS bookstore

Lecture Notes on Motivic Cohomology
Carlo Mazza, Vladimir Voevodsky, Charles Weibel
PDF file (1.3 MB)PDF file with cover (1.7 MB)
Print version at the AMS bookstore

Mirror Symmetry
Cumrun Vafa and Eric Zaslow
PDF file (4.7 MB)PDF file with cover (4.8 MB)
Print version at the AMS bookstore

Proceedings

A Celebration of Algebraic Geometry
Brendan Hassett, James McKernan, Jason Starr and Ravi Vakil
PDF file with cover (5.1 MB)
Print version at the AMS bookstore

Evolution Equations
David Ellwood, Igor Rodnianski, Gigliola Staffilani and Jared Wunsch
PDF file with cover (4.2 MB)
Print version at the AMS bookstore

Topics in Noncommutative Geometry
Guillermo Cortiñas
PDF file with cover (2.6 MB)
Print version at the AMS bookstore

Probability and Statistical Physics in Two and More Dimensions
David Ellwood, Charles Newman, Vladas Sidoravicius and Wendelin Werner
PDF file with cover (7.5 MB)
Print version at the AMS bookstore

Grassmannians, Moduli Spaces and Vector Bundles
David Ellwood and Emmma Previato
PDF file with cover (2.5 MB)
Print version at the AMS bookstore

On Certain L-Functions
Arthur, James W. Cogdell, Steve Gelbart, David Goldberg, Dinakar Ramakrishnan and Jiu-Kang Yu
PDF file with cover (6 MB)
Print version at the AMS bookstore

Motives, Quantum Field Theory, and Pseudodifferential Operators
Alan Carey, David Ellwood, Sylvie Paycha and Steven Rosenberg
PDF file with cover (4.1 MB)
Print version at the AMS bookstore

Quanta of Maths
Étienne Blanchard, David Ellwood, Masoud Khalkhali, Matilde Marcolli, Henri Moscovici and Sorin Popa
PDF file with cover (8.7 MB)
Print version at the AMS bookstore

Homogeneous Flows, Moduli Spaces and Arithmetic
Manfred Einsiedler, David Ellwood, Alex Eskin, Dmitry Kleinbock, Elon Lindenstrauss, Gregory Margulis, Stefano Marmi and Jean-Christophe Yoccoz
PDF file with cover (5.8 MB)
Print version at the AMS bookstore

The Geometry of Algebraic Cycles
Reza Akhtar, Patrick Brosnan and Roy Joshua
PDF file with cover (1.9 MB)
Print version at the AMS bookstore

Arithmetic Geometry
Henri Darmon, David Ellwood, Brendan Hassett and Yuri Tschinkel
PDF file with cover (4.9 MB)
Print version at the AMS bookstore

Analytic Number Theory: A Tribute to Gauss and Dirichlet
William Duke and Yuri Tschinkel
PDF file (2.2 MB)PDF file with cover (2.6 MB)
Print version at the AMS bookstore

Surveys in Noncommutative Geometry
Nigel Higson, John Roe
PDF file (1.8 MB)
Print version at the AMS bookstore

Floer Homology, Gauge Theory, and Low Dimensional Topology
David Ellwood, Peter Ozsváth, András Stipsicz, Zoltán Szabó
PDF file (2.8 MB)PDF file with cover (3.1 MB)
Print version at the AMS bookstore

Harmonic Analysis, the Trace Formula, and Shimura Varieties
James Arthur, David Ellwood, Robert Kottwitz
PDF file (4.5 MB)PDF file with cover (4.8 MB)
Print version at the AMS bookstore

Global Theory of Minimal Surfaces
David Hoffman
PDF file (27.2 MB)
Print version at the AMS bookstore

Strings and Geometry
Michael Douglas, Jerome Gauntlett, Mark Gross
PDF file (2.9 MB)PDF file with cover (5.6 MB)
Print version at the AMS bookstore

Public Lectures

Are there still unsolved problems about the numbers 1, 2, 3, 4, ... ?
Barry Mazur with figures by William Stein. MIT, May 3, 2005

Is there such a thing as infinity?
Timothy Gowers. Harvard University, March 2004

Research Academy Series

The Clay Research Academy has been suspended for the time being. The Clay Research Academy provided students of exceptional ability the opportunity to experience the challenge and thrill of mathematical research. Students were selected from an international field of applicants to work in close collaboration with leading mathematical researchers.

In addition to the research component of the program, the Academy opened its doors to the local mathematical community through a series of introductory lectures in topics of interest to current research. Guest lectures were given by distinguished mathematicians and physicists from around the world. A list of previous lectures and notes are available from the following links.

2005   2004  2003

Research Award Lectures

Primes: Past, Present, and Future
Ben Green
Harvard University, Nov 5, 2004

The Fundamental Lemma for Unitary Groups
Gérard Laumon and Bao-Chaû Ngô
Harvard University, Nov 5, 2004

Senior Scholar Lectures

The Mathematics of Evolution
Bob Griffiths, Montreal, 2013

Physmatics
Eric Zaslow
Fields Institute, June 2005

Tilings
Federico Ardila and Richard Stanley
IAS/PCMI, July 2004

Tropical Mathematics
David Speyer and Bernd Sturmfels
IAS/PCMI, July 2004

Masterclasses 2014

These notes are included by kind permission of Alexander Ritter.  They are based on lectures he gave for the masterclasses at  Wadham College, Oxford, in August 2014, organised by Wadham College and the CMI-PROMYS Alliance.  Their use is licensed by Alexander Ritter under Creative Commons Licence BY-NC-ND (Attribution-NonCommercial-NoDerivs).

Part 1: Lecture notes on Geometry and Topology (version: September 4, 2014) 
Part 2: Lecture notes on Penrose tilings (version: September 8, 2014)

Summer School 2012

The Resolution of Singular Algebraic Varieties
Summaries, notes, and worksheets from the 2012 Summer School

CRC 2007

The Work of Hacon and McKernan
Alessio Corti, CRC 2007