# 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

**The Resolution of Singular Algebraic Varieties**

David Ellwood, Herwig Hauser, Shigefumi Mori, Josef Schicho

PDF file with cover (2.9 MB)

Print version at the AMS bookstore

**The Poincaré Conjecture**

James Carlson

PDF file (23.4 MB)

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**A Celebration of Algebraic Geometry**

Brendan Hassett, James McKernan, Jason Starr and Ravi Vakil

PDF file with cover (5.1 MB)

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**Evolution Equations**

David Ellwood, Igor Rodnianski, Gigliola Staffilani and Jared Wunsch

PDF file with cover (4.2 MB)

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**Topics in Noncommutative Geometry**

Guillermo Cortiñas

PDF file with cover (2.6 MB)

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**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)

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**Grassmannians, Moduli Spaces and Vector Bundles**

David Ellwood and Emmma Previato

PDF file with cover (2.5 MB)

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**On Certain L-Functions**

Arthur, James W. Cogdell, Steve Gelbart, David Goldberg, Dinakar Ramakrishnan and Jiu-Kang Yu

PDF file with cover (6 MB)

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**Motives, Quantum Field Theory, and Pseudodifferential Operators**

Alan Carey, David Ellwood, Sylvie Paycha and Steven Rosenberg

PDF file with cover (4.1 MB)

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**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)

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**Arithmetic Geometry**

Henri Darmon, David Ellwood, Brendan Hassett and Yuri Tschinkel

PDF file with cover (4.9 MB)

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**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)

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**Surveys in Noncommutative Geometry**

Nigel Higson, John Roe

PDF file (1.8 MB)

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**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.

## 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