Clay Mathematics Institute

Dedicated to increasing and disseminating mathematical knowledge

Lectures and Other Publications

Algebraic Geometry: Salt Lake City 2015

Hall algebras and Donaldson-Thomas invariants
Tom Bridgeland

Stability of algebraic varieties and Kähler geometry
Simon K. Donaldson

Boundedness of varieties of log general type
Christopher D. Hacon, James McKernan, and Chenyang Xu

Enumerative geometry and geometric representation theory
Andrei Okounkov

A calculus for the moduli space of curves
Rahul Pandharipande

The Cremona group
Serge Cantat

Some fundamental groups in arithmetic geometry
Hélène Esnault

Instrinsic mirror symmetry and punctured Gromov-Witten invariants
Mark Gross and Bernd Siebert

Print version available at the AMS bookstore

Clay Lecture Notes

Lectures on Geometry

PROMYS Europe 2015

Patterns in the Primes
James Maynard

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)

Senior Scholar Lectures

The Mathematics of Evolution
Bob Griffiths, Montreal, 2013

Eric Zaslow
Fields Institute, June 2005

Federico Ardila and Richard Stanley
IAS/PCMI, July 2004

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

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

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