Video Catalogue
2019 Clay Research Conference
 Cohomology of moduli spaces
Oscar RandalWilliams  Challenges in modular representation theory
Geordie Williamson  First order rigidity of highrank arithmetic groups
Alex Lubotzky  On the conjectures of Gan, Gross, and Prasad
Benedict Gross  The work of Wei Zhang
Christopher Skinner
Clay Lectures

Decomposition of the diagonal and nilpotence
Claire Voisin, ICMS, November 2018
CMI at 20 (2018)
On September 2426, 2018 CMI held a 20th anniversary conference to celebrate its many contributions to the international mathematcal comminity. CMI at 20 highlighted the outstanding achievements of its research fellows, award winners, and others whom it has supported.
 Perelman's work on the Poincaré Conjecture and geometrization of 3manifolds
John Morgan
Correction: the work cited at 1:02:30 is of Richard Bamler.  The anatomy of integers and permutations
Ben Green  New results on rationality questions
Claire Voisin  Twenty years of the Birch SwinnertonDyer conjecture
Andrew Wiles  On the Hankel transform and functional equation of automorphic Lfunctions
Ngô Bao Châu  padic geometry
Peter Scholze  The work of Jason Miller and Scott Sheffield
Wendelin Werner  Percolation crossings and complex analysis
Stanislav Smirnov  Smoothing finite group actions on threemanifolds
John Pardon  Characters and difference equations
Andrei Okounkov
2017 Clay Research Conference
 Introduction to decoupling (Summary)
Larry Guth  Algebraic geometry, categories and trace formulas (Summary)
Bertrand Töen  From second order equations to nonlocal PDEs (Summary)
Ovidiu Savin  Dynamics, arithmetic progressions and approximate cohomology (Summary)
Tamar Ziegler  The work of Aleksandr Logunov and Eugenia Malinnikova
Carlos Kenig  The work of Maryna Viazovska
Henry Cohn
PROMYS Europe 2016
2016 Clay Research Conference
 Representation theory as gauge theory. Slides are also available
David BenZvi  What is the Birch and SwinnertonDyer Conjecture, and what is known about it?
Manjul Bhargava  The mean curvature flow
Bill Minicozzi  Celestial surfaces and quadratic forms
János Kollár
2015 Clay Research Conference
 Algebraic and motivic vector bundles
Mike Hopkins  Cohomology of algebraic varieties
Peter Scholze  Formation of singularities in fluid interfaces
Charles Fefferman  Enumerative geometry and representation theory
Andrei Okounkov  The work of Maryam Mirzakhani
Howard Masur  Mathematics without borders: Larry Guth and Nets Katz
Gil Kalai
2015 AMS Summer Institute in Algebraic Geometry
2014 Clay Research Conference
The 2014 Clay Research Conference was held in the Andrew Wiles Building at the University of Oxford
 The Schanuel paradigm
Jonathan Pila  Chinese dragons and mating trees
Scott Sheffield  Steenrod squares and symplectic fixed points
Paul Seidel  Higherorder Fourier analysis and applications
Ben Green  Presentation of the Clay Research Award
Michael Rapoport
2013 Clay Research Conference
The 2013 Clay Research Conference was held in the Andrew Wiles Building at the University of Oxford
 On the NavierStokes Equations
Peter Constantin  A Personal View of the P versus NP Problem
Lance Fortnow  The Birch—Swinnerton–Dyer Conjecture: a Status Report
Fernando Rodriguez Villegas  A New Look at the Jones Polynomial of a Knot
Ed Witten  The Clay Research Award
Richard Thomas  Animation, Teeth and Skeletons
Ingrid Daubechies
2012 Clay Research Conference
The 2012 Clay Research Conference was held in the Martin Wood Lecture Theatre at the University of Oxford.
 Multiple zeta values
Francis Brown  The quantum content of the gluing equations
Stavros Garoufalidis  The good pants homology and the Ehrenpreis conjecture
Jeremy Kahn  The Dehn surgery problem
Marc Lackenby  Virtual geometry of Riemann surfaces and hyperbolic 3manifolds
Vladimir Markovic  Perfectoid spaces
Peter Scholze
2010 Clay Research Conference
The topic of the 2010 Clay Research Conference was Grigoriy Perelman's proof of the Poincaré conjecture and Thurston's Geometrization conjecture. Perelman's proof, which appeared in a series of three preprints posted on ArXiv.org in 2002 and 2003, is based on Riemannian geometry and Hamilton's theory of Ricci flow. For that work he was awarded the first Clay Millennium Prize.
 "Les maths ne sont qu'une histoire de groupes" – H. Poincaré, 1881  HR Version
Étienne Ghys  Geometry in 2, 3 and 4 Dimensions  HR Version
Michael Atiyah  History of the Poincaré Conjecture  HR Version
John Morgan  The evolution of geometric structures on 3manifolds  HR Version
Curtis McMullen  The Mystery of 3Manifolds  HR Version
William Thurston  Problems in Topology, PostPerelman
Stephen Smale  Invariants of manifolds and the classification problem  HR Version
Simon Donaldson  Volumes of hyperbolic 3manifolds  HR Version
David Gabai  What is a manifold?  HR Version
Mikhail Gromov  Collapsing with lower curvature bounds  HR Version
Bruce Kleiner  Collapsing irreducible 3manifolds with nontrivial fundamental group  HR Version
Gérard Besson  Metric geometry and analysis of 4manifold  HR Version
Gang Tian
2009 Clay Research Conference
On May 45, the Clay Mathematics Institute held its 2009 Clay Research Conference in Harvard Science Center, Lecture Hall E. The program featured eight lectures on recent research advances, as well as presentation of the Clay Research Awards.
 Resolution of singularities in zero and positive characteristic  HR Version
Herwig Hauser  Resolution of singularities in algebraic geometry  HR Version
Heisuke Hironaka  Presentation of the Clay Research Awards  HR Version
Awardees: JeanLoup Waldspurger, Ian Agol, Danny Calegari, and David Gabai  Some remarks on SLE and an extended Sullivan dictionary  HR Version
Peter Jones  Topology and geometry of ends of hyperbolic 3manifolds  HR Version
Yair Minsky  Functoriality: ubiquity and progress  HR Version
Dinakar Ramakrishnan  Endoscopy and harmonic analysis on reductive groups  HR Version
JeanLoup Waldspurger  Billiards and moduli spaces  HR Version
Curtis T. McMullen  Quantum unique ergodicity and number theory  HR Version
Kannan Soundararajan
2008 Clay Research Conference
On May 1213, at MIT, the Clay Mathematics Institute held its 2008 Clay Research Conference. The program consisted of a twoday series of lectures on recent research developments, together with presentation of the Clay Research Awards. The conference was hosted by the MIT Mathematics Department.
 A Wilsonian point of view on renormalization of quantom field theories  HR
Kevin Costello  A generalized Fredholm theory and some new ideas in nonlinear analysis and geometry  HR
Helmut Hofer  Local integrability of holomorphic functions HR
János Kollár  Monopoles, closed Reeb orbits and spectral flow: Taubes' work on the Weinstein conjecture  HR
Tom Mrowka  Probabilistic reasoning in quantitative geometry  HR
Assaf Naor  Curve counting via stable pairs in the derived category  HR
Rahul Pandharipande  Quantum gravity and the SchrammLoewner evolution  HR
Scott Sheffield  Hodge structures, cohomology algebras and the Kodaira problem  HR
Claire Voisin  Awards Ceremony  HR
Public Lectures
 A Tribute to Euler  HR Version
William Dunham, Harvard University, October 2008  The Music of the Primes  HR Version
Marcus du Sautoy, MIT, May 2008  Beyond Computation
Michael Sipser, MIT, October 2006
2004 Annual Meeting
 Fundamental Lemma for Unitary Groups
Gerárd Laumon, Harvard University, November 2004  Primes: Past, Present, and Future
Ben Green, Harvard University, November 2004
2002 Annual Meeting
 A History of Primes
Manindra Agrawal, American Academy of Arts and Sciences, October 2002  An Intuitive Introduction to Motivic Homotopy Theory
Vladimir Voevodsky, American Academy of Arts and Sciences, October 2002
2001 Annual Meeting
On July 13, 2001 the Clay Mathematics Institute organized the closing ceremonies of the International Mathematics Olympiad in Washington, DC, and incorporated this event into its 2001 Annual Meeting. The events brought approximately five hundred of the world's best high school mathematics students in contact with a crosssection of the world's best research mathematicians, including Edward Witten, Andrew Wiles, and Arthur Jaffe. The meeting of the Clay Mathematics Institute took place at the John F. Kennedy Center for the Performing Arts at 2:00 PM on July 13. This ceremony included the presentation of the Clay Research Awards and two inspirational talks by CMI Scientific Advisory Board members Andrew Wiles and Edward Witten. Following the ceremony at the Kennedy Center was a reception and dinner at the National Building Museum in Washington, DC. The dinner involved almost eleven hundred guests, and included talks by Alfred R. Berkeley, III, Chairman of NASDAQ, and Rita Colwell, Director of the National Science Foundation, as well as other forms of entertainment including a live performance by Christopher Thompson, accompanied by Milton Granger, of an excerpt fromFermat's Last Tango.
Millennium Meeting
These videos document the Institute's landmark Paris millennium event which took place on May 2425, 2000, at the Collège de France. On this occasion, CMI unveiled the "Millennium Prize Problems," seven mathematical quandaries that have long resisted solution. The announcement in Paris honored the 100year anniversary of David Hilbert's apress of 1900 to the International Congress of Mathematicians in Paris, in which he outlined 23 mathematics problems that set the tone for much 20th century mathematical research.
 The Millennium Prize Problems I
John Tate, Riemann hypothesis, Birch and SwinnertonDyer Conjecture, P vs NP  The Millennium Prize Problems II
Michael Atiyah, Poincaré conjecture, Hodge conjecture, Quantum YangMills problem, NavierStokes problem  The Importance of Mathematics  HR Version
Timothy Gowers  The Millennium Meeting
2001 University of Texas Lectures on the Millennium Problems
 Birch and SwinnertonDyer Conjecture
Fernando RodriguezVillegas  Hodge Conjecture
Daniel Freed  NavierStokes Existence and Smoothness
Luis Caffarelli  P Versus NP
Vijaya Ramachandran  Riemann Hypothesis
Jeffrey Vaaler  YangMills Existence and Mass Gap
Lorenzo Sadun