Video Catalogue
CMI-HIMR Integrable Probability Summer School 2020
Hugo Duminil-Copin, One the free energy of the six-vertex model
Talk 1, July 27, 2020
Talk 2, July 29, 2020
Talk 3, July 31, 2020
Rick Kenyon, Limit shapes and variational principles
Talk 1, July 29, 2020
Talk 2, July 30, 2020
Talk 3, July 31, 2020
Greta Panova, Talk 1: Algebraic combinatorics basics; Talk 2 and 3: Algebraic combinatorics meets probability: statistical mechanics and asymptotics
Talk 1, July 28, 2020
Talk 2, July 30, 2020
Talk 3, July 31, 2020
Fabio Toninelli, (2+1)-dimensional growth models and the AKPZ universality class
Talk 1, July 27, 2020
Talk 2, July 28, 2020
Talk 3, July 29, 2020
Michael Wheeler, An invitation to the q-Whittaker polynomials
Talk 1, July 28, 2020
Talk 2, July 29, 2020
Talk 3, July 30, 2020
Friday Seminars
- Limit shapes and local statistics for the stochastic six-vertex mode
Amol Aggarwal - Relaxation time limit of periodic TASEP
Jinho Bail - Two-point convergence of the stochastic six-vertex model to the Airy process
Evgeni Dimitrov - On eigenvector statistics in non-normal random matrices
Yan Fyodorov - Random matrices as seen from infinite beta, Part 1; Part 2
Vadim Gorin - KPZ universality via Brownian Gibbs analysis
Alan Hammond - Invariant measure for the open KPZ equation
Alisa Knizel - Symmetric functions from vertex models
Leonid Petrov - From TASEP to the KPZ fixed point and KP
Jeremy Quastel - Spin current statistics for the quantum 1D XX spin chain and the Bessel kernel
Tomohiro Sasamoto - Moments and tails of stochastic PDEs
Li-Cheng Tsai - Reflecting Brownian motions and point-to-line last passage percolation
Jon Warren - Variants of RSK and polymers
Nikos Zygouras
2019 Clay Research Conference
- Cohomology of moduli spaces
Oscar Randal-Williams - Challenges in modular representation theory
Geordie Williamson - First order rigidity of high-rank arithmetic groups
Alex Lubotzky - On the conjectures of Gan, Gross, and Prasad
Benedict Gross - The work of Wei Zhang
Christopher Skinner
Clay Lectures
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Decomposition of the diagonal and nilpotence
Claire Voisin, ICMS, November 2018
CMI at 20 (2018)
On September 24-26, 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 3-manifolds
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 Swinnerton-Dyer conjecture
Andrew Wiles - On the Hankel transform and functional equation of automorphic L-functions
Ngô Bao Châu - p-adic 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 three-manifolds
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 Ben-Zvi - What is the Birch and Swinnerton-Dyer 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 Schanuel paradigm
Jonathan Pila - Chinese dragons and mating trees
Scott Sheffield - Steenrod squares and symplectic fixed points
Paul Seidel - Higher-order Fourier analysis and applications
Ben Green - Presentation of the Clay Research Award
Michael Rapoport
2013 Clay Research Conference
- On the Navier-Stokes 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
- 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 3-manifolds
Vladimir Markovic - Perfectoid spaces
Peter Scholze
2011 Clay Research Conference
- Stationary measures on finite volume homogeneous spaces (I)
Jean-François Quint - Stationary measures on finite volume homogeneous spaces (II)
Yves Benoist - The SL(2,R) action on moduli spaces of Riemann surfaces
Alex Eskin - The relevance of logic to transcendental number theory: a motivated account
Alex Wilkie - Diophantine geometry via o-minimality
Jonathan Pila - Recent progress in mathematical general relativity
Mihalis Dafermos - The average rank of elliptical curves
Manjul Bhargava
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 3-manifolds | HR Version
Curtis McMullen - The Mystery of 3-Manifolds | HR Version
William Thurston - Problems in Topology, Post-Perelman
Stephen Smale - Invariants of manifolds and the classification problem | HR Version
Simon Donaldson - Volumes of hyperbolic 3-manifolds | HR Version
David Gabai - What is a manifold? | HR Version
Mikhail Gromov - Collapsing with lower curvature bounds | HR Version
Bruce Kleiner - Collapsing irreducible 3-manifolds with nontrivial fundamental group | HR Version
Gérard Besson - Metric geometry and analysis of 4-manifold | HR Version
Gang Tian
2009 Clay Research Conference
On May 4-5, the Clay Mathematics Institute held its 2009 Clay Research Conference in Harvard Science Center, Lecture Hall E.
- 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: Jean-Loup 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 3-manifolds | HR Version
Yair Minsky - Functoriality: ubiquity and progress | HR Version
Dinakar Ramakrishnan - Endoscopy and harmonic analysis on reductive groups | HR Version
Jean-Loup 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 12-13, at MIT, the Clay Mathematics Institute held its 2008 Clay Research Conference. 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 Schramm-Loewner 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 cross-section 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 24-25, 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 100-year 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 Swinnerton-Dyer Conjecture, P vs NP - The Millennium Prize Problems II
Michael Atiyah, Poincaré conjecture, Hodge conjecture, Quantum Yang-Mills problem, Navier-Stokes problem - The Importance of Mathematics | HR Version
Timothy Gowers - The Millennium Meeting
2001 University of Texas Lectures on the Millennium Problems
- Birch and Swinnerton-Dyer Conjecture
Fernando Rodriguez-Villegas - Hodge Conjecture
Daniel Freed - Navier-Stokes Existence and Smoothness
Luis Caffarelli - P Versus NP
Vijaya Ramachandran - Riemann Hypothesis
Jeffrey Vaaler - Yang-Mills Existence and Mass Gap
Lorenzo Sadun