# Video Catalogue

## PROMYS Europe 2016

## 2016 Clay Research Conference

- Representation Theory as Gauge Theory (Slides)

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 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 - Higher-order 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 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

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 3-manifolds

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 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. 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: 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 program consisted of a two-day 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 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*