# Past news

## Higher Structures in Topology and Number Theory

A workshop on *Higher structures in topology and number theory* was held in Oxford in April 2013. The goal of this workshop was to bring together research communities working on realization of higher alegebraic structures in number theory and topology as well as geometry and mathematical physics.

Invited speakers included Hidekazu Furusho, Ezra Getzler, Jeff Giansiracusa, André Henriques Jonathan Pridham, Tomer Schlank and Don Zagier.

## Peter Scholze awarded Prix Peccot

**Collège de France.** Peter Scholze has been awarded the 2013 *Prix Peccot* by the *Fondation Claude-Antoine Peccot*. In March, he will lecture at the Collège de France on *a p-adic analogue of Riemann's classification of complex abelian varieties*. Peter Scholze was appointed to a five-year Clay Research Fellowship in 2011.

## New Scientific Advisory Board Member

**August 8, 2012.** Andrei Okounkov has joined the CMI's Scientific Advisory Board in succession to Gregory Margulis. Professor Okounkov is the Samuel Eilenberg Professor of Mathematics at Columbia University. He works on representation theory and its applications to algebraic geometry, mathematical physics, probability theory and special functions. He was awarded a Fields medal in 2006 for his 'contributions bridging probability, representation theory and algebraic geometry', his work having revealed 'profound new connections between different areas of mathematics'.

## 2012 Clay Research Awards

CMI announces the 2012 Clay Research Awards: to **Jeremy Kahn** (Brown University) and **Vladimir Markovic** (Caltech) for their work in hyperbolic geometry.

## Clay Mathematics Institute New President

The Clay Mathematics Institute announces today that as of June 30, 2012, the office of its president will move from Cambridge, Massachusetts, to Oxford, UK. At that time Professor Nicholas Woodhouse of Oxford University will assume the position of president. He will succeed Professor James Carlson, formerly of the University of Utah.

## 2012 Clay Research Fellows

The Clay Mathematics Institute (CMI) announces the appointment of two Research Fellows, **Ivan Corwin** and **Jack Thorne**, for four and five years, respectively.

## 2012 Clay Research Scholar

CMI announces the appointment of **Roman Travkin** as a Clay Research Scholar, for a period of three years.

## Clay Chair at the Institut Henri Poincaré

The Clay Mathematics Institute (CMI, Cambridge, Massachusetts) and the Institut Henri Poincaré (IHP, Paris) have announced at a press conference the establishment of the Poincaré Chair, a postdoctoral position for mathematicians in the early stages of their career. Those named to the chair will hold their position at the Institut Henri Poincaré for a term of six months to one year. The chair is financed for a period of five years with the Clay Millennium Prize funds for resolution of the Poincaré conjecture. The conjecture was solved in the affirmative by Grigoriy Perelman, for which he was awarded the Millennium Prize in 2010. Dr. Perelman subsequently declined to accept the prize money. In establishing this chair with IHP, CMI aims to provide an exceptional opportunity for mathematicians of great promise to develop their ideas and pursue their research, just as Grigoriy Perelman was afforded such an opportunity by a fellowship at the Miller Institute in 1993-95. A public call for nominations by the Institut Henri Poincaré will be made at a later date.

## First Clay Mathematics Institute Millennium Prize Announced

**March 18, 2010.** The Clay Mathematics Institute (CMI) announces today that Dr. Grigoriy Perelman of St. Petersburg, Russia, is the recipient of the Millennium Prize for resolution of the Poincaré conjecture.

## Workshops at CMI

A workshop on *Sage Days 18: Computations related to the Birch and Swinnerton-Dyer conjecture* was held in the offices of CMI on December 1-5, 2009.

A workshop on *Geometry of outer space* was held in the offices of CMI on October 19-22, 2009.

## 2009 Summer School

The 2009 CMI Summer School was held from June 15 to July 10 on *Galois Representations* at the University of Hawaii at Manoa, Honolulu.

## Sir Michael Atiyah 80th Birthday Conference

The 80th birthday of Sir Michael Atiyah was celebrated with a special conference on Geometry and Physics at the University of Edinburgh, April 20-22, 2009.

## Conference in honor of Richard Melrose

A conference in honor of Richard Melrose on his 60th birthday was held at MIT on April 4, 2009. Speakers were Jean-Michel Bismut, Rafe Mazzeo, Robert McPherson, Peter Sarnak, Isadore Singer and Johannes Sjöstrand.

## 2009 Clay Research Fellow Announced

Sucharit Sarkar has been selected for a Clay Research Fellowship beginning July 1, 2009.

## 2009 Clay Research Conference

The Clay Mathematics Institute held its 2009 Research Conference May 4-5 in Harvard Science Center.

## 2009 Clay Research Awards Announced

March 10, 2009. The Clay Mathematics Institute announced Jean-Loup Waldspurger, Ian Agol, Danny Calegari and David Gabai as the recipients of the 2009 Clay Research Awards.

## 2008 CMI Annual Report

The 2008 CMI annual report includes a letter from the president and a summary of 2008 research activities.

## 2008/09 Clay Lectures on Mathematics

Lectures were hosted by Research Institute for Mathematical Sciences Kyoto University Japan on March 2-5, 2009.

## Workshop at CMI

A workshop on *Geometry and Physics of the Landau-Ginzburg Model* was held in the offices of CMI on January 12-16, 2009.

## Clay Public Lecture

A Tribute to Euler, William Dunham of Muhlemberg College, delivered the Clay Public Lecture at Harvard on October 14, 2008.

## Workshop at CMI, October 13 to 16

A workshop on the Stringy Reflections on LHC was held in the offices of the CMI on October 13-16, 2008.

## Oded Schramm, in Memoriam

Oded Schramm died September 1, 2008, in a tragic hiking accident on Guye Peak, Washington. Oded was an extroardinary mathematician, who transformed our understanding of critical processes in two dimensions through his introduction of the Stochastic Loewner evolution, tying probability theory to complex analysis in a completely novel way. He also made fundamental contributions to circle packings, random spanning trees, percolation, noise sensitivity of Boolean functions, random permutations and metric geometry.

## Workshop at CMI, August 4 to 15

A workshop on the Foundations of Algebraic Geometry: Grothendieck's EGA Unbound was held in the offices of the CMI on August 4-15, 2008.

## 2008 Summer School

The 2008 CMI Summer School was held from June 23 to July 18 at the Eidgenössische Technische Hochschule, Zürich, Switzerland.

## 2008 Clay Research Conference

The Clay Research Conference was held May 12-13 at MIT Media Lab, Bartos Theater.

## Clay Public Lecture

The Music of the Primes, Marcus du Sautoy of Oxford University, delivered the Clay Public Lecture at MIT on May 8, 2008.

## 2008 Clay Research Awards Announced

February 21, 2008. The Clay Mathematics Institute announces Cliff Taubes and **Claire Voisin** as the recipients of the 2008 Clay Research Awards.

## 2008 Clay Research Fellows

The Clay Mathematics Institute announces the selection of its 2008 Research Fellows: **Spyros Alexakis** (Princeton University), **Adrian Ioana** (Caltech), **Xinyi Yuan** (Columbia University).

## Screening of the film Julia

The Clay Mathematics Institute screened George Csicsery's film "*Julia Robinson and Hilbert's Tenth Problem*" at the AMS Joint Mathematics Meetings in San Diego, January, 2008.

## Workshop at CMI, March 28-30

A workshop on Automorphic Forms in Moduli Problems of Schottky and Brill-Noether Type was held on March 28-30, 2008.

## Workshop at CMI, March 20-23

A workshop on K3's: Modular Forms, Moduli, and String Theory was held on March 20-23, 2008.

## Workshop at CMI, January 31-February 3

A workshop on Shrinking Target Properties was held from January 31 to February 3, 2008, in the Brandeis University and the Clay Mathematics Institute.

## Clay Lectures on Mathematics, December 10-14

Elon Lindenstrauss of Princeton University and Mircea Mustata of University of Michigan delivered the 2007 Clay Lectures on Mathematics at the Tata Institute of Fundamental Research, Mumbai, India.

## Workshop at CMI, September 30-October 3

A workshop on Computational Arithmetic Geometry took place at CMI from September 30 to October 3, 2007.

## Workshop at CMI, September 18-21

A workshop on Solvability and Spectral Instability took place at CMI from September 18 to 21, 2007.

## 2007 Clay Research Fellows Announced

The Clay Mathematics Institute announced the appointment of four Research Fellows: Mohammed Abouzaid of the Massachusetts Institute of Technology, Soren Galatius of Stanford University, Davesh Maulik of Princeton University, and Teruyoshi Yoshida of Harvard University. They were selected for their research achievements and their potential to make significant future contributions to the field.

## 2007 Clay Research Awards Announced

The Clay Mathematics Institute announced the recipients of the Clay Research Award for 2007. Because the Institute's annual meeting has been changed from the fall to the spring, CMI presents three awards this year. The recipients are: Alex Eskin (University of Chicago), Christopher Hacon and James McKernan (University of Utah and UC Santa Barbara, respectivey) and Michael Harris and Richard Taylor (Université de Paris VII and Harvard University, respectively).

## Workshop at CMI, May 16-17

A two day workshop on Higher Dimensional Algebraic Geometry took place at CMI on May 16 and 17, 2007.

## Clay Research Conference, May 14-15

The Clay Research Conference, was held May 14-15, 2007 in Cambridge, Massachusetts, inaugurated an expanded format for the Institute's annual meeting.

## Workshop on recent developments in Symplectic Topology

Workshop at CMI on Symplectic Toplogy took place from April 20 to 22, 2007.

## Surfing with Wavelets

Ingrid Daubechies of Princeton University presented the Clay Public Lecture at MIT, Stata Center on April 10, 2007.

## Conference on Hilbert's 10th Problem, March 15-16, 2007

The conference opened with a few words by George Csicsery, director and producer of *Julia Robinson and Hilbert's Tenth Problem*, and Constance Reid, biographer of David Hilbert, Julia Robinson, and other mathematicians. Csicsery showed a short clip of his work in progress. The rest of the program was devoted to mathematical talks.

## Workshop on Hopf Algebras and Props

Workshop at CMI on Hopf Algebras and Props took place from March 5 to 9, 2007.

## Clay Lectures on Mathematics

Ben Green and Akshay Venkatesh delivered the 2006 Clay Lectures on Mathematics at the Centre for Mathematical Sciences, Cambridge University, UK from Nov. 28 to Dec. 1.

## Beyond Computation

Michael Sipser of MIT presented the Clay Public Lecture at Harvard University on October 3, 2006.

## New Publications

*Surveys in Noncommutative Geometry*

The Proceedings of the Clay Mathematics Institute instructional symposium on Noncommutative Geometry is published.

*Millennium Prize Problems*

The book on Millennium Prize Problems which gives the official description of each of the seven problems and the rules governing the prizes is published.

*Floer Homology, Gauge Theory and Low Dimensional Topology*

The Proceedings of the Clay Mathematics Institute 2004 summer school at the Alfréd Rényi Institute of Mathematics in Budapest, Hungary is published.

*Lecture notes on Motivic Cohomology*

The book on Motivic Cohomology is published.

## Workshop on Moduli Spaces of Vector Bundles, October 6-10, 2006

Vector bundles have been a key topic in algebraic geometry since the inception of sheaf theory in the 1950s. More recently, they have also assumed a central role in mathematical physics as objects whose moduli spaces model important equations. Coherent sheaves are the "next level", more difficult to analyze and richer in information about the base variety.

## 2006 Summer School

The Clay Mathematics Institute held its 2006 summer school on Arithmetic Geometry at the Mathematisches Institut, Georg-August-Universität Göttingen, Germany, from July 17 to August 11..

## Mathematics and Magic Tricks

In a talk presented at MIT on April 25, 2006, Stanford statistician Persi Diaconis discussed how the way a magic trick works is sometimes even more amazing than the trick itself.

## 2006 Senior Scholars

Two Clay Senior Scholars were in residence at MSRI for the period January - May, 2006. First is Jean-Louis Colliot-Thelene (Université de Paris-Sud), who is participating in the program on Integral Points on Higher-Dimensional Varieties. Second is Yongbin Ruan (University of Wisconsin), who is participating in the program on New Topological Methods in Physics.

## Lie Groups: Dynamics, Rigidity, Arithmetic

On February 24 - 27, 2006, Yale University hosted a conference in honor of the 60th birthday of Gregory Margulis.

## 2006 Clay Research Fellows

On February 2, 2006, the Clay Mathematics Institute announced the appointment of Research Fellows Artur Avila, Sophie Morel and Sam Payne. These outstanding young mathematicians were selected for their research achievements and their potential to make significant future contributions.

## New Publications

*Harmonic Analysis, the Trace Formula, and Shimura Varieties*

The proceedings of the Clay Mathematics Institute 2003 summer school at Fields Institute is now available.

*Global Theory of Minimal Surfaces*

The proceedings of the Clay Mathematics Institute 2001 summer school at MSRI is now available.

## Manjul Bhargava on NPR

Clay Research Fellow Manjul Bhargava discusses mathematics and music.

## Workshop on Algebraic Statistics and Computational Biology, November 12-14, 2005

Algebraic Statistics is a new field in which ideas, combinatorics, geometry of polytopes, computational algebra and algebraic geometry contribute to the formulation, interpretation, and solution of statistical problems. Many of the motivating problems in algebraic statistics arise from problems in computational biology: sequence analysis and reconstruction of phylogenetic trees from sequence data, to name two.

## Escher and the Droste Effect

In a talk presented at Harvard on October 25, 2005, Hendrik Lenstra of Leiden University discussed the pattern hidden in M C Escher's 1956 lithograph, *the Print Gallery*.

## 2005 Clay Research Awards Annnounced

Manjul Bhargava (Princeton University) and Nils Dencker (Lund University) have been named recipients of the 2005 Clay Research Awards.

## Euclid and His Heritage

On October 7-8, 2005, a conference on Euclid and His Heritage took place at the University of Oxford's St. Catherine's College. The conference marked the occasion of the publication, for the first time, of a complete digital edition of the oldest surviving manuscript of Euclid's Elements.

## A Celebration of Mathematical Thought

The Clay Mathematics Institute held its 7th Annual Meeting at the University of Oxford on October 11, 2005. The meeting featured presentation of the Clay Research Awards and a special public lecture, "Solving Equations," by Professor Andrew Wiles.

## 2005 Summer School

The Clay Mathematics Institute will hold its 2005 summer school on Ricci Flow, Three-Manifolds and Geometry, at the Mathematical Sciences Research Institute (MSRI) in Berkeley, June 20-July 15.

## 2005 Olympiad Scholar Award announced June 27

Miss Sherry Gong, a 10th grade student at Phillips Exeter Academy, was named the 2005 Clay Olympiad Scholar at a ceremony in Washington DC on June 27, 2005.

## Physmatics

A public lecture by Clay Senior Scholar Eric Zaslow.

Fields Institute, June 2, 2005.

## Eigenvarieties

Special Program on Eigenvarieties at Harvard culminated in a workshop May 10-15, 2005 at CMI.

## Are there unsolved problems about numbers?

Public lecture by Barry Mazur, Harvard University

May 3, 2005 at 7pm

Stata Center, MIT

32 Vassar Street, Cambridge

Hosted by the MIT Mathematics Department.

## Four thousand years of mathematics in images

Public lecture by Bill Casselman, U. of British Columbia

April 26, 2005 at 7pm

Science Center Lecture Hall B, Harvard University

Hosted by the Harvard University Mathematics Department

## 2005 Research Academy

Led by Professors Pavel Etingoff and Richard Stanley of MIT, the 2005 Clay Mathematics Research Academy began on Friday, April 22 with a group of sixteen high school students. For eight days they participated in an intense program of introduction to research. The program's colloquium series was open to the public.

## Riemann Hypothesis

Peter Sarnak has written an article, Problems of the Millennium: The Riemann Hypothesis (2004) for the 2004 CMI Annual report. His text expands on the comments in Enrico Bombieri's article and also discusses some recent developments.

See the CMI web page on the Riemann Hypothesis. There you will also find a link to a digital facsimile of Riemann's original manuscript. The facsimile is courtesy of Niedersächsische Staats- und Universitätsbibliothek Göttingen.

## 2005 Clay Research Fellows Announced

March 16, 2005 (Cambridge, MA) - The Clay Mathematics Institute (CMI) announced today the appointment of Research Fellows Bo'az Klartag and David Speyer. These outstanding young mathematicians were selected for their research achievements and their potential to make significant future contributions.

## Workshops at CMI

CMI plans to hold four to six small workshops each year at its offices at One Bow Street, Cambridge, Massachusetts. These will be of three to six days duration. For more information or to make a proposal, please contact David Ellwood (ellwood at claymath dot org, 617-995-2600) or Jim Carlson (carlson at claymath dot org, 617-995-2600).

## Senior Scholars David Donoho and Peter Winkler. January 2005

David Donoho of Stanford University and Peter Winkler of Dartmouth College will begin their appointments as Clay Senior Scholars at MSRI in January of 2005. They will be participating in the programs on Mathematical, Computational and Statistical Aspects of Image Analysis and Probability, Algorithms and Statistical Physics, respectively.

## November 2004 - The Primes Go On Forever

To increase public awareness of mathematics, CMI commissioned this poster about primes to be exhibited in Boston T stations during the month of November, 2004. Poster design by Laura McFadden.

## Senior Scholar Eric Zaslow. November 2004

Eric Zaslow was named Clay Senior Scholar at the Thematic Program on The Geometry of String Theory 2004 - 2005, a joint program of the Fields Institute and Perimeter Institute for Theoretical Physics. He will spend November 2004 and two months residence in Spring 2005.

## November 5, 2004 - Annual Meeting

The sixth Annual Meeting of the Clay Mathematics Institute will be held on November 5, from 2:00-5:00 PM at the Harvard Science Center (Lecture Hall C), One Oxford Street, Cambridge, Massachusetts. The program features talks by Gérard Laumon and Ben Green, followed by announcemnt of the Clay Research Awards.

## November 3, 4, 2004 - Research Fellow Lecture Series

CMI announces a series of lectures by three of its research fellows. The lectures will be held on November 3 and 4, from 1:30-5:30 PM at CMI, One Bow Street, Cambridge, Massachusetts.

- Manjul Bhargava:
*Counting field extensions of the rational numbers* - Dennis Gaitsgory:
*Two faces of geometric Eisenstein series* - Maryam Mirzakhani:
*Counting simple closed geodesics on hyperbolic surfaces and intersection theory on the moduli spaces of curves*

## Manjul Bhargava on NPR, October 18, 2004

Manjul Bhargava discusses mathematics and music. Bhargava is a Clay Research Fellow

## Senior Scholars Stanley and Sturmfels. July 2004

Richard Stanley (MIT) and Bernd Sturmfels (UC Berkeley), named as CMI's first Senior Scholars, delivered public lectures on July 16 and 20 at the IAS Park City Mathematics Institute. Sturmfels' lecture, " Tropical Mathematics," written with David Speyer, is now available at arXiv.org.

## 2003 Annual Report

Article by Mike Douglas on Quantum Yang-Mills, report on the Independent University of Moscow, full text of the interview with Terry Tao.

## Clay Olympiad Scholar Award. June 21, 2004

At the official awards dinnner for the US American Mathematics Olympiad (USAMO) held July 21, 2004, CMI President Jim Carlson presented the Clay Olympiad Scholar Award to Mathew Ince. The award is given for the solution to an Olympiad problem judged most creative.

## Budapest Summer School

June 2004. The Clay Mathematics Institute held a summer school on Floer Homology, Gauge Theory, and Low Dimensional Topology at the Alfréd Rényi Institute of Mathematics aimed at graduate students and mathematicians within five years of their Ph.D.

## 2004 Liftoff Fellows

On April 19, 2004, CMI announced eighteen new liftoff fellows. Each will be supported by CMI for one month in the summer of 2004. This year's fellows were drawn from thirteen universities.

## Clay Public Lecture. March 22, 2004

Timothy Gowers, recipient of the 1998 Fields Medal for his contributions to functional analysis, delivered the first Clay Public Lecture on Monday, March 22 at 7pm in Lecture Hall A of the Science Center, Harvard University. Gowers spoke on "Is there such a thing as infinity?" This year's public lecture was hosted by the Harvard Mathematics Department.

## Senior Scholars Program. March 19, 2004

The Clay Mathematics Institute announces its Senior Scholars program. Its aim is to foster mathematical research and the exchange of ideas by providing support for senior mathematicians who will play a central role in a topical program at an institute or university.

## Research Academy Colloquium Series

March 19-28, 2004. The Clay Research Academy, led by Richard Stanley and Pavel Etingof of MIT, conducted an introduction to research program for 12 high school students at its offices at One Bow Street in Cambridge. Some of the Colloquium Series lecture notes are now available.

## Clay Research Academy. March 19, 2004

The 2004 Clay Mathematics Research Academy will begin on Friday, March 19 at CMI in Cambridge, MA.

## Research Fellows. February 25, 2004

Ciprian Manolescu and Maryam Mirzakhani of Harvard University, and András Vasy and Akshay Venkatesh of MIT are named as Clay Research Fellows.

## Research Award. November 14, 2003

Richard Hamilton and Terence Tao each receive the Clay Research Award