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2007 Integral

2007 Integral

Autumn 2007 Volume 2 Massachusetts Institute of Technology 1ntegral news from the department at mit Inside • New faculty 2 • Leighton and Akamai 6 • Awards and achievements 3 • Campaign for Math update 6 • The UMO 4 • Faculty chairs 7 • Project Laboratory 4 • News bits 8 • Putnam Competition 5 • Simons Lectures 5

Dear Friends,

Welcome to the second edition of Integral, Speaking of undergraduate education, a careers. That conference is planned for our department’s annual newsletter. major MIT task force has just completed April 12-13, 2008, and will follow a A year has flown by since we published a comprehensive review of the General meeting of the department’s Visiting our inaugural edition in September 2006. Institute Requirements (GIRs) that shape Committee. Much has happened and much more is the undergraduate experience of all MIT planned. students and it has made recommendations Thanks to the overwhelming support for various changes in these requirements. of our alumni and other friends, our First of all, we’ve had an ambitious recruit- MIT faculty and administrators are cur- $15 million fundraising “Campaign for ment effort and are delighted to be rently reviewing these proposed changes, Mathematics” has been going exceedingly welcoming six new faculty to the depart- some of which will undoubtedly be imple- well. At the present time, we are 90 percent ment this year: Professors Paul Seidel mented. Our department is considering the of the way to our goal, so that means you and James McKernan; tenured Associate impact of these changes on our programs still have time to participate and we hope Professors Ju-Lee Kim and ; and whether we ought to review our own you do! Please look inside for additional and Assistant Professors Jon Kelner and offerings and requirements. Feel free to details. Abhinav Kumar. You can learn more send ideas about restructuring our math- about them and about their mathematics ematics major programs directly to me at As we move forward and look toward an on page 2. [email protected]. unusually high number of faculty eligible for retirement over the next few years, The job market for is This year, the huge turnouts for our we are planning to continue our active quite strong these days, a big change from Simons lectures given by Terry Tao and recruitment efforts. To that end, we are what I remember back in the 1970s, when necessitated finding larger also thinking about the directions within jobs were few and far between. Now we lecture halls. MIT helped with publicity mathematics that we want to develop within face very tough competition from other by spotlighting the series on the main the department. The MIT administration great mathematics departments for Institute home page. The Simons lecturers has been tremendously supportive of our top people, yet we’ve been remarkably next spring will be John Conway and efforts and we have a close relationship successful. We are excited about the Peter Teichner. In the fall term, Assaf with the new dean of science, Marc Kastner. diversity of experience they will bring Naor of New York University’s Courant Our future looks very bright indeed. to our community, and we are proud to Institute of Mathematical Sciences will welcome them to MIT. give the Wiener Lectures.

Our fantastic students are another source We’re in the early stages of planning a of great pride. With the stunning achieve- conference for women mathematics ments of our undergraduate students on PhDs who are graduate and undergraduate Michael Sipser the Putnam and MCM competitions, and alumnae of the MIT Department of Department Head the spectacular successes of our graduate Mathematics. Participants will speak about students at getting offers of the very best their research, and will lead panel discus- faculty positions, we know we’re doing sions of their individual experiences of something right. what helped or hindered them in their 

Mathematics welcomes six new faculty

James McKernan, Professor of Mathematics, is a major figure in higher dimensional algebraic . Paul Seidel, Professor of Mathematics, is well known for his A recipient of a 2007 Clay Research outstanding work in symplectic , a field originating in the Award for his groundbreaking work with study of Hamiltonian mechanics and now connected to string on the Minimal theory. A recipient of the European Mathematical Society Prize Model Program, he earned a BA from in 2000, he received his Diploma from Trinity College in 1985 and a PhD from in 1994 and the PhD from Oxford University in 1998. in 1991.

Jacob Lurie, Associate Professor of Mathematics with tenure, is a rising star in algebraic topology. A winner of several awards, including 1st place in the 1996 Westinghouse Science Talent Ju-Lee Kim, Associate Professor of Mathematics with tenure, Search, the 2000 Morgan Prize, and an AIM five-year fellowship has made important contributions to p-adic in 2004, he holds a BA from Harvard University in 2000 and a and harmonic analysis, with connections to the local Langlands PhD from MIT in 2004. program. Her undergraduate studies in the Korea Advanced Institute of Science and Technology were completed in 1991 and she received her PhD from in 1997.

Abhinav Kumar, Assistant Professor of Jonathan Kelner, Assistant Professor of Mathematics, is a Mathematics, works in number theory. theoretical computer scientist. Recipient of the 2002 David A 1998 IMO Gold Medalist and Putnam Mumford Award and the 2004 STOC best student paper award, Fellow in 1999 and 2000, he received he earned a BA from Harvard University in 2002 and a PhD his SB from MIT in 2002 and his PhD from MIT in 2006. from Harvard in 2006. 

Awards and achievements

Tom Mrowka received the AMS Oswald Veblen Prize in Geometry with Peter Kronheimer from Harvard, “for their joint contributions to both three and four- dimensional topology through the devel- opment of deep analytical techniques and applications.” Gil Strang received the MAA Deborah and Franklin Tepper Haimo Award, the ICIAM Su Buchin Prize and the ETH/SIAM Peter Henrici Peter Kronheimer and Tom Mrowka Prize for research in applied analysis Gilbert Strang and mathematics education worldwide. Peter Shor was named one of Caltech’s “Distinguished Alumni.” Eric Lauga received the Andreas Acrivos Dissertation Award in Fluid Dynamics from the American Physical Society. Mark Behrens and Katrin Wehrheim both received Sloan Research Fellowships. Michel Goemans received a Guggenheim Fellowship in computer science. Victor Kaç and Tom Mrowka are newly elected members of the American Academy of Arts and Sciences. Victor Kaç received the Diploma of Academic Merit from the Romanian Academy. David Vogan has been appointed as the Robert Collins Distinguished Scholar. Peter Shor Associate Professors Martin Bazant and Alex Postnikov received tenure. was promoted to Associate Professor.

Dan Kane ’07 was awarded the Bucsela Prize for outstanding MIT mathematics major. Dan also received the AMS-MAA- SIAM Frank and Brennie Morgan Prize for outstanding undergraduate research in Mark Behrens mathematics. Yaim Cooper ’07 received the AMITA Senior Academic Award. She was also runner-up for the Schafer Prize for Undergraduate Women in Mathematics. Graduate student Pavlo Pylyavskyy was selected for a Clay Liftoff Fellowship. For their outstanding George Lusztig research papers, Silvia Montarani and Luis Rademacher each received the Charles and Jennifer Johnson Prize. Possible future Ilya Elson, with Jason Burns and Teena Gerhardt as runners-up, received the Ilaria Seidel, Charles and Holly Housman Award for daughter of Excellence in Undergraduate Teaching. Paul Seidel and Graduate awards: Haynes Miller, Teena Michael Manapat received the Dean’s Ju-Lee Kim. Gerhardt, and Jason Burns. Education Award. Andrew Sutherland received an EECS Sprouls Award for an outstanding thesis in computer science. Staff member Kim Makara was awarded MIT’s Infinite Mile Award. Academic administrator Joanne Jonsson received the Dean’s Recognition Award.



The UMO Project laboratory class creates “eureka!” moments for students

Imagine a billiards table with no friction “The first thing to understand about these or spin. The ball is struck and hits the projects is that they are not well-defined,” sides in some sequence. What sequences Miller said. “Part of the challenge to the are theoretically possible? What if the students is to find an aspect of the problem table is triangular or pentagonal? that is interesting and approachable. So every time a team does a project it comes MIT students explored this scenario out differently.” recently through the Mathematics Project Laboratory. Projects are drawn from many mathemati- cal areas, including dynamical systems, Developed by Professors Michael Artin number theory, , fluid mechanics, and Haynes Miller, the Mathematics asymptotic analysis, knot theory and Project Laboratory has no syllabus, no probability. Students choose from a The Undergraduate Mathematics Office, problem sets, and meets sporadically. selection of problems or design one one of the first offices for undergraduate Students, predominantly seniors, work of their own. During the semester, each administration at MIT and still one of in groups and select open-ended math- group of three students works on three the few Institute offices devoted solely to ematical questions to investigate. Experi- questions in which they design and run undergraduate education, was a revolu- ments are generally conducted on a experiments, analyze the results and tionary entity when Professor Arthur computer, but some students use old- present their findings to the class. Mattuck created it 30 years ago. Joanne fashioned paper and pencil. Jonsson and her colleagues, Debbie Bower, A recent project invited students to think Stephanie (Stevie) Gallarelli and Anna “I found that the class was an excellent through a mathematical model of water Ferrigno Ward now provide essential way to gain experience with working in a seeping through a sand bed. The sand coordination of our extensive offerings of group and making discoveries together,” bed is riddled with tiny, interconnected basic mathematics subjects such as calculus said Curtis Fonger, a senior mathematics channels, each open or blocked with and linear algebra to students across all major. “The class was a terrific way to some probability. Is there is a connected disciplines, as well as caring, individualized learn the basics of mathematical research sequence of open channels that goes all guidance to our mathematics majors. and presentation.” the way through the bed?

Finding instructors for recitation sections, The class, fully subscribed in both 2006 – “This is a classic threshold phenomenon: mentoring students, coordinating faculty 2007 semesters, allows students to meet there is almost surely not an open with classes, and keeping everyone content an Institute undergraduate laboratory sequence until the probability of a specific are just a few of the wide umbrella of requirement while experimenting with channel being open reaches a certain tasks that Joanne Jonsson has taken on complex mathematical situations and critical value,” Miller said. “Each team that in her more than two decades running formulating explanations for patterns they has worked on this project has discovered our UMO. Jonsson is widely known and observe. The class, 18.821, was developed some new aspect of this problem.” respected at MIT for her expertise. under a grant from the Cambridge-MIT According to Gallarelli, “Her vast Institute, a wide-ranging partnership During a sabbatical leave, Artin set up knowledge of MIT policies and her aimed at enhancing the UK economy. and ran an analogous, ongoing course diplomatic nature make her very effective This grant funded an exchange of ideas at the . A number at identifying problems and finding for computer-based explorations, starting of other universities, he said, have also solutions.” Faculty know that she is the from and enhancing a large collection expressed interest in setting up a Math- person to call when they are uncertain of such projects long in use at Cambridge ematics Project Laboratory of their own. about advising a student, especially in University. difficult cases. Department Head Michael Sipser says, “We’re all deeply grateful that Joanne works so hard to make the department run smoothly, allowing the faculty to concentrate on research and teaching.”

This year, the UMO is getting a much- needed renovation. Uppermost in Jonsson’s and her colleagues’ minds is maintaining the welcoming feeling that has been their hallmark. Undergraduate students, graduate students, instructors and faculty will then continue to drop in regularly, chat, have candy, and find answers to all of their problems. 

Spectacular performance (again!) 2007 Simons lectures on the Putnam Competition

This year’s Simons Lectures in Mathemat- ics featured Professors from UCLA and David Donoho from . The lecture series, named for benefactor and MIT math alumnus Jim Simons, has run annually for five years.

Each speaker gave three lectures over the course of three days on various mathemat- ical topics. Tao, a Fields medalist, focused MIT undergraduate students, including For the team component of the exam, the on “the dichotomy between structure many math majors, dominated the 67th MIT team finished third behind Princeton and randomness” and drew over 400 William Lowell Putnam Mathematical and Harvard and earned $15,000 for the people to his first lecture. Donoho spoke Competition held in early December. The Math Department’s Putnam Fund. The on problems surrounding sparse solutions competition drew 3,640 undergraduates team members were Oleg Goldberg ’08, to underdetermined systems. from 508 colleges and universities in the Daniel Kane ’07, and Kuat Yessenov ’08. United States and Canada. This year, @E J@DFE 126 MIT students spent a Saturday taking We thank Professors Hartley Rogers and the exam. That is the highest number Richard Stanley and Associate Professor D of students taking the exam from a single Kiran Kedlaya for their dedication to 8 K J institution in Putnam history. the competition. As the results show, all ?

.*53PPN° J new Fellows are Hensheng Diao ’09, 3FDFQUJPOBUQN J

Daniel Kane ’07, and Yufei Zhao ’10.  ;Xm`[;fef_f  Along with the honor of being named %FQBSUNFOUPG4UBUJTUJDT 4UBOGPSE6OJWFSTJUZ )''. a Fellow, these three students each "QSJM   °QN received a $2,500 prize. Daniel Kane is D@K;

Leighton family leads the way  Campaign on track in supporting MIT mathematics to hit 2008 goal

Tom Leighton and Bonnie Berger with their children Alex and Rachel and Tom’s parents, David and Helen Leighton. The math department has raised more than $10 million to date in the first-ever Campaign for Math. Announced in April 2006, the capital campaign is on track to reach its goal of $15 million by April 2008.

“Clearly, the extraordinary generosity of the math department’s friends, alumni and alumnae is at the heart of this success,” Tom Leighton’s lifelong love for math- As the World Wide Web developed, said Director of Development Elizabeth ematics has taken him far beyond his Leighton recalled, so did the worldwide Chadis. “Alumni, former Moore Instruc- childhood goal of teaching his favorite wait. In 1995, many Internet users found tors and other friends have responded subject. As an MIT mathematics PhD who the level of congestion terribly frustrating. to our request for support from all over joined the faculty in 1982, Leighton Leighton recognized that the solution to the globe.” played an early role in establishing web congestion could be found in applied theoretical computer science in the mathematics and algorithms. With grad- The money will be used for faculty Department of Mathematics. A popular uate student Danny Lewin, Leighton recruitment and retention and to support lecturer, Leighton still occasionally teaches developed the mathematical algorithms graduate students. the 100-plus students who regularly enroll to handle the routing of content. in “Mathematics for Computer Science,” The premiere issue of Integral featured a subject he helped design through the Leighton will tell you that running a the $6 million matching gift from Visiting departments of mathematics and electrical company is a whole different experience Committee Chair John Reed ’61, retired engineering and computer science. from being a math professor. “For starters, Chairman of Citigroup, Inc, and his wife, summer isn’t much different from the Cynthia. When he heard about the But it’s Leighton’s achievements at Akamai other three seasons. However, the culture campaign, Visiting Committee member Technologies, which he co-founded at Akamai is like MIT in that it’s intense, Jim Simons ’58, President of Renaissance in 1998, that have earned him worldwide challenging and you get to work with Technologies Corporation, added an recognition as one of the Top 10 Tech- really smart people, many from MIT. incentive to help the department reach its nology Innovators in U.S. News & World Most of all there’s a prevailing attitude goal. Jim offered to give the department Report. Akamai, based in Cambridge, that you can do anything if you work hard the final $3 million once $12 million is Mass., is the leading global service enough,” he said. reached. Since that time, Professors Tom provider for accelerating content and Leighton ’81 and Bonnie Berger ’90 business processes online. As chief Leighton is determined to spread the word and Tom’s parents, David ’48 and Helen, scientist, Leighton is Akamai’s technology that MIT’s math department is a fantastic have given a Chair to the department. visionary as well as a key member of the environment for teaching and research. (See full story on this page) team that sets the company’s direction. “When it comes to fundraising, the math “The success of this campaign is terribly A preeminent authority on algorithms department is probably at the bottom of important to the future of the depart- for network applications, Leighton, the totem pole. It shouldn’t be, because ment,” stressed Department Head Michael through Akamai, created the world’s it’s the leading department of mathematics Sipser. “It is vital to sustaining the quality largest distributed computing platform with the best and the brightest,” he said. of teaching and scholarship and it demon- that dynamically routes content and “I want to give back to the department strates the degree of commitment and applications across a network of more that has been instrumental in the success support the department enjoys. “The than 18,000 servers. At MIT, Leighton of my career and I want to help the depart- campaign has raised the visibility of our serves as head of the Algorithms Group ment remain strong.” department within the Administration and in MIT’s Computer Science and Artificial increased fund-rising momentum,” he Intelligence Laboratory. said. “With your help, we are confident we will meet Jim Simons’ challenge and complete the campaign successfully.”



Four faculty named to chairs

Michel Goemans Tom Mrowka Professor Michel Goemans is the first holder of the Leighton Professor Tom Mrowka was appointed to a Simons Professorship. Family Professorship. Michel is a world leader in approximation Tom is a major figure in gauge theory and low dimensional algorithms for combinatorial optimization. A winner of the topology. Last year Tom received the Oswald Veblen Prize in Fulkerson Prize in 2000 for outstanding work in discrete math- Geometry, joining a distinguished list of mathematicians including ematics, along with many other distinctions, he has also contrib- Jim Simons himself. Tom has worked vigorously since 2004 as uted in major ways to the life of the department as an educator Chair of the Pure Mathematics Committee, overseeing the consid- and advisor. Michel holds BS and MS degrees from the Université eration of many new faculty. He received an SB from MIT in 1983 Catholique de Louvain and a PhD from MIT. He began his and a PhD from UC Berkeley in 1988, joining our faculty as career at MIT as an Applied Mathematics Instructor in 1990. Professor in 1996.

Gigliola Staffilani Katrin Wehrheim Professor Gigliola Staffilani was appointed as Abby Rockefeller Assistant Professor Katrin Wehrheim has been appointed as Mauzé Professor of Mathematics. Gigliola is one of the leading Rockwell International Career Development Assistant Professor experts in the field of non-linear partial differential equations. of Mathematics. Katrin is one of the rising young stars in low A superb teacher, she gives well-received calculus lectures for dimensional symplectic topology. She has been running highly two hundred freshmen, and is an inspiring mentor and role model successful seminars for our graduate students, and is co-organizing for our women graduate students. She holds a laurea degree from (with Gigliola Staffilani) an MIT conference celebrating women the Università di Bolognà and a PhD from the University of mathematicians. She holds a Diploma from Imperial College and Chicago. She joined our department as a tenured Associate a PhD from ETH Zurich. She began her career at MIT as an Professor in 2002. Assistant Professor in 2005. 

A fraction of the news

Throbbing oil Talented math musicians team makes history mystery solved shine at IAP recital (and finds happiness)

Alfred Noël, David Vogan, and Peter Trapa Tim Nguyen plays Rachmaninoff. An international team of 18 mathemati- The theme from the Final Fantasy VIII video cians including our own David Vogan game and Beethoven’s Sonata No. 9 were has mapped one of the largest and most among the selections showcased at the complicated structures in mathematics. annual IAP Mathematics Department Music If written out on paper, the calculation Recital. This annual concert, organized describing the structure known as E8 this year by graduate student Tim Nguyen, would cover an area the size of Manhattan. gives the MIT mathematics community, John Bush collaborates with former family and friends a chance to perform instructor Roman Stocker, now in MIT’s This mathematical feat made international for one another. civil and environmental engineering headlines and received a commendation department, to explain why a mixture in Congress from Rep. Jerry McNerney Among this year’s performances, graduate of mineral oil and detergent will pump (D-Calif.). McNerney concluded, “The student Peter Buchak showed his virtuosity like a beating heart when a drop is participants are to be commended for their on the concertina with selections of Irish squeezed onto water. work that has expanded the limits of human dance music, while editorial assistant knowledge and brings hitherto unknown Mike Collver sang ballads accompanied beauty and power to grace our human by his wife, Glorianne, on the lute. The condition.” McNerney’s commendation is Upcoming event musically mathematical couple Lauren posted on YouTube. Search for “Congress Williams, violin, and Associate Professor E8” at www.youtube.com or use the link Women in Math Conference Denis Auroux, piano, played the Finale listed under “Events” on the math depart- from Beethoven’s Sonata No. 9. ment website: math.mit.edu. MIT Women in Mathematics: A Celebra- tion, will be held on the weekend of The afternoon concluded with Kobi April 12-13, 2008, at the Massachusetts Kremnitzer and Avshalom Manela, applied Institute of Technology. Seven mathe- mathematics instructors, providing the maticians, both pure and applied, will hands for Francis Poulenc’s “Sonata for speak on their research. Two panels Piano Four Hands.” will discuss the lives of women in math- ematics at different stages of their careers. More information can be found at math.mit.edu/womeninmath.

In memoriam mit department of mathematics Professor Emeritus George B. Thomas, who served on our faculty from 1944 to 1978, died on October 31, 2006 at the age of Department of Mathematics 92. In the early 1950s he authored the widely-used textbook, Thomas’ Calculus as Massachusetts Institute of Technology it is known today, now in its 11th edition Headquarters Office by Addison Wesley Publishing. Telephone: 617-253-4381 Building 2, Room 236 Fax: 617-253-4358 77 Massachusetts Avenue Web: math.mit.edu Cambridge, MA 02139-4307 Integral contributors

Writing: Deborah Halber • Photography: Donna Coveny, John Nikolai, Mark Ostow • E8 image: John Stembridge • Design: Tim Blackburn • Printing: Arlington Lithograph PSB 07.03.0271

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