In April, 2003, Stony Brook hosted a landmark two-week lecture series by Grisha Perelman of the Steklov Institute, St Petersburg, in which Perelman described his recent work on the Ricci flow for Riemannian metrics and its application to the geometrization of 3-manifolds. The lectures were anxiously attended by experts from all over the country, as well as by a crowd of curious non-mathematicians who had heard rumors that something big was afoot.

The Ricci flow, first introduced by Richard Hamilton in the early 1980's, is a non-linear, metric-valued generalization of the ordinary scalar heat equation. Just as heat tends to flow throughout an object so that it asymptotically tends toward a state of constant temperature, the Ricci flow might be hoped to gradually change a given Riemannian metric until it eventually tends toward a metric of constant Ricci curvature. There is already a broad consensus among the cognoscenti that Perelman's work represents a major breakthrough in this direction.

Perelman went on to outline an argument whereby he believes that this circle of ideas implies the Thurston geometrization conjectures, including the Poincaré conjecture. Because the stakes are so high, and because the papers in question have not yet been refereed, it seems too soon to tell whether this aspect of Perelman's program is essentially complete and correct. However, experts who have studied the papers seem at present to be cautiously optimistic. For more details, visit the Perelman web-site maintained by Bruce Kleiner and John Lott.

Perelman's lectures at Stony Brook were organized by Michael Anderson, and were made possible by the generous support of the Simons Mathematical Physics Endowment and the Clay Foundation. 

The last year has seen the department hosting one important conference after another. In 2002, we celebrated Blaine Lawson's 60th birthday with an international conference honoring his deep and wide-ranging contributions to geometry. And in May, the mathematics department, in collaboration with the ITP and computer science, held a major conference in quantum computing.

But this August proved to be a period of remarkably intense activity, with two extended workshops bringing together mathematicians and physicists with overlapping interests. On one hand, Jim Simons had decided to extend his already generous benefaction to include a new, five-year program of Simons Workshops in Mathematical Physics; the first of these began in August, and featured a month-long visit by Harvard string theorist Cumrun Vafa. At the same time, Dennis Sullivan and his brand-new NSF-sponsored Focused Research Group (FRG) were running a workshop on topics in algebraic topology inspired by string theory. The resulting prolonged and intense exchange of ideas between mathematicians and physicists has already led a flurry of papers. In particular, conversations between Vafa and mathematician Nikolai Reshetikhin led to new relationships between the geometry of Calabi-Yau manifolds and the statistical mechanics of crystals.

Stony Brook's Mathematics department and Institute for Mathematical Studies have been selected to participate in the Carnegie Initiative on the Doctorate (CID), a multi-year research and action project aimed at improving doctoral education at American universities as one of eight Partner Departments in mathematics. CID Partner Departments will analyze all aspects of their doctoral programs and link specific activities to desired outcomes. Departments will begin this analysis by clarifying their goals for doctoral education in their respective disciplines, and will commit to creating experiments in doctoral education to better meet their identified goals. The Stony Brook study is led by Irwin Kra and Dusa McDuff. 

Last year the department conducted surveys of our graduate alumni as well as current students, asking what aspect of the program most needed attention. The broad consensus was that there is a real need for better advising of first and second year students, and this aspect of our program is therefore being rethought. As one step in this direction, the department has already begun to run a series of mini-courses intended to introduce these students to various active areas of current research. To date, this lecture series has featured such topics as quantum computing, mathematical biology, and the theory of D-modules.

The CID initiative has also led the department to re-emphasize the importance of teaching; in this context, Neil Portnoy will begin to organize a re-imagined Creative Teaching seminar next semester, and the department also plans to soon offer an optional course in mathematical pedagogy.

The Mathematics Department is currently chaired by Detlef Gromoll, who has successfully led us through four difficult years, despite the trying times facing the state, the university, and the region.  In August, Gromoll was co-organizer of the third international workshop on Curvature and Shape, sponsored by the Deutsches Forschungsgesellschaft, and held at the University of Münster.  He and Blaine Lawson were also plenary speakers at a recent Conference in Rio de Janeiro celebrating IMPA's 50th bithday; these invitations highlight the long-standing close ties between Stony Brook and Brazilian mathematics.

In 2004, the chairmanship will pass to David Ebin. Ebin is currently the department's Associate Chair, and is also in charge of graduate admissions.

The Department is now recognized as the flagship of Mathematics Education in the region. Under the leadership of Bernie Maskit, a new MA Program in Mathematics Education has just received final NYS approval, and our well-established undergraduate MAE Program has been certified according to the new tougher State and national NCATE standards.  We welcome Neil Portnoy as the new Director of Mathematics Education. Maskit will also continue to serve the program, as Co-Director.

On December 31, Irwin Kra will complete a three year term as an elected member of the Nominating Committee of the American Mathematical Society. The committee consists of nine mathematicians, and selects nominees for the presidency of the AMS and other AMS offices.

Dusa McDuff's work in symplectic geometry continues to burnish her international reputation. Her recent talks have included addresses at the Hodge Centennial celebration in Edinburgh, Scotland, and at the Harvard/MIT "Unity of Mathematics" conference in honor of Gelfand's 90th birthday. She has also recently given colloquia at Wisconsin, Chicago, Penn, and ETH, as well as a lecture series at the Czech Winter School in Geometry and Physics.

Stony Brook was well represented at the XVIIIth Annual Geometry Festival, held at Duke University, where two of the plenary speakers were Claude LeBrun and Justin Sawon. LeBrun also recently delivered a Kuwait Foundation Lecture at Cambridge University, two series of conference lectures in Japan, a Presidential Lecture at Florida International University, colloquia at Wisconsin and Toronto, and seminars at Oxford and Minnesota.

It is a pleasure to annouce two new additions to our tenured faculty. Alexander Kirillov and Sorin Popescu were both recently promoted to the rank of Associate Professor. As a consequence, Popescu then turned down an attractive offer from the University of Nice. Yair Minsky was recently made a full professor, in recognition of his celebrated recent proof of Thurston's Laminated End Conjecture. Unfortunately, however, Minsky has decided to leave us, in order to accept a position at Yale.

We are all relieved to see that Mark de Cataldo, so recently faced with great personal tragedy, has nonetheless been flourishing as a mathematician. A recent series of papers on Hodge Theory by de Cataldo and his collaborator Luca Migliorini have been greeted with invitations to speak at Princeton, the IAS, and several international conferences. He also the recently received grants from both the NSF and the NSA.

To everyone's amazement, Marie-Louise Michelsohn has suddenly emerged as an international star of track and field. She recently set a world record for the mile for women of her age group, after having previously broken world records for the 1500 and 3000 meter categories.

Although nominally retired, Tony Knapp continues to be an active researcher, a prolific writer, and a lively member of the department. This year he published four research articles, as well as a number of expository articles and book reviews, and is currently working on a new edition of one of his books. Knapp is also active in volunteer work, and dedicates a substantial amount of his time to charitable organizations such as Meals on Wheels.

Stony Brook's Putnam team put in a spectacular showing this year. Raymond Cassella placed 6th in a field of 3349 contestants, and the team, which also included Junmeng Chen, Greg Grinberg, Yao Hoa Mai, and Ruan Yi-Lun, placed 25th among of the 476 participating teams. The team's coach, Sorin Popescu, has obviously done an extraordinary job.

The Math Club recently moved to a new home in the Math Learning Center. The club, which is supervised by Mathew Kudzin has been remarkably effective in building an enthusiastic core of undergraduate majors. Last year some of them visited the Hudson meeting for Undergraduate Research in Mathematics, and we hope that a group will go in February 2004 to Lincoln, Nebraska, for a meeting of undergraduate women in mathematics.

Our Undergraduate program is currently headed by Scott Sutherland, who has been working very hard to keep our whole teaching enterprise afloat through a period of exploding enrollments. Compared with a decade ago, enrollments in math classes are up by 75%, while the students body as a whole grew by only about 25%. We now have over 250 majors, and more than 50 graduated last year. Unfortunately, however, the math faculty actually shrank by about a quarter during the same period!

We now have a number of different projects underway which are aimed at improving our undergraduate program. Of these, one of the most notable is a new course designed by Bernie Maskit, MAT 200 (Language, Proof and Logic), that provides a solid introduction to mathematical logic and deductive Euclidean geometry. This course has noticeably helped many of our students begin to master the complex patterns of reasoning so often taken for granted in our advanced courses. An excellent indication of the success of such efforts is that an increasing number of our majors are now carrying out independent study projects and writing honors theses.

In recent years, the Mathematics Department has received several gifts that have become increasingly essential to our functioning at at a premier level. Of these, the most important is Jim Simons' partial funding of six postdoctoral lines. Simons has also recently set up a Mathematical Physics Endowment fund that provides the Mathematics and Physics Departments, the Institute of Mathematical Sciences and the Yang Institute of Theoretic Physics each with about $17,000 per year for five years. This sizable gift is used to invite visitors and run a summer workshop led by Cumrun Vafa from Harvard.

The department would like to enlarge these funds in order to increase the significance of their impact. It would be particularly gratifying to be able to also offer some undergraduate fellowships, as well as more graduate fellowships. To this end, we have recently set up a current use fund. Those wishing to contribute to this important cause are encouraged to contact Lucille Meci (lmeci@notes.cc.sunysb.edu) for more details.

Pictures courtesy of: MIT website (Perelman), USC website (Sullivan), Harvard website (Vafa), Stony Brook website (String Theory Logo).