MATHDepartment of Mathematics CornellMATTERS University Ithaca NY November 2010 LETTER FROM THE CHAIR, LAURENT SALOFF-COSTE I want to thank the staff and The next decade will role in allowing specific Cornell faculty of the department for their undoubtedly be dominated by hiring programs to be worldwide leaders in work and support during what, not activities in a very competitive their field. Obviously, this ambitious surprisingly, turned out to be a very environment. It is likely that half goal calls for a premier College of difficult year. Dan Barbasch had the department will change during Arts and Sciences, including a first- managed the first round of budget the next ten years or so. The result rate department of mathematics. As cuts efficiently, leaving our program of these hiring activities will have a a direct consequence of the budget in good shape. The significance of tremendous effect on the future of crisis, I had no choice but to collect the second round of cuts, similar in mathematics at Cornell. and immerse myself in a great size to the first round, will only be Cornell belongs to a relatively quantity of data searching to answer understood over time. small and very select group of the question: what are the important Throughout this challenging institutions that aspire to exceptional characteristics of a premier year, the department maintained quality and leadership over the department of mathematics? a high level of very successful entire spectrum of intellectual Data regarding the top 100 activities in the areas of instruction, activities. This bold, institution- departments of mathematics in research and outreach including wide aspiration plays an essential Continued on page 3. the Chelluri, Kieval, and Evans Lectures, and the annual Topology MATH AWARENESS MONTH Festival. Let me acknowledge the BY MARY ANN HUNTLEY very positive impact of the generous The Mathematics Department patterns — even by computer. gifts of Kirk Twiss and several holds a public lecture each April Although siteswap is mostly used by anonymous donors. The Twiss fund in conjunction with the national experienced jugglers, Knutson says provides support for the recruitment, celebration of Mathematics it’s also useful as a steppingstone retention, and research efforts of our Awareness Month. This year’s for people learning harder things. faculty. Together with other gifts, it lecture featured Professor Allen allows the department to support Knutson, who discussed the activities that are essential to our mathematics of juggling. Professor scientific output, such as visits by Knutson joined the faculty here in preeminent mathematicians and 2009; his research interests include collaborators. algebraic geometry and algebraic The 2010 International Congress combinatorics. Until 1995, he held of Mathematicians, the quadrennial a juggling world record for passing world gathering of mathematicians (12 balls between two people). where Fields Medal recipients are The mathematics of juggling announced, was held this summer in was codified about 25 years ago, Hyderabad, India. Karen Vogtmann when three different groups of had the honor to chair the official jugglers came up with the same U.S. delegation to the congress and way of mathematically representing Professor Knutson’s lecture two of our faculty, Lou Billera and a juggling pattern. This notational and demonstration is available on Justin Moore, gave invited lectures. system, called “siteswaps,” made CornellCast: Congratulations to Karen, Lou, and it easy to record patterns, note www.cornell.edu/video Justin! similarities, and find new juggling VISITING ITHACA BY PATRICIA HERSH Spending fall semester of 2010 to College-town visiting the Cornell math department, for pizza for lunch thanks to the generous support of the one day. Recently I Ruth I. Michler Memorial Prize, is a visited the breath- wonderful opportunity for me. Not taking gorge and only is there the strong geometric series of cascades combinatorics group comprised leading to Lucifer of Lou Billera, Ed Swartz, and Falls in Robert H. Allen Knutson, but also numerous Treman State Park other people using combinatorics (thanks to Ravi (particularly my specialty area Ramakrishna’s of topological combinatorics) in recommendation). exciting, highly nontrivial ways: With fresh energy Irena Peeva in conjunction with just after seeing free resolutions, Ken Brown in Lucifer Falls, a connection with group theory, and collaborator and Karen Vogtmann in her work on the I made a break- space of phylogenetic trees, just to through on how to name a few. Indeed, I am learning think about a strati- Laurent Saloff-Coste, Patricia Hersh, a lot from talking with an array of fied space related to and Georgia Benkart, President of the AWM different people and have identified phylogenetic trees. a few possible joint projects with This past weekend I attended a real learning opportunity for all Cornell faculty members, still in an impressive series of talks at the involved. early stages. conference Approaches to Group It is a very nice thing that I am also finding a little time Theory honoring Ken Brown. the Michler family has done in to enjoy Ithaca. Tara Holm took Speaker after speaker made his creating this prize as a tribute to me to the farmer’s market and or her talk understandable for Ruth Michler. I can say from my then to Gimme Coffee on my first people from all different areas of own firsthand experience that this Saturday morning here. Ed Swartz math, sharing perspective on their is clearly having a very positive took me walking along the gorge areas, and making the conference impact for its recipients. INTERNATIONAL CONGRESS OF MATHEMATICIANS BY JUSTIN MOORE Every four years, there is notable recent developments in the of Geneva). Louis Billera and Justin an International Congress of field. Moore presented invited talks, Mathematicians, and in 2010 the This year the math department at representing combinatorics and Congress was held in Hyderabad, Cornell was represented at the ICM logic, respectively. Finally, Keith India. Among the highlights of this in a number of different capacities. Dennis was among those recognized event is the awarding of the Fields Karen Vogtmann was the chair of for their contribution to the project Medal, the award in mathematics the U.S. delegation to the general of digitizing the proceedings of all generally regarded as the equivalent assembly of the International of the previous congresses, dating of the Nobel Prize. To be invited to Mathematical Union (the primary back to 1893. The entire database speak at the ICM is a coveted honor, political organization associated can be accessed at: with only a handful of people chosen with the ICM). Harry Kesten from each of the major divisions of presented the Fields medal laudation www.mathunion.org/ICM mathematics to speak on the most for Stanislav Smirnov (University 2 LETTER FROM THE CHAIR Continued from page 3. postdoctoral and visitor program per tenure/tenure-track faculty, or the U.S. clearly demonstrates that was average in size when compared per undergraduate student. a lively postdoctoral and visitor to the top 50 departments of The university’s “2010-2015 program is an essential component mathematics. This program directly Strategic Plan” calls for Cornell to of successful departments. With impacted approximately one third be recognized worldwide as a top- few exceptions, the rule is: the of our scientific activities in terms ten university. There are no top-ten better the department, the larger the of publications and seminars. In universities without a superb depart- postdoctoral and visitor program. the last two years, this essential ment of mathematics. There are no The resources supporting these component of the scientific life well-ranked departments of math- programs are mostly internal and of the department has been cut by ematics without a lively postdoc- tied to instruction. In this way, more than 65%. Today, among the toral and visitor program. Failing to mathematics service instruction 4 top mathematics programs in recognize this undisputable reality plays an essential role in supporting the state of New York (Columbia, now is sure to have very undesirable research activities at the best Cornell, NYU, Stony Brook), our long-term effects on our department departments of mathematics. department has, by far, the smallest and our university and is the chal- Looking at our department over postdoctoral and visitor program, lenge we will be addressing for the the past ten years, one finds that our whether measured in absolute size, next several years. FASHION STATEMENT BY LAURENT SALOFF-COSTE In the late 1970s, Bill Thurston Dai Fujiwara at the presentation three-dimensional topologies.” formulated his geometrization con- of the Miyake Collection which Jenny Barchfield from the Associated jecture for 3-dimensional manifolds. was entirely inspired by his Press writes: “The collection, in an This far-reaching conjecture states geometrization conjecture. The eye-popping rainbow of mostly that all 3-manifolds can be decom- notes accompanying the collection high-tech fabrics, riffed on the idea posed into pieces that belong to a described the Thurston theory as of oblong shapes and loops, circles short list of eight model geometries. “a comprehensive vision of eight and spirals — Thurston’s model The geometrization conjecture con- geometries that are sufficient to metaphors for the universe.” tains as a special case the famous form an ideal shape for all possible In spring 2010, the Clay conjecture made by the French Institute announced that the mathematician Henri Poincaré Millennium Prize for the (1854-1912) that the 3-sphere Poincaré conjecture was is the only closed 3-dimen- awarded to Grigoriy Perelman. sional manifold on which As he had done earlier with any loop can be retracted to a the Fields medal, Perelman point. The Poincaré conjecture refused the Millennium Prize is one of the seven Millennium of $1 million but the math- Problems for the solution ematical community cele- of which the Clay Institute brated Perleman’s astonishing established a $1 million award achievements including his in 2000.