NASHVILLE, Tenn. ñ Alain Connes, widely considered to be one of the three most influential living mathematicians, has accepted a position of distinguished professor at Vanderbilt, enabling the University to become a base for training new mathematicians to fill the ranks left vacant by a retiring generation of scholars.
Under the arrangement, Connes, who is a professor of mathematics at the College de France and holds the Motchane Chair at l’Institut des Hautes …tudes Scientifiques in France, will spend several weeks each spring in Nashville to collaborate with members of the Vanderbilt math department and participate in an annual workshop for young mathematicians.
In 1982, Connes received the Fields Medal, the highest award given by the international mathematics community, and in 2001 he was awarded the $500,000 Crafoord Prize by the Royal Swedish Academy of Sciences.
In his introduction to Connes at the Crafoord Prize ceremony, Sir M. F. Atiyah, master of Trinity College and director of the Isaac Newton Institute for Mathematical Sciences in Cambridge, declared that Connes is one of those major figures in mathematics who appear through history whose vision "transcends" the fragmentation into separate disciplines, whose work "helps to forge new bonds between the diverging branches" and whose legacy "is a rejuvenated discipline."
"Connes has taken geometry to whole new level ñ one that is finding important applications in theoretical physics," explains Guoliang Yu, a Vanderbilt mathematics professor who works in the area.
Called noncommutative geometry, Connes’ new approach is allowing mathematicians to solve a number of classical problems that have proven intractable to older approaches, Yu says. One of the most famous problems that is currently under attack with noncommutative techniques is the Riemann hypothesis. This hypothesis provides an approximate answer to the question of how many prime numbers are contained in an arbitrarily large string of integers. Despite the fact that this hypothesis has never been proved, mathematicians have created hundreds of different theorems that assume it is correct. That has led the Clay Foundation to offer a reward of $1 million for the person who can prove (or disprove) it.
Three Vanderbilt mathematicians ñ Yu, Dietmar Bisch and Gennadi Kasparov ñ initially contacted Connes to invite him to give the annual Shanks lecture. Since 1986 the Vanderbilt math department has put on an annual lecture and conference funded by an endowment from the family of Baylis and Olivia Shanks. Baylis Shanks was a prominent mathematician who taught at Vanderbilt from 1947 until 1978. When the Vanderbilt mathematicians contacted Connes, however, the French mathematician suggested that they put on a workshop for young mathematicians instead of the traditional conference.
"Connes has great enthusiasm for the field and a real interest in training the best young minds," says Michael Mihalik, the math department chairman. The U.S. in particular is facing a serious pipeline problem: Few top students are going into mathematics and a large percentage of those teaching mathematics today are scheduled to retire within a few years. "In just seven years about half the members of our department will be 65 or older and we don’t know where the young mathematicians will come from to replace us when we retire!" Mihalik says.
The Vanderbilt math department embraced Connes’ suggestion enthusiastically. They obtained additional funding from the Clay Mathematics Institute, the National Science Foundation and the Vanderbilt administration so they could invite top-notch speakers and pay all the expenses of 80 graduate students and post-doctoral studentsñ two thirds from the U.S. and one third from overseas ñ for a 12-day training session in noncommutative geometry.
The meeting was held last May and, by all accounts, was a smashing success. "Connes loved Vanderbilt and Nashville. He said the city was very cultured," reports Yu, who was one of his hosts. The famous mathematician was impressed enough that he agreed to accept a position at Vanderbilt when it was offered. The position will allow him to use Nashville a base in the United States for training future mathematicians. He and his new Vanderbilt colleagues are in the process of planning and fund raising for next year’s workshop, which they say will be slightly smaller and organized around a specific mathematical theme.
Connes’ arrangement with Vanderbilt is open-ended. He will be paid for the amount of time he spends on campus. Mihalik and the other campus mathematicians hope that, beginning with the annual workshops, Connes will find the intellectual and cultural environment in Nashville so enticing that he will spend increasing amounts of time here.
"We currently have a very strong team in noncommutative geometry," says Yu, "and the association with Connes can only make us stronger."
Media Contact: David Salisbury, (615) 343-6803 david.salisbury@vanderbilt.edu