The American Mathematical Society (AMS) awarded two Stony Brook University faculty and one former faculty member with the 2019 Oswald Veblen Prize in Geometry. Among this year’s recipients are Xiuxiong Chen, a professor in the Department of Mathematics; Sir Simon Donaldson, a permanent member of the Simons Center for Geometry and Physics and a professor in the Department of Mathematics; and Song Sun, currently in the Department of Mathematics at University of California, Berkeley.
Considered the premier international award in geometry, the Veblen Prize is given for outstanding research work in geometry or topology that has appeared in the past six years. It is awarded every three years.
“These awards are further validation of the impact of our extraordinary faculty in the Department of Mathematics and the Simons Center for Geometry and Physics on topology and geometry” said Stony Brook President Samuel L. Stanley Jr. “It is wonderful to see these outstanding mathematicians recognized for their groundbreaking studies in these important fields.”
In 1982 Shing-Tung Yau received the Fields Medal in part for his proof of the so-called Calabi Conjecture. He later conjectured that a solution in the case of Fano manifolds, i.e., those with positive first Chern class, would necessarily involve an algebro-geometric notion of stability. Seminal work of Gang Tian and then Donaldson clarified and generalized this idea. The resulting conjecture—that a Fano manifold admits a Kähler-Einstein metric if and only if it is K-stable—became one of the most active topics in geometry.
In their three-part breakthrough paper, “Kähler-Einstein metrics on Fano manifolds,” which was published in the Journal of the American Mathematical Society, professors Chen, Donaldson and Sun proved a remarkable nonlinear Fredholm alternative for the Kähler-Einstein equations on Fano manifolds. According to the Veblen Prize citation, one nominator states that their work “is certainly the biggest result in Kähler geometry since Yau’s solution of the Calabi conjecture 35 years earlier. It is already having a huge impact that will only grow with time.”
“I am delighted that these three Stony Brook people won the prize,” said Jim Simons, chair of the Simons Foundation, and former chairman of Stony Brook’s Department of Mathematics. “This adds considerably to the long list of our math department’s Veblen Prize winners and makes me proud of my work in helping found this department fifty years ago.”
“We are thrilled that our faculty members have been recognized with such a magnificent honor in their field,” said Michael Bernstein, Provost and Senior Vice President for Academic Affairs. “It is testament to the extraordinary work conducted in our Department of Mathematics and the Simons Center. Congratulations to Dr. Chen and Sir Donaldson, as well as to our former faculty member, Dr. Sun.”
Chen received his PhD from University of Pennsylvania, and has been a professor at Stony Brook since 2009. With interests in differential geometry and complex differential geometry, Chen was named a 2015 Fellow of the American Mathematical Society and a 2016 Simons Fellow in Mathematics.
Donaldson, who received his D.Phil. from University of Oxford, England, joined Stony Brook in 2014. His previous awards include the Junior Whitehead Prize; Fields Medal; Crafoord Prize; King Faisal International Prize; Nemmers Prize in Mathematics; Shaw Prize in Mathematics; and Breakthrough Prize in Mathematics.
“I am delighted to see this triumvirate of Stony Brook mathematicians recognized for their solution to a long-standing challenge in geometry,” said Nicole Sampson, interim dean of the College of Arts and Sciences.
Robert Lazarsfeld, professor and chair of the College of Arts and Sciences Department of Mathematics, agreed with that sentiment. “This major award recognizes their spectacular proof of the most important open problem in Kähler geometry,” he said.
“I am especially thrilled that Sir Simon Donaldson, one of the senior professors in the Simons Center, is sharing the Veblen Prize with two highly accomplished and respected colleagues in the Simons Center, professors Xiuxiong Chen, and Song Sun,” said Luis Alvarez-Gaume, director of the Simons Center for Geometry and Physics. “It is a privilege to count on Simon’s presence at the Center. Through the years, he’s been a kind of ‘King Midas’ of mathematics; whatever he touches turns into gold.”
Lazarsfeld and Alvarez-Gaume both noted that since the founding of the modern mathematics department by James Simons in the late 1960s, Stony Brook has been celebrated as one of the premier international centers of research in geometry. Several of Stony Brook University’s most distinguished current and former faculty are previous winners of the prize; Lazarsfeld says he’s delighted that the tradition continues.
The Veblen Prize was established in 1961 in memory of Professor Oswald Veblen through a fund contributed by former students and colleagues. The fund was later doubled by the widow of Professor Veblen. An anonymous donor generously augmented the fund in 2008. In 2013, in honor of her late father, John L. Synge, who knew and admired Oswald Veblen, Cathleen Synge Morawetz and her husband, Herbert, substantially increased the endowment.
The $5,000 prize will be awarded at the 2019 AMS Joint Mathematics Meetings, January 16-19, 2019 in Baltimore.
Previous Veblen Prize winners at Stony Brook University include:
- Dennis Sullivan, distinguished professor in the Department of Mathematics; awarded in 1971
- Jim Simons, awarded in 1976
- Mikhail Gromov (currently at NYU), awarded in 1981
- Jeff Cheeger (currently at NYU), awarded in 2001