The LeBrun manifolds, a collection of self-dual manifolds identified in 1989, bear the name of the American mathematician Claude LeBrun. His research primarily investigates Riemannian geometry, specifically focusing on four-dimensional manifolds and their intersections with complex and differential geometry. He remains an active scholar in the field, currently serving as a professor in the United States.
Early Academic Training
Born in Dallas in 1956, LeBrun entered Rice University at the age of 16. He completed his Master of Arts in mathematics at that institution in 1977. in 1980 under the supervision of Roger Penrose. He was 23 years old at the time of graduation.
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LeBrun accepted a faculty position at Stony Brook University in 1980, marking the beginning of a long association with the institution where he currently holds the title of Distinguished Professor. Beyond his tenure at Stony Brook, he has served at several research centers. These include the Institut des Hautes Études Scientifiques from 1981 to 1982, the Simons Laufer Mathematical Sciences Institute between 1982 and 1983, and the Institute for Advanced Study during 1989 and 1990.
Research and Contributions
Beyond the manifolds that carry his name, LeBrun is recognized for his contributions to the study of Einstein manifolds and the Yamabe invariant. His work provided counterexamples to the converse of the Hitchin–Thorpe inequality, demonstrating that an infinite number of four-dimensional compact, smooth, simply connected manifolds exist that satisfy the inequality yet do not admit Einstein metrics.
Honors and Recognition
LeBrun was an invited speaker at the 1994 International Congress of Mathematicians. He was named a Fellow of the American Mathematical Society in 2013. The professional community has marked his influence through several conferences, including an event in 2016 at the Centre de Recherches Mathématiques in Montreal and a 2026 conference at the International Center for Theoretical Physics in Trieste, Italy.
Fast facts
- Born: 1956, Dallas
- Education: Rice University, University of Oxford
- Current Position: Distinguished Professor, Stony Brook University
- Research Interests: Riemannian, complex, and differential geometry
- Key Discovery: LeBrun manifolds (1989)
- Fellowship: American Mathematical Society (2013)
- Citizenship: United States
Questions readers ask
What are LeBrun manifolds?
They are a family of self-dual manifolds discovered by Claude LeBrun in 1989, named for him by Michael Atiyah and Edward Witten.
Where has Claude LeBrun held academic positions?
He has worked at Stony Brook University, the Institut des Hautes Études Scientifiques, the Simons Laufer Mathematical Sciences Institute, and the Institute for Advanced Study.
Achievements
- Held posts at Stony Brook University, Institute for Advanced Study and Simons Laufer Mathematical Sciences Institute
