Claude R. LeBrun (born 1956) is an American mathematician who holds the position of Distinguished Professor of Mathematics at

Stony Brook University Stony Brook University (SBU), officially the State University of New York at Stony Brook, is a public university, public research university in Stony Brook, New York, United States, on Long Island. Along with the University at Buffalo, it is on ...

. Much of his research concerns the

Riemannian geometry Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, defined as manifold, smooth manifolds with a ''Riemannian metric'' (an inner product on the tangent space at each point that varies smooth function, smo ...

of 4-manifolds, or related topics in complex and differential geometry. After enrolling as an undergraduate at

Rice University William Marsh Rice University, commonly referred to as Rice University, is a Private university, private research university in Houston, Houston, Texas, United States. Established in 1912, the university spans 300 acres. Rice University comp ...

at age 16, LeBrun received his

Master of Arts A Master of Arts ( or ''Artium Magister''; abbreviated MA or AM) is the holder of a master's degree awarded by universities in many countries. The degree is usually contrasted with that of Master of Science. Those admitted to the degree have ...

in mathematics from

Rice Rice is a cereal grain and in its Domestication, domesticated form is the staple food of over half of the world's population, particularly in Asia and Africa. Rice is the seed of the grass species ''Oryza sativa'' (Asian rice)—or, much l ...

in 1977. He then went on to earn his D.Phil. (Oxford equivalent of a Ph.D.) from the

University of Oxford The University of Oxford is a collegiate university, collegiate research university in Oxford, England. There is evidence of teaching as early as 1096, making it the oldest university in the English-speaking world and the List of oldest un ...

in 1980, for a thesis on complex differential geometry written under the supervision of

Roger Penrose Sir Roger Penrose (born 8 August 1931) is an English mathematician, mathematical physicist, Philosophy of science, philosopher of science and Nobel Prize in Physics, Nobel Laureate in Physics. He is Emeritus Rouse Ball Professor of Mathematics i ...

. That same year, he then accepted his first faculty position at Stony Brook.Math Department and Institute Faculty - by Rank
Stony Brook University, retrieved 2013-01-30. Although he would eventually go on to spend most of his career at Stony Brook, he has also held positions at a number of other institutions, including the

Institut des Hautes Études Scientifiques The Institut des hautes études scientifiques (IHÉS; English: Institute of Advanced Scientific Studies) is a French research institute supporting advanced research in mathematics and theoretical physics (also with a small theoretical biology g ...

, the Mathematical Sciences Research Institute, and the

Institute for Advanced Study The Institute for Advanced Study (IAS) is an independent center for theoretical research and intellectual inquiry located in Princeton, New Jersey. It has served as the academic home of internationally preeminent scholars, including Albert Ein ...

. He is the namesake of the LeBrun manifolds, a family of self-dual manifolds that he discovered in 1989 and that was named after him by Michael Atiyah and

Edward Witten Edward Witten (born August 26, 1951) is an American theoretical physics, theoretical physicist known for his contributions to string theory, topological quantum field theory, and various areas of mathematics. He is a professor emeritus in the sc ...

. LeBrun is also known for his work on Einstein manifolds and the Yamabe invariant. In particular, he produced examples showing that the converse of the Hitchin–Thorpe inequality does not hold: there exist infinitely many four-dimensional compact smooth simply connected

manifold In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n-dimensional manifold, or ''n-manifold'' for short, is a topological space with the property that each point has a N ...

s that obey the inequality but do not admit Einstein metrics. LeBrun was an invited speaker at the 1994

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the IMU Abacus Medal (known before ...

. In 2012, he became a Fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

. In 2016, a conference in his honor was held in Montreal. In 2018, he became a Simons Foundation Fellow in Mathematics. In 2020, he was appointed as Distinguished Professor at the State University of New York. Stony Brook University
retrieved 2020-12-10.

References

{{DEFAULTSORT:Lebrun, Claude Living people 20th-century American mathematicians Rice University alumni Alumni of the University of Oxford Stony Brook University faculty Fellows of the American Mathematical Society Differential geometers 1956 births 21st-century American mathematicians