Claude R. LeBrun (born 1956) is an American mathematician who holds the position of SUNY 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 research university in Stony Brook, New York. Along with the University at Buffalo, it is one of the State University of New York system's ...

. Much of his research concerns the

Riemannian geometry Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, smooth manifolds with a ''Riemannian metric'', i.e. with an inner product on the tangent space at each point that varies smoothly from point to poin ...

of 4-manifolds, or related topics in complex and differential geometry. LeBrun earned his

D.Phil. A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is ...

(Oxford equivalent of a Ph.D.) from the

University of Oxford , mottoeng = The Lord is my light , established = , endowment = £6.1 billion (including colleges) (2019) , budget = £2.145 billion (2019–20) , chancellor ...

in 1980, under the supervision of

Roger Penrose Sir Roger Penrose (born 8 August 1931) is an English mathematician, mathematical physicist, philosopher of science and Nobel Laureate in Physics. He is Emeritus Rouse Ball Professor of Mathematics in the University of Oxford, an emeritus fello ...

, and in the same year took a faculty position at Stony Brook.Math Department and Institute Faculty - by Rank
Stony Brook University, retrieved 2013-01-30. Since then, he has also held positions at 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. It is located in Bures-sur-Yvette, just ...

, the

Mathematical Sciences Research Institute The Simons Laufer Mathematical Sciences Institute (SLMath), formerly the Mathematical Sciences Research Institute (MSRI), is an independent nonprofit mathematical research institution on the University of California campus in Berkeley, Califo ...

, and the

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

. 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 Sir Michael Francis Atiyah (; 22 April 1929 – 11 January 2019) was a British-Lebanese mathematician specialising in geometry. His contributions include the Atiyah–Singer index theorem and co-founding topological K-theory. He was awarded the ...

and

Edward Witten Edward Witten (born August 26, 1951) is an American mathematical and theoretical physicist. He is a Professor Emeritus in the School of Natural Sciences at the Institute for Advanced Study in Princeton. Witten is a researcher in string theory, q ...

. LeBrun is also known for his work on

Einstein manifold In differential geometry and mathematical physics, an Einstein manifold is a Riemannian or pseudo-Riemannian differentiable manifold whose Ricci tensor is proportional to the metric. They are named after Albert Einstein because this condition i ...

s and the

Yamabe invariant In mathematics, in the field of differential geometry, the Yamabe invariant, also referred to as the sigma constant, is a real number invariant associated to a smooth manifold that is preserved under diffeomorphisms. It was first written down ind ...

. In particular, he produced examples showing that the

converse Converse may refer to: Mathematics and logic * Converse (logic), the result of reversing the two parts of a definite or implicational statement ** Converse implication, the converse of a material implication ** Converse nonimplication, a logical c ...

of the

Hitchin–Thorpe inequality In differential geometry the Hitchin–Thorpe inequality is a relation which restricts the topology of 4-manifolds that carry an Einstein metric. Statement of the Hitchin–Thorpe inequality Let ''M'' be a closed, oriented, four-dimensio ...

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 Nevanlinna Prize (to be rename ...

. 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

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 {{US-mathematician-stub