Claude R. LeBrun is an American mathematician and professor of mathematics at Stony Brook University. Much of his research concerns the Riemannian geometry of 4-manifolds, or related topics in complex and differential geometry.
LeBrun earned his D.Phil. (= Ph.D.) from the University of Oxford in 1980, under the supervision of Roger Penrose, and in the same year took a faculty position at Stony Brook. Since then, he has also held positions at the Institut des Hautes Études Scientifiques, the Mathematical Sciences Research Institute, and the Institute for Advanced Study.
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. 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 manifolds that obey the inequality but do not admit Einstein metrics.
LeBrun was an invited speaker at the 1994 International Congress of Mathematicians. In 2012 he became a Fellow of the American Mathematical Society. In 2016, a conference in his honor was held in Montreal. 
- Claude R. LeBrun at the Mathematics Genealogy Project
- Math Department and Institute Faculty - by Rank, Stony Brook University, retrieved 2013-01-30.
- A Community of Scholars | Institute for Advanced Study, retrieved 2013-05-15.
- Atiyah, Michael; Witten, Edward (2002), "M-theory dynamics on a manifold of G2 holonomy", Advances in Theoretical and Mathematical Physics, 6 (1): 1–106, ISSN 1095-0761
- List of Fellows of the American Mathematical Society, retrieved 2013-01-27.
- Conference on Differential Geometry, retrieved 2016-10-08.