Claude LeBrun

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Claude LeBrun at Oberwolfach, 2012

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,[1] and in the same year took a faculty position at Stony Brook.[2] 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.[3]

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.[4] 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.[2] In 2012 he became a Fellow of the American Mathematical Society.[5]