Jean-Luc Brylinski (born in 1951) is a French- American

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

. Educated at the Lycée Pasteur and the

École Normale Supérieure École may refer to: * an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée) * École (river), a tributary of the Seine flowing in région Île-de-France * École, S ...

Paris Paris () is the Capital city, capital and List of communes in France with over 20,000 inhabitants, most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), ma ...

, after an appointment as researcher with the C. N. R. S., he became a Professor of Mathematics at Pennsylvania State University. He proved the Kazhdan–Lusztig conjectures with Masaki Kashiwara. He has also worked on

gerbe In mathematics, a gerbe (; ) is a construct in homological algebra and topology. Gerbes were introduced by Jean Giraud (mathematician), Jean Giraud following ideas of Alexandre Grothendieck as a tool for non-commutative cohomology in degree 2. Th ...

cyclic homology In noncommutative geometry and related branches of mathematics, cyclic homology and cyclic cohomology are certain (co)homology theories for associative algebras which generalize the de Rham (co)homology of manifolds. These notions were independen ...

, Quillen bundles, and

geometric class field theory In mathematics, geometric class field theory is an extension of class field theory to higher-dimensional geometrical objects: much the same way as class field theory describes the abelianization of the Galois group of a local or global field, geom ...

, among other geometric and algebraic topics. Brylinski is currently residing in

Boston Boston (), officially the City of Boston, is the state capital and most populous city of the Commonwealth of Massachusetts, as well as the cultural and financial center of the New England region of the United States. It is the 24th- mo ...

, where he is a CTO and co-CEO of ''Brylinski Research'', together with his wife

Ranee Brylinski Ranee Kathryn Brylinski (née Gupta, born January 28, 1957) is an American mathematician known for her research in representation theory and quantum logic gates. Formerly a professor of mathematics at Pennsylvania State University, she left academi ...

Books

*''Loop Spaces, Characteristic Classes and Geometric Quantization'' (1992)

References

* * * {{DEFAULTSORT:Brylinski, Jean-Luc 20th-century French mathematicians 21st-century French mathematicians Living people 1951 births Lycée Pasteur (Neuilly-sur-Seine) alumni