Ranee Kathryn Brylinski (née Gupta, born January 28, 1957) is an American mathematician known for her research in

representation theory Representation theory is a branch of mathematics that studies abstract algebraic structures by ''representing'' their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essen ...

and

quantum logic gate In quantum computing and specifically the quantum circuit model of computation, a quantum logic gate (or simply quantum gate) is a basic quantum circuit operating on a small number of qubits. They are the building blocks of quantum circuits, li ...

s. Formerly a professor of mathematics at

Pennsylvania State University The Pennsylvania State University (Penn State or PSU) is a public state-related land-grant research university with campuses and facilities throughout Pennsylvania. Founded in 1855 as the Farmers' High School of Pennsylvania, Penn State becam ...

, she left academia in 2003 to found the mathematical consulting company Brylinski Research with her husband,

Jean-Luc Brylinski Jean-Luc Brylinski (born in 1951) is a French- American mathematician. Educated at the Lycée Pasteur and the École Normale Supérieure in Paris, after an appointment as researcher with the C. N. R. S., he became a Professor of Mathematics at Pen ...

Education and career

Brylinski was born in

Detroit, Michigan Detroit ( , ; , ) is the largest city in the U.S. state of Michigan. It is also the largest U.S. city on the United States–Canada border, and the seat of government of Wayne County. The City of Detroit had a population of 639,111 at ...

. She graduated from

Princeton University Princeton University is a private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the n ...

in 1977, and completed her Ph.D. at the

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a Private university, private Land-grant university, land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern t ...

(MIT) in 1981. Her dissertation, ''Abelian Algebras and Adjoint Orbits'', was supervised by

Steven Kleiman Steven Lawrence Kleiman (born March 31, 1942) is an American mathematician. Professional career Kleiman is a Professor of Mathematics at the Massachusetts Institute of Technology. Born in Boston, he did his undergraduate studies at MIT. He rece ...

. After a year as an NSF Mathematical Sciences Postdoctoral Fellow at MIT, she joined the faculty at Brown University as Tamarkin Assistant Professor of Mathematics in 1982. She moved from Brown to Pennsylvania State University in 1991. At Pennsylvania State, she was co-director of the Center for Geometry and Mathematical Physics.

Contributions

The Brylinski–Kostant filtration of weight spaces is named after her. She originally developed this filtration in 1989, motivated by earlier work of Bertram Kostant. She is also known for Brylinski's theorem, a theorem from her dissertation on the closures of orbits of

algebraic group In mathematics, an algebraic group is an algebraic variety endowed with a group structure which is compatible with its structure as an algebraic variety. Thus the study of algebraic groups belongs both to algebraic geometry and group theory. ...

s. Another result, also called "Brylinski's theorem", comes from a paper written jointly by Brylinski and her husband, characterizing universal quantum logic gates.

Recognition

Brylinski won a

Sloan Research Fellowship The Sloan Research Fellowships are awarded annually by the Alfred P. Sloan Foundation since 1955 to "provide support and recognition to early-career scientists and scholars". This program is one of the oldest of its kind in the United States. ...

in 1990. In 1998, she won the

G. de B. Robinson Award The Canadian Mathematical Society (CMS) (french: Société mathématique du Canada) is an association of professional mathematicians dedicated to the interests of mathematical research, outreach, scholarship and education in Canada. It serves th ...

of the Canadian Mathematical Society for her work on quantization of algebraic groups.

Selected publications

With Goong Chen, Brylinski is the editor of the book ''Mathematics of Quantum Computation'' (Chapman & Hall/CRC, 2002). She is also one of the editors of ''Lie Theory and Geometry: In Honor of Bertram Kostant'' (Springer, 1994) and ''Advances in Geometry'' (Springer, 1999). Her research papers include:

References

{{DEFAULTSORT:Brylinski, Ranee 1957 births Living people 20th-century American mathematicians American women mathematicians Princeton University alumni Brown University faculty Pennsylvania State University faculty Massachusetts Institute of Technology School of Science alumni Sloan Research Fellows 20th-century women mathematicians 20th-century American women 21st-century American women