Jane Piore Gilman (born 1945) is an 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, mathematical structure, structure, space, Mathematica ...

, a distinguished professor of mathematics at

Rutgers University Rutgers University (; RU), officially Rutgers, The State University of New Jersey, is a public land-grant research university consisting of four campuses in New Jersey. Chartered in 1766, Rutgers was originally called Queen's College, and wa ...

.Curriculum vitae
February 8, 2013, retrieved 2014-06-14. Her research concerns

topology In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ho ...

and

group theory In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ...

Education and career

Gilman is one of three children of physicist

Emanuel R. Piore Emanuel (Mannie) Ruben Piore (19 July 1908 – 9 May 2000) was a scientist and a manager of industrial research.. Piore was born on 19 July 1908 in Vilnius, Lithuania to a Jewish family. In 1917, his family moved to the United States, and in ...

. She did her undergraduate studies at the

University of Chicago The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private university, private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park, Chicago, Hyde Park neighborhood. The University of Chic ...

, graduating in 1965, and received her Ph.D. from

Columbia University Columbia University (also known as Columbia, and officially as Columbia University in the City of New York) is a private research university in New York City. Established in 1754 as King's College on the grounds of Trinity Church in Manha ...

in 1971. Her thesis, supervised by

Lipman Bers Lipman Bers ( Latvian: ''Lipmans Berss''; May 22, 1914 – October 29, 1993) was a Latvian-American mathematician, born in Riga, who created the theory of pseudoanalytic functions and worked on Riemann surfaces and Kleinian groups. He was also k ...

, was entitled ''Relative Modular Groups in Teichmüller Spaces''. She worked for a year as an instructor 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 syste ...

before joining Rutgers in 1972.

Books

Gilman is the author of a monograph on the problem of testing whether pairs of elements of PSL(2,R) (the group of orientation-preserving

isometries In mathematics, an isometry (or congruence, or congruent transformation) is a distance-preserving transformation between metric spaces, usually assumed to be bijective. The word isometry is derived from the Ancient Greek: ἴσος ''isos'' mea ...

of the

hyperbolic plane In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate of Euclidean geometry is replaced with: :For any given line ''R'' and point ''P'' ...

) generate a

Fuchsian group In mathematics, a Fuchsian group is a discrete subgroup of PSL(2,R). The group PSL(2,R) can be regarded equivalently as a group of isometries of the hyperbolic plane, or conformal transformations of the unit disc, or conformal transformations ...

discrete subgroup In mathematics, a topological group ''G'' is called a discrete group if there is no limit point in it (i.e., for each element in ''G'', there is a neighborhood which only contains that element). Equivalently, the group ''G'' is discrete if and ...

of PSL(2,R)). It is ''Two-generator Discrete Subgroups of ''PSL(2, R) (Memoirs of the American Mathematical Society 117, 1995). With Irwin Kra and Rubí E. Rodríguez she is the co-author of a graduate-level textbook on

complex analysis Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebra ...

, ''Complex Analysis: In the Spirit of Lipman Bers'' (

Graduate Texts in Mathematics Graduate Texts in Mathematics (GTM) ( ISSN 0072-5285) is a series of graduate-level textbooks in mathematics published by Springer-Verlag. The books in this series, like the other Springer-Verlag mathematics series, are yellow books of a standa ...

245, Springer, 2007; 2nd ed., 2013).

Recognition

In 2014 she was elected as a

fellow A fellow is a concept whose exact meaning depends on context. In learned or professional societies, it refers to a privileged member who is specially elected in recognition of their work and achievements. Within the context of higher education ...

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 ...

"for contributions to topology and group theory, and for service to her department and the larger community."2014 Class of the Fellows of the AMS
retrieved 2014-06-16.

References

{{DEFAULTSORT:Gilman, Jane Piore 1945 births Living people 20th-century American mathematicians 21st-century American mathematicians Columbia University alumni Stony Brook University faculty Rutgers University faculty American people of Lithuanian descent Fellows of the American Mathematical Society American women mathematicians 20th-century women mathematicians 21st-century women mathematicians 20th-century American women 21st-century American women