Nancy Burgess Hingston is a mathematician working in

algebraic topology Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariant (mathematics), invariants that classification theorem, classify topological spaces up t ...

and

differential geometry Differential geometry is a Mathematics, mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of Calculus, single variable calculus, vector calculus, lin ...

. She is a professor emerita of mathematics at

The College of New Jersey The College of New Jersey (TCNJ) is a public university in Ewing Township, New Jersey. It is part of New Jersey's public system of higher education. Established in 1855 as the New Jersey State Normal School, TCNJ was the first normal school, ...

Early life and education

Nancy Hingston's father William Hingston was superintendent of the

Central Bucks School District The Central Bucks School District (CBSD) is a school district located in Pennsylvania and the third-largest school district in the state. The district covers the Boroughs of Chalfont, Pennsylvania, Chalfont, Doylestown, Pennsylvania, Doylest ...

in Pennsylvania; her mother was a high school mathematics and computer science teacher. She graduated from the

University of Pennsylvania The University of Pennsylvania (Penn or UPenn) is a Private university, private Ivy League research university in Philadelphia, Pennsylvania, United States. One of nine colonial colleges, it was chartered in 1755 through the efforts of f ...

with a double major in

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

and

physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...

. After a year studying physics as a graduate student, she switched to mathematics, and completed her PhD in 1981 from

Harvard University Harvard University is a Private university, private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the History of the Puritans in North America, Puritan clergyma ...

under the supervision of

Raoul Bott Raoul Bott (September 24, 1923 – December 20, 2005) was a Hungarian-American mathematician known for numerous foundational contributions to geometry in its broad sense. He is best known for his Bott periodicity theorem, the Morse–Bott function ...

Career

Before joining TCNJ, she taught at the University of Pennsylvania. She has also been a frequent visitor to the

Institute for Advanced Study The Institute for Advanced Study (IAS) is an independent center for theoretical research and intellectual inquiry located in Princeton, New Jersey. It has served as the academic home of internationally preeminent scholars, including Albert Ein ...

, and has been involved with the Program for Women and Mathematics at the Institute for Advanced Study since its founding in 1994.

Contributions

Nancy Hingston made major contributions in Riemannian geometry and Hamiltonian dynamics, and more specifically in the study of

closed geodesic In differential geometry and dynamical systems, a closed geodesic on a Riemannian manifold is a geodesic that returns to its starting point with the same tangent direction. It may be formalized as the projection of a closed orbit of the geodesic f ...

s and, more generally,

periodic orbits In mathematics, specifically in the study of dynamical systems, an orbit is a collection of points related by the evolution function of the dynamical system. It can be understood as the subset of phase space covered by the trajectory of the dyn ...

of Hamiltonian systems. In her very first paper, she proved that a generic

Riemannian metric In differential geometry, a Riemannian manifold is a geometric space on which many geometric notions such as distance, angles, length, volume, and curvature are defined. Euclidean space, the N-sphere, n-sphere, hyperbolic space, and smooth surf ...

on a closed manifold possesses infinitely many closed geodesics. In the 1990s, she proved that the growth rate of closed geodesics in Riemannian 2-spheres is at least the one of prime numbers. In the years 2000s, she proved the long-standing Conley conjecture from symplectic geometry: every Hamiltonian diffeomorphism of a standard symplectic torus of any even dimension possesses infinitely many periodic points (the result was subsequently extended by Viktor Ginzburg to more general symplectic manifolds).

Recognition

Nancy Hingston was an

invited speaker at the International Congress of Mathematicians An invitation system is a method of encouraging people to join an organization, such as a Club (organization), club or a website. In regular society, it refers to any system whereby new members are chosen; they cannot simply apply. In relation to w ...

in 2014.. She is a fellow 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 differential geometry and the study of closed geodesics."2017 Class of the Fellows of the AMS

, retrieved 2016-11-06.

Personal

Her husband, Jovi Tenev, is a lawyer.. She has three children.

References

{{DEFAULTSORT:Hingston, Nancy Year of birth missing (living people) Living people 20th-century American mathematicians 21st-century American mathematicians University of Pennsylvania alumni Harvard University alumni The College of New Jersey faculty American geometers Fellows of the American Mathematical Society 20th-century American women mathematicians 21st-century American women mathematicians