Frank Wilson Warner III (born March 2 1938 in

Pittsfield, Massachusetts Pittsfield is the most populous city and the county seat of Berkshire County, Massachusetts, United States. It is the principal city of the Pittsfield, Massachusetts Metropolitan Statistical Area which encompasses all of Berkshire County. Pittsfi ...

) is an

American American(s) may refer to: * American, something of, from, or related to the United States of America, commonly known as the "United States" or "America" ** Americans, citizens and nationals of the United States of America ** American ancestry, p ...

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 ...

, specializing in

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 ...

Education and career

Warner graduated in 1959 with a bachelor's degree from

Pennsylvania State University The Pennsylvania State University (Penn State or PSU) is a Public university, public Commonwealth System of Higher Education, state-related Land-grant university, land-grant research university with campuses and facilities throughout Pennsyl ...

and in 1963 with a Ph.D. in mathematics from the

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a Private university, private research university in Cambridge, Massachusetts, United States. Established in 1861, MIT has played a significant role in the development of many areas of moder ...

. His thesis, written under the supervision of

Isadore M. Singer Isadore Manuel Singer (May 3, 1924 – February 11, 2021) was an American mathematician. He was an Emeritus Institute Professor in the Department of Mathematics at the Massachusetts Institute of Technology and a Professor Emeritus of Mathemat ...

, is entitled ''Conjugate Locus of a Riemannian Manifold''. At the

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California), is a Public university, public Land-grant university, land-grant research university in Berkeley, California, United States. Founded in 1868 and named after t ...

, Warner was an assistant professor from 1965 to 1968. At 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 ...

, he became an associate professor in 1968 and a full professor in 1973. He was from 1995 to 1997 the deputy dean of the

University of Pennsylvania School of Arts and Sciences The University of Pennsylvania School of Arts and Sciences (also known as SAS) is the academic institution encompassing the humanities, social sciences, and natural sciences at the University of Pennsylvania. Formerly known as the Faculty of Ar ...

. In 2000, he retired as professor emeritus. In the 1970s he and

Jerry Kazdan Jerry Lawrence Kazdan (born 31 October 1937 in Detroit, Michigan) is an American mathematician noted for his work in differential geometry and the study of partial differential equations. His contributions include the Berger–Kazdan compariso ...

, as collaborators, made important contributions to the theory of

Riemannian manifold 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 ...

s with prescribed scalar curvature. They proved in 1975 that any smooth function can be realized as a scalar curvature if it becomes negative somewhere on the manifold. Their further research dealt with

conjugate point In differential geometry, conjugate points or focal points are, roughly, points that can almost be joined by a 1-parameter family of geodesics. For example, on a sphere, the north-pole and south-pole are connected by any meridian. Another viewpoi ...

s on Riemannian manifolds. Warner was a

Guggenheim Fellow Guggenheim Fellowships are grants that have been awarded annually since by the John Simon Guggenheim Memorial Foundation, endowed by the late Simon and Olga Hirsh Guggenheim. These awards are bestowed upon individuals who have demonstrated d ...

for the academic year 1976–1977. He was elected in 1994 a Fellow of the

American Association for the Advancement of Science The American Association for the Advancement of Science (AAAS) is a United States–based international nonprofit with the stated mission of promoting cooperation among scientists, defending scientific freedom, encouraging scientific responsib ...

Selected publications

Articles

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Books

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References

{{DEFAULTSORT:Warner, Frank W Pennsylvania State University alumni Massachusetts Institute of Technology alumni University of Pennsylvania faculty Mathematicians at the University of Pennsylvania Fellows of the American Association for the Advancement of Science 20th-century American mathematicians 21st-century American mathematicians Differential geometers 1938 births Living people