Francis Thomas Farrell (born November 14, 1941, in
Ohio
Ohio ( ) is a U.S. state, state in the Midwestern United States, Midwestern region of the United States. It borders Lake Erie to the north, Pennsylvania to the east, West Virginia to the southeast, Kentucky to the southwest, Indiana to the ...
, United States) is an American mathematician who has made contributions in the area of
topology
Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...
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 ...
. Farrell is a distinguished professor emeritus of mathematics at
Binghamton University
The State University of New York at Binghamton (Binghamton University or SUNY Binghamton) is a public university, public research university in Binghamton metropolitan area, Greater Binghamton, New York, United States. It is one of the four uni ...
. He also holds a position at the Yau Mathematical Sciences Center,
Tsinghua University
Tsinghua University (THU) is a public university in Haidian, Beijing, China. It is affiliated with and funded by the Ministry of Education of China. The university is part of Project 211, Project 985, and the Double First-Class Constructio ...
.
Biographical data
Farrell got his bachelor's degree in 1963 from the
University of Notre Dame
The University of Notre Dame du Lac (known simply as Notre Dame; ; ND) is a Private university, private Catholic research university in Notre Dame, Indiana, United States. Founded in 1842 by members of the Congregation of Holy Cross, a Cathol ...
and earned his
Ph.D
A Doctor of Philosophy (PhD, DPhil; or ) is a terminal degree that usually denotes the highest level of academic achievement in a given discipline and is awarded following a course of graduate study and original research. The name of the deg ...
in Mathematics from
Yale University
Yale University is a Private university, private Ivy League research university in New Haven, Connecticut, United States. Founded in 1701, Yale is the List of Colonial Colleges, third-oldest institution of higher education in the United Stat ...
in 1967. His Ph.D. advisor was
Wu-Chung Hsiang
Wu-Chung Hsiang (; born 12 June 1935) is a Taiwanese-American mathematician, specializing in topology. Hsiang served as chairman of the Department of Mathematics at Princeton University from 1982 to 1985 and was one of the most influential Topolog ...
, and his doctoral thesis title was "The Obstruction to Fibering a Manifold over a Circle". He was a NSF Post-doctoral Fellow at the
University of California at Berkeley
The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California), is a public land-grant research university in Berkeley, California, United States. Founded in 1868 and named after the Anglo-Irish philosopher George Berkele ...
from 1968 to 1969, and became an assistant professor there from 1969 to 1972. He then went to
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 ...
, where he was promoted to professor in 1978. Later he joined the
University of Michigan
The University of Michigan (U-M, U of M, or Michigan) is a public university, public research university in Ann Arbor, Michigan, United States. Founded in 1817, it is the oldest institution of higher education in the state. The University of Mi ...
(1979–1985) and
Columbia University
Columbia University in the City of New York, commonly referred to as Columbia University, is a Private university, private Ivy League research university in New York City. Established in 1754 as King's College on the grounds of Trinity Churc ...
(1984–1992). Since 1990 Farrell has been a faculty member at SUNY Binghamton.
In 1970, Farrell was invited to give a 50-minute address at the
International Congress of Mathematicians
The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU).
The Fields Medals, the IMU Abacus Medal (known before ...
about his thesis in
Nice
Nice ( ; ) is a city in and the prefecture of the Alpes-Maritimes department in France. The Nice agglomeration extends far beyond the administrative city limits, with a population of nearly one million
In 1990, for their joint work on Rigidity in Geometry and Topology, his co-author Lowell E. Jones was invited to give a 45-minute address at the International Congress of Mathematicians in
Kyoto
Kyoto ( or ; Japanese language, Japanese: , ''Kyōto'' ), officially , is the capital city of Kyoto Prefecture in the Kansai region of Japan's largest and most populous island of Honshu. , the city had a population of 1.46 million, making it t ...
, Japan.
Mathematical contributions
Much of Farrell's work lies around the
Borel conjecture
In geometric topology, the Borel conjecture (named for Armand Borel) asserts that an aspherical closed manifold is determined by its fundamental group, up to homeomorphism. It is a rigidity conjecture, asserting that a weak, algebraic notion of ...
. He and his co-authors have verified the conjecture for various cases, most notably flat manifolds,.nonpositively curved manifolds..
In his thesis, Farrell solved the problem of determining when a
manifold
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n-dimensional manifold, or ''n-manifold'' for short, is a topological space with the property that each point has a N ...
(of dimension greater than 5) can
fiber
Fiber (spelled fibre in British English; from ) is a natural or artificial substance that is significantly longer than it is wide. Fibers are often used in the manufacture of other materials. The strongest engineering materials often inco ...
over a circle..
In 1977, he introduced Tate–Farrell cohomology,. which is a generalization to infinite groups of the
Tate cohomology In mathematics, Tate cohomology groups are a slightly modified form of the usual cohomology groups of a finite group that combine homology and cohomology groups into one sequence. They were introduced by , and are used in class field theory.
Defini ...
theory for finite groups.
In 1993, he and his co-author Lowell E. Jones introduced the Farrell–Jones conjecture. and made contributions on it. The conjecture plays an important role in manifold topology.