The doctoral thesis completed by F. Thomas Farrell in 1967 addressed the obstruction to fibering a manifold over a circle, establishing a trajectory for his research in topology and differential geometry. Born in Ohio in 1941, he pursued his undergraduate degree at the University of Notre Dame before concluding his graduate studies at Yale University.
Academic Appointments and Early Career
After receiving his doctorate, Farrell held positions at several prominent institutions. He served as an assistant professor at the University of California at Berkeley between 1969 and 1972. Subsequently, he moved to Pennsylvania State University, where he achieved the rank of professor in 1978. His career progression continued through roles at the University of Michigan from 1979 to 1985 and Columbia University between 1984 and 1992. Since 1990, he has been a faculty member at Binghamton University, where he currently holds the title of distinguished professor emeritus. He also maintains an affiliation with the Yau Mathematical Sciences Center at Tsinghua University.
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Farrell gained early professional recognition in 1970 when he delivered a 50-minute address at the International Congress of Mathematicians in Nice, France, regarding the research presented in his thesis. His work involves the exploration of the Borel conjecture, specifically focusing on flat manifolds and nonpositively curved manifolds. In 1977, he developed the Tate–Farrell cohomology, a mathematical framework that extends the existing Tate cohomology theory for finite groups to encompass infinite groups.
The Farrell-Jones Conjecture
In 1993, Farrell and his frequent collaborator Lowell E. Jones introduced the Farrell–Jones conjecture, a development that occupies a significant position in the field of manifold topology. The partnership between Farrell and Jones had previously gained notice in 1990, when Jones presented their joint findings on rigidity in geometry and topology at the International Congress of Mathematicians held in Kyoto, Japan.
Fast facts
- Born: 1941, Ohio
- Undergraduate Degree: University of Notre Dame, 1963
- Doctoral Degree: Yale University, 1967
- Ph.D. Advisor: Wu-Chung Hsiang
- Primary Fields: Topology and differential geometry
- Key Collaborator: Lowell E. Jones
- Current Roles: Professor emeritus at Binghamton University and researcher at Tsinghua University
Questions readers ask
What is the Farrell–Jones conjecture?
It is a mathematical conjecture introduced by F. Thomas Farrell and Lowell E. Jones in 1993 that serves as a critical component in the study of manifold topology.
Where did Farrell teach before joining Binghamton University?
He held positions at the University of California at Berkeley, Pennsylvania State University, the University of Michigan, and Columbia University.
Achievements
- Held posts at University of Michigan, Binghamton University and Tsinghua University
