David Fisher, an associate professor at Indiana University, is a mathematician with broad interests in analysis, dynamics, and geometry. His main focus is on rigidity—for example, instances when the way things can flow in a space completely determine its geometry or when the geometry of a space uniquely determines the flows that can take place within it. Some of his more recent work focuses on issues of large-scale geometry and rigidity—when the geometry of a space is determined by its asymptotic properties.
While at Radcliffe, Fisher will focus on problems in asymptotic geometry by developing new analytic techniques in this area. In joint work with Alex Eskin and Kevin Whyte, Fisher developed a notion of coarse differentiation, which allows one to define a derivative (as in first-year calculus) for coarse maps. These maps are not even defined locally, and normal differentiation simply does not make sense. Coarse differentiation has led to dramatic advances in asymptotic geometry and has been applied in theoretical computer science. Fisher will also work on notions of higher-order differentiability for coarse maps. A good theory of higher-order coarse differentiation is a key step for solving many problems.
After earning his PhD at the University of Chicago, Fisher spent three years at Yale University, partially supported by a National Science Foundation (NSF) postdoctoral fellowship. He worked at Lehman College and The Graduate Center of The City University of New York before moving to Indiana University. Fisher is the recipient of an NSF CAREER award.