Ezra Miller

Professor of Mathematics

External address: 
209 Physics Bldg, 120 Science Drive, Durham, NC 27708
Internal office address: 
Box 90320, Durham, NC 27708-0320
Phone: 
(919) 660-2846

Dr. Miller is the co-principal investigator for the National Science Foundation Phase II Noyce Fellowship program, and the NSF Capacity Building Noyce Fellowship grant.

Overview

Professor Miller's research centers around problems in geometry, algebra, topology, combinatorics, statistics, probability, and computation originating in mathematics and the sciences, including biology, chemistry, computer science, and medical imaging.

The techniques range, for example, from abstract algebraic geometry or commutative algebra of ideals and varieties to concrete metric or discrete geometry of polyhedral spaces; from deep topological constructions such as equivariant K-theory and stratified Morse theory to elementary simplicial and persistent homology; from functorial perspectives on homological algebra in the derived category to specific constructions of complexes based on combinatorics of cell decompositions; from geodesic contraction applied to central limit theorems for samples from stratified spaces to dynamics of explicit polynomial vector fields on polyhedra.

Beyond motivations from within mathematics, the sources of these problems lie in, for example, graphs and trees in evolutionary biology and medical imaging; mass-action kinetics of chemical reactions; computational geometry, symbolic computation, and combinatorial game theory; and geometric statistics of data sampled from highly non-Euclidean spaces.  Examples of datasets under consideration include MRI images of blood vessels in human brains and in mouse lungs, vein structures in fruit fly wings for developmental morphological studies, and atmospheric pressure elevation as a time-varying function on the globe.

Education

  • Ph.D., University of California at Berkeley 2000
  • B.S., Brown University 1995

Bendich, P, Marron, JS, Miller, E, Pieloch, A, and Skwerer, S. "Persistent homology analysis of brain artery trees (Accepted)." Annals of Applied Statistics. Open Access Copy

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