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
Webpages: 

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 & Training

  • Ph.D., University of California at Berkeley 2000

  • B.S., Brown University 1995

Combinatorics in geometry awarded by National Science Foundation (Principal Investigator). 2010 to 2016

Conference Proposal: Meeting on Combinatorial Commutative Algebra (MOCCA 2014) awarded by National Science Foundation (Principal Investigator). 2014 to 2015

CAREER: Discrete Structures in Continuous Contexts awarded by National Science Foundation (Principal Investigator). 2009 to 2011

Berenstein, A, Braverman, M, Miller, E, Retakh, V, and Weitsman, J. "Andrei Zelevinsky, 1953–2013." Advances in Mathematics 300 (September 2016): 1-4. Full Text

Berenstein, A, Braverman, M, Miller, E, Retakh, V, and Weitsman, J. "Andrei Zelevinsky, 1953-2013." Advances in Mathematics 299 (August 20, 2016): 601-604. Full Text

Kahle, T, Miller, E, and O’Neill, C. "Irreducible decomposition of binomial ideals." Compositio Mathematica 152.06 (June 2016): 1319-1332. Full Text

Bendich, P, Marron, JS, Miller, E, Pieloch, A, and Skwerer, S. "Persistent Homology Analysis of Brain Artery Trees." The annals of applied statistics 10.1 (January 2016): 198-218. Open Access Copy

Miller, E. "Fruit Flies and Moduli: Interactions between Biology and Mathematics." Notices of the American Mathematical Society 62.10 (November 1, 2015): 1178-1184. Full Text

Miller, E, Owen, M, and Provan, JS. "Polyhedral computational geometry for averaging metric phylogenetic trees." Advances in Applied Mathematics 68 (July 2015): 51-91. Full Text

Huckemann, S, Mattingly, J, Miller, E, and Nolen, J. "Sticky central limit theorems at isolated hyperbolic planar singularities." Electronic Journal of Probability 20.0 (2015). Full Text Open Access Copy

Berkesch Zamaere, C, Griffeth, S, and Miller, E. "Systems of parameters and holonomicity of  A -hypergeometric systems." Pacific Journal of Mathematics 276.2 (2015): 281-286. Full Text

Skwerer, S, Bullitt, E, Huckemann, S, Miller, E, Oguz, I, Owen, M, Patrangenaru, V, Provan, S, and Marron, JS. "Tree-oriented analysis of brain artery structure." Journal of Mathematical Imaging and Vision 50.1 (January 1, 2014): 126-143. Full Text

Gopalkrishnan, M, Miller, E, and Shiu, A. "A Geometric Approach to the Global Attractor Conjecture." SIAM Journal on Applied Dynamical Systems 13.2 (January 2014): 758-797. Full Text

Pages

Miller, E, and Sturmfels, B. "Monomial ideals and planar graphs." Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 1719 (January 1, 1999): 19-28. Full Text