Ezra Miller
 Professor of Mathematics
 Professor in the Department of Statistical Science (Secondary)
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 Ktheory 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; massaction kinetics of chemical reactions; computational geometry, symbolic computation, and combinatorial game theory; and geometric statistics of data sampled from highly nonEuclidean spaces. Examples of datasets under consideration include MRI images of blood vessels in human brains, vein structures in fruit fly wings for developmental morphological studies, and weather data.
Hotz, T, Huckemann, S, Le, H, Marron, JS, Mattingly, JC, Miller, E, Nolen, J, Owen, M, Patrangenaru, V, and Skwerer, S. "Sticky central limit theorems on open books." The Annals of Applied Probability 23 (2013): 22382258. (Academic Article) Full Text Open Access Copy
Guo, A, and Miller, E. "Algorithms for Lattice Games." International Journal of Game Theory 42.4 (2013): 777788. Full Text
Thomas Kahle, . "Decompositions of commutative monoid congruences and binomial ideals (Accepted)." Algebra & Number Theory (2012). (Academic Article)
Gopalkrishnan, M, and Shiu, A. "A projection argument for differential inclusions, with applications to persistence of massaction kinetics (Accepted)." SIGMA (Symmetry, Integrability, and Geometry: Methods and Applications) (2012). (Academic Article)
Guo, A, and Miller, E. "Erratum: Lattice point methods for combinatorial games (Advances in Applied Mathematics (2011) 46:1 (363378))." Advances in Applied Mathematics 48.1 (2012): 269271. Full Text
Guo, A, and Miller, E. "Lattice point methods for combinatorial games." Advances in Applied Mathematics 46.14 (2011): 363378. Full Text
Anderson, D, Griffeth, S, and Miller, E. "Positivity and Kleiman transversality in equivariant Ktheory of homogeneous spaces." Journal of the European Mathematical Society 13.1 (2011): 5784. Full Text
Miller, E, Novik, I, and Swartz, E. "Face rings of simplicial complexes with singularities." Mathematische Annalen 351.4 (2011): 857875. Full Text
Dickenstein, A, Matusevich, LF, and Miller, E. "Binomial Dmodules." Duke Mathematical Journal 151.3 (January 1, 2010): 113.
Ezra Miller, . "Binomial Dmodules." Duke Mathematical Journal 151.3 (2010): 385429. (Academic Article)
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Current Graduate Students

Ashleigh Thomas (08/2013  Present)