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Ezra Miller CV

Professor of Mathematics
Mathematics
Box 90320, Durham, NC 27708-0320
209 Physics Bldg, 120 Science Drive, Durham, NC 27708
CV

Overview


Professor Miller's research centers around problems in geometry,
algebra, topology, probability, statistics, and computation
originating in mathematics and the sciences, including biology,
chemistry, computer science, and 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 collapse 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; Lie 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 lungs, 3D
folded protein structures, and photographs of fruit fly wings for
developmental morphological studies.

Office Hours


Office hours: Tuesday, 13:00 – 14:15 in Physics 209 or outside
                      Thursday, 13:00 – 14:15 in Physics 209 or outside

Current Appointments & Affiliations


Professor of Mathematics · 2009 - Present Mathematics, Trinity College of Arts & Sciences

In the News


Published April 24, 2015
Geometry of Harmony in Impressionist Music
Published March 20, 2014
Ezra Miller: Odds of winning Warren Buffett’s billion-dollar NCAA bracket challenge
Published March 17, 2014
Playing Warren Buffet’s billion-dollar NCAA bracket challenge? Consider the odds

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Recent Publications


Minimal resolutions of lattice ideals

Journal Article Journal of Pure and Applied Algebra · March 1, 2025 A canonical minimal free resolution of an arbitrary co-artinian lattice ideal over the polynomial ring is constructed over any field whose characteristic is 0 or any but finitely many positive primes. The differential has a closed-form combinatorial descri ... Full text Cite

MINIMAL FREE RESOLUTIONS OF NUMERICAL SEMIGROUP ALGEBRAS VIA APÉRY SPECIALIZATION

Journal Article Pacific Journal of Mathematics · January 1, 2025 Numerical semigroups with multiplicity m are parametrized by integer points in a polyhedral cone Cm, according to Kunz. For the toric ideal of any such semigroup, the main result here constructs a free resolution whose overall structure is identical for al ... Full text Cite
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Recent Grants


RTG: Linked via L-functions: training versatile researchers across number theory

Inst. Training Prgm or CMEKey Faculty · Awarded by National Science Foundation · 2023 - 2028

R2 [Reciprocal Relationships]: Mentorships to Strengthen and Sustain STEM Teachers

Inst. Training Prgm or CMECo-Principal Investigator · Awarded by National Science Foundation · 2020 - 2025

HDR TRIPODS: Innovations in Data Science: Integrating Stochastic Modeling, Data Representation, and Algorithms

ResearchSenior Investigator · Awarded by National Science Foundation · 2019 - 2023

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Education, Training & Certifications


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