| Office Location: | 209 Physics |
| Office Phone: | (919) 660-2846 |
| Email Address: | |
| Web Page: | http://math.duke.edu/~ezra |
Teaching (Spring 2012):
| PhD | University of California, Berkeley (Math) | 2000 |
| ScB | Brown University (Math) | 1995 |
| AB | Brown University (Music) | 1995 |
Professor Miller's research centers around
problems in geometry, algebra, topology,
combinatorics, and computation originating in
mathematics and the sciences, including biology,
physics, chemistry, computer science, medical
imaging, and statistics. A unifying idea in
this research has been to isolate or exploit
combinatorial structures that govern or arise
from continuous contexts. For example, if a
continuous process carries underlying discrete
data, then those data might be harnessed to
produce algorithms for the continuous process.
On theother hand, the goal could be to
understand the combinatorics rather than the
geometry; the geometry then serves as a vehicle
for interpolating between different
interpretations of the combinatorics.
The techniques range, for example, from abstract
algebraic geometry of 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 homology; from functorial perspectives
on homological algebra in the derived category to
constructions of complexes based on combinatorics
of cell decompositions; or from central limit
theorems on 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,
branching structures in evolutionary biology and
medical imaging; mass-action kinetics of
chemical reactions; computational geometry,
symbolic computation, and combinatorial game
theory; and statistics of object data, sampled
from markedly non-Euclidean spaces.