|Office Location:||209 Physics|
|Office Phone:||(919) 660-2846|
|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, chemistry, computer
science, medical imaging, and statistics.
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 via geodesic contraction 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, 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.