## 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.

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, 14:40 – 16:00 in Physics 209 or outside

Wednesday, 14:00 – 15:10 in Physics 209 or outside

## Current Appointments & Affiliations

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

Professor of Statistical Science
·
2015 - Present
Statistical Science,
Trinity College of Arts & Sciences

## Education, Training & Certifications

University of California, Berkeley ·
2000
Ph.D.

Brown University ·
1995
B.S.