I grew up in Virginia in a small town and received a Ph.D. in Mathematics at the University of Virginia in Charlottesville. After completing my Ph. D. work at Oxford and teaching for two years at The University of California at Irvine, I came to Denison where I have spent the last 12 years. I have a wife, Nancy, and two kids, Joseph (21) and Emily (18). Mathematically, I am interested in operator theory, probability, and statistics. Outside of mathematics, I am interested in Jesus Christ first and foremost. I am also interested in games, history, sports statistics, indie rock, and showing mercy to the poor, lonely, and marginalized.
Recently, I have done research with students in NBA basketball analytics. I try to determine what players are worth, which five man-units play well together, and which coaching strategies are most successful. To do this, I use statistical modeling methods that are commonly used in most real world industries. Hence, research in NBA analytics is an excellent preparation for any career that involves analyzing data to solve problems.
Much of my research is in Functional Analysis and Algebra. More specifically, I study the algebra, geometry and topology of spaces of operators. Operators represent the basic observables of the universe, like energy and momentum. Although my work is theoretical, the problems I solve are motivated by probabilistic questions in Quantum Mechanics. I have had success working with students on such problems. Unlike my basketball analytics projects discussed above, operator theory requires students to be somewhat advanced in their mathematical education. Students who want to pursue a Ph. D. in Mathematics will benefit most from this kind of work.
- Applied Calculus Textbook (in preparation 2020)
- Contractive Projections and Real Positive Maps on Operator Algebras (with D. Blecher), Studia Math, to appear 2020
- Non-commutative Topology and Jordan Operator Algebras (with D. Blecher), Mathematische Nachrichten, 292, Issue 3, (2019) 481-510.
- Completely Contractive Projections on Operator Algebras (with D. Blecher), Pacic J. Math. 283 (2016) 289-324
- A holomorphic characterization of operator algebras (with B. Russo), Math. Scand. Vol 115, No 2 (2014), (229-268).
- Metric characterizations II (with D. Blecher), Illinois J. Math. Volume 57, Number 1 (2013), 25-41.
- Open projections in operator algebras II: compact projections. Studia Mathematica (with D. Blecher), 209 (2012), 203-224
- Open projections in operator algebras I: comparison theory (with D. Blecher), Studia Mathematica 208 (2012),117-150
- Metric characterizations of isometries and of unital operator spaces and systems (with D. Blecher), Proceedings of the American Mathematical Society 139 (2011), 985-998.
- Existence of contractive projections on preduals of JBW*-triples (with B. Russo), Israeli Journal of Mathemaics 182 (2011), 293-331
Selected student research projects:
- Modeling player value in the NBA, Danny Persia, Summer 2013 (awarded a Pi Mu Epsilon Research Presentation Award, Math Fest 2013)
- Metric-linear characterizations of operator algebra structures, Matt Gibson, 2012-2013 (presented at Joint AMS/MAA meetings, 2013)
- Toward a metric-linear characterizations of operator algebras, Nathan Zakhari, 2010-2011 (awarded a research presentation award, Math Fest 2010)
- Toward a classification of n-uniform frames in linear coding theory, Glen Sutula, 2011 (presented at Math Fest 2010)