Matthew Neal

Matthew Neal

Neal
George R. Stibitz Distinguished Professor of Mathematics Chair
Position Type 
Faculty
Service 
2001 - Present

Overview

Biography 

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 (14) and Emily (11).  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.

Degree(s) 
B.A. (Mathematics and History), Ph.D., University of Virginia

Research

Overview 
Operator algebras, statistical modeling — I study operator algebras and statistical modeling. Operator algebras generalize problems in virtually every undergraduate class and model observable quantities in quantum physics. My statistical work is concerned with player evaluation in the NBA.
Details 

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.

Works

Publications 

Selected publications:

  • A holomorphic characterization of operator algebras (with B. Russo) to appear in Mathematica Scandinavica, 2013
  • Metric characterizations II (with D. Blecher) to appear in the Illinois Journal of Mathematics, 2013
  • Open projections in operator algebras II: compact projections (with D. Blecher), Studia Mathematica 208, pp. 203-224, 2012
  • Open projections in operator algebras I: comparison theory (with D. Blecher). Studia Mathematica 209, pp. 117-150, 2012
  • Metric characterizations of isometries and of unital operator spaces and systems (with D. Blecher). Proceedings of the American Mathematical Society 139, pp. 985-998, 2011

Other

Student Collaborations 

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)