Dr. Matthew Neal
Ph.D. in Mathematics from University of Virginia, 1999
View Matthew's personal page.
I was born in Columbus, OH but lived most of my life in Virginia. After receiving my PhD, I was visiting assistant professor at The University of California at Irvine for 2 years. In 2001, I happily came to Denison. Currently, I hold the rank of associate professor. I have a wife, Nancy, and 2 children, Joseph (9) and Emily (6). My main interests (besides Math and my family) are Christ, History, games, and showing mercy to the poor and marginalized.
I love teaching all Math classes but have specific interests in teaching Linear Algebra, Differential equations, Analysis, Fourier Analysis, Abstract Algebra, applications to physics, Probability, applications to sports, and Differential Geometry. I like teaching because (A) It's one of the few situations in life where people willingly sign up to talk to me about Math and (B) I like mentoring young men and women.
My main research interests is in functional analysis and algebra. Specifically, I study operator spaces, C*-algebras, and JB*-triples. Recently, I have developed secondary interests in linear coding, sports statistics and quantum information theory. I feel like I solve puzzles for a living, which is so much fun I would do it for free.
Metric characterizations of isometries and of unital operator spaces and systems (with D. Blecher)
Contractively complemented subspaces of pre-symmetric spaces (with B. Russo)
Ordered involutive operator spaces (with D. P. Blecher, K. Kirkpatrick, and W. Werner)
in Positivity 11 (2007), 497-510.
Open partial isometries and positivity in operator spaces (with D. Blecher)
in Studia Math 182 (2007), 227-262.
Hereditary subalgebras of operator algebras (with D. Blecher and D. May)
in J. of Operator Theory (2008).
Classification of contractively complemented Hilbertian operator spaces (with B. Russo and E. Ricard)
in J. of Funct. Anal. 237 (2006) 589-616.
Representation of contractively complemented Hilbertian operator spaces on the Fock space (with B. Russo)
in Proc. Amer. Math. Soc. 134, No. 2, 475-485 (2005).
State spaces of JB*-triples (with B. Russo)
in Math. Ann. 328, 585-624, (2004).
Normal contractive projections preserve type (with C.H. Chu and B. Russo)
in J. Operator Theory 51, 281-301, (2004).
Contractive projections and operator spaces (with B. Russo)
in Trans. Amer. Math. Soc., Vol. 355, No.6, p. 2223-2262, (2003).
Operator space characterizations of C*-algebras and ternary rings (with B. Russo)
in Pac. J. Math., Vol. 209, No. 2, (2003).
Spectrum preserving maps on JBW*-triples
in Archiv der Math., 79, p.258-267, (2002).
Projecteurs contractifs et espaces doperateurs (with B. Russo)
in C. R. Acad. Sci. Paris, t. 331, Serie I, p. 873-878, (2000).
Inner ideals and facial structure of the quasi-state space of a JB-algebra
in J. Funct. Anal. 173 No. 2, p. 284-307, (2000).
Dissertation, Facial Structure in JB- algebras and their dual spaces
University of Virginia, (1999).