University of Mississippi
305 Hume Hall
Department of Mathematics
P.O. Box 1848
Office: Hume Hall, #335
Telephone: (662) 915-5646
FAX: (662) 915-5491
I am an Associate Professor, working in the area of Commutative Algebra. I earned my Ph.D at the University of Illinois at Urbana-Champaign in 2003 under the direction of Phillip Griffith, and I held a post-doctoral position at the University of Utah from 2003-2006, working with Paul Roberts.
Connectedness and Lyubeznik numbers, with L Nunez-Betancourt and E. Witt, International Math Research Notices, to appear.
On the structure of S_2-ifications of complete local rings, with S. Sather-Wagstaff, Rocky Mountain Math J., 48, no. 3 (2018) to appear.
The tropical semi-ring in higher dimensions, with J. Norton, Involve Math J., 11, no. 3 (2018) 477-488.
Torsion in kernels of induced maps on divisor class groups, with S. Sather-Wagstaff, J. Alg Appl., 14, (2015) 23 pages.
On invariants of complete intersections, Michigan Math. J., 62 (2013) 209-223.
The vanishing of a higher codimension analogue of Hochster's theta invariant, with W.F. Moore, G. Piepmeyer, and M.E. Walker, Math. Z., 273, no. 3 (2013) 907-920.
On zero divisor graphs, with J. Coykendall, S. Sather-Wagstaff, and L. Sheppardson, Progress in Comm. Alg., Vol. 2, de Gruyter, April 2012, 241-299.
Five point zero divisor graphs determined by equivalence classes of zero divisors, with F. Levidiotis, Involve, 4, no. 1 (2011) 53-64.
Hochster's theta invariant and the Hodge Index Theorem, with W. F. Moore, G. Piepmeyer, and M. Walker, Advances in Math, 226, no. 2 (2010) 1692-1714; .pdf
A zero divisor graph determined by equivalence classes of zero divisors, with C. Wickham, Communications in Alg., 39 (2011) 2338-2348; .pdf
Maps on divisor class groups induced by ring homomorphisms of finite flat dimension, with S. Sather-Wagstaff, J. Commutative Algebra, 1, no. 3 (2009) 567-590.
An algebraic proof of the commutativity of intersection with divisors, with P. Roberts, J. Algebra, 320 (2008) 2165-2180; .pdf
Divisor class groups of graded hypersurfaces, with A. Singh, Contemp. Math, 448 (2007) 237-243; .pdf
Asymptotic growth of powers of ideals, with C. Ciuperca and F. Enescu, Illinois J. Math, 51, no. 1 (2007) 29-39; .pdf
Restriction of divisor
classes to hypersurfaces in characteristic p, with Phillip Griffith,
J. Algebra, 275 (2004) 801-814; .pdf
The limiting behavior on
the restriction of divisor classes to hypersurfaces,
J. Pure Appl.
186 (2004) 77-89; .pdf
(Travel to BIRS partially supported by AWM ADVANCE
grant NSF-HRD 1500481)
I have long been interested in the teaching of mathematics. As a
former high school teacher and teaching assistant, I have taught a variety of
courses, using several different instructional methods. As a Visiting Assistant Professor at the University of Nebraska-Lincoln during the summer of 2007, I team taught an Algebra course for incoming graduate students based on a publication in Communications in Algebra. At Seattle University, I implemented the WeBWorK homework system, which I learned how to use at the University of Utah. As a graduate student at
the University of
Illinois, I worked as a
Research Assistant, in the area of secondary mathematics teacher education, with
Professors Susan Tolman and John Sullivan. Their
project, a cooperation between the Mathematics and
Education departments at the University and Danville High School,
sought to improve teacher preparation. At the University of Utah,
I was an active participant in the Math
Circle program for high school students, directed by Peter Trapa.
Moreover, I have worked with REU students through the VIGRE
grant. Some of my old course experience is listed in the table below. An old summary of my
educational experience, is available in this teaching vita.
Calculus I, II, Bus. Calc.
College & High School
Calculus and Mathematica , Merit Workshop , Active
College & Intermediate Algebra
Geometry, Algebra, Basic Math
- President of the University of Mississippi Chapter of Phi Beta Kappa
- AMS Graduate Chapter Advisor/Co-Founder
Past Professional Activities