University of Mississippi
305 Hume Hall
Department of Mathematics
P.O. Box 1848
Office: Graduate House, #207
Telephone: (662) 915-7474
FAX: (662) 915-6557
Assistant Dean of Professional Development & Communication in the Graduate School, and Professor of Mathematics, working in the area of Commutative Algebra. Ph.D earned at the University of Illinois at Urbana-Champaign in 2003, advised by Phillip Griffith. Post-doctoral position at the University of Utah from 2003-2006, mentored by Paul Roberts. Served as a program director at the National Science Foundation from 2020 to 2022. Curriculum vita
Automation of the Hilbert-Kunz multiplicity and F-signature calculation for intersection algebras, with G. Johnson*. Software files: hilbert-kunz-and-f-sig.zip
Software Instructions: directions for use
Powers of graphs and applications to resolutions of powers of monomial ideals, with S. Cooper, S. El Khoury, S. Faridi, S. Mayes-Tang, S. Morey, and L. Sega, Res. Math. Sciences, 9 (2022), no. 2, Paper No. 31, 25pp. ArXiv
Morse resolutions of powers of square-free monomial ideals of projective dimension one, with S. Cooper, S. El Khoury, S. Faridi, S. Mayes-Tang, S. Morey, and L. Sega, J. Algebraic Combinatorics, 55 (2022), no. 4, 105--1122. ArXiv
Simplicial resolutions for the second power of square-free monomial ideals, with S. Cooper, S. El Khoury, S. Faridi, S. Mayes-Tang, S. Morey, and L. Sega, Women in Commutative Algebra-Proceedings of the 2019 WICA Workshop, Springer and Association for Women in Mathematics, 29, 193-205 ArXiv
Ladder determinantal rings over normal domains, with S. Sather-Wagstaff and T. Se, Communications in Algebra, 49 (2021), no. 7, 2804-2828.
Generic constructions and semidualizing modules, with S. Sather-Wagstaff and T. Se, Algebras and Representation Theory, 24 (2020), no. 4, 1071-1081.
On conditionally defined Fibonacci and Lucas sequences and periodicity, with S. Irby*, Bull. Korean Math. Soc., 57 (2020), no. 4, 1033-1048.
Semidualizing modules of 2x2 ladder determinantal rings, with S. Sather-Wagstaff and T. Se, J. Algebra, 538 (2019) 232-252. ArXiv
Connectedness and Lyubeznik numbers, with L. Nunez-Betancourt and E. Witt, International Math Research Notices, 2019 (2019), no. 13, 4233-4259. ArXiv
On semidualizing modules of ladder determinantal rings, with S. Sather-Wagstaff and T. Se, Illinois J. Math, 63 (2019), no. 1, 165-191. ArXiv
Automating the calculation of the Hilbert-Kunz multiplicity and F-signature, with G. Johnson*, Software X, 9 (2019) 35-38. .pdf
Computing the invariants of intersection algebras of principal monomial ideals, with F. Enescu, Int. J. Alg. and Comp., 29 (2019), no. 2, 309-332. ArXiv
On the structure of S_2-ifications of complete local rings, with S. Sather-Wagstaff, Rocky Mountain Math J., 48 (2018), no. 3, 947-965. ArXiv
The tropical semi-ring in higher dimensions, with J. Norton*, Involve Math J., 11 (2018), no. 3, 477-488.
Torsion in kernels of induced maps on divisor class groups, with S. Sather-Wagstaff, J. Alg Appl., 14 (2015) 23 pages. ArXiv
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, M.E. Walker, Math. Z., 273 (2013), no. 3, 907-920. ArXiv
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 (2011), no. 1, 53-64.
A zero divisor graph determined by equivalence classes of zero divisors, with C. Wickham, Communications in Alg., 39 (2011) 2338-2348; .pdf
Hochster's theta invariant and the Hodge Index Theorem, with W. F. Moore, G. Piepmeyer, and M. Walker, Advances in Math, 226 (2010), no. 2, 1692-1714; .pdf
Maps on divisor class groups induced by ring homomorphisms of finite flat dimension, with S. Sather-Wagstaff, J. Commutative Algebra, 1 (2009), no. 3, 567-590. ArXiv
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 (2007), no. 1, 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. Alg, 186 (2004) 77-89; .pdf
* Indicates University of Mississippi student.
Inclusion and Equality Initiatives
Co-organized with Karen Smith (Michigan); Irena Swanson (Reed); Emily Witt (Kansas). Travel to BIRS is supported by NSF
grant NSF-DMS 1934391 and AWM ADVANCE
grant NSF-HRD 1500481.
AWM Research Symposium 2019 at Rice University in Houston, TX: Special Session in Commutative Algebra co-organized with Adela Vraciu, University of South Carolina.
Confirmed speakers include Susan Cooper (Manitoba); Haydee Lindo (Williams); Rebecca R.G. (George Mason); Alexandra Seceleanu (Nebraska-Lincoln);
Liana Sega (Missouri-K.C.); Hema Srinivasan (Missouri); Janet Vassilev (New Mexico); Oana Veliche (Northeastern)
- 2019 "Women in Commutative Algebra", National Science Foundation DMS-1934391, PI
- 2019 "Promoting diversity in mathematics in Mississippi", Elsevier Mathematical Sciences Fund: Philanthropy Category, #150, PI
- 2018 "Lyubeznik Numbers & Connectedness and Other Questions", Simons Foundation Collaboration Grant for Mathematicians 548932, PI
- 2012 "An Invariant for Complete Intersections", Simons Foundation Collaboration Grant for Mathematicians 245926, PI
- 2008 AWM-NSF Mentoring Grant, Association for Women in Mathematics, AWM-NSF 192332, (M.E. Walker, University of Nebraska-Lincoln, Mentor)
- 2006 Conference grant: "Homological Conjectures in Commutative Algebra, A Conference in Honor of Paul C. Roberts 60th Birthday", Snowbird, UT NSF DMS-0555525 and NSA H98230-06-1-0091, Co-PI (M. Hochster, University of Michigan, PI)
- 2005 Conference grant: "Commutative Algebra Conference Honoring the Contributions of Phillip Griffith", Urbana-Champaign, IL NSA H98230-05-1-0268, Co-PI (M. Miller, University of South Carolina, PI)
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 brief 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
Professional Activities (select)