- Faculty Scholarship Lunch talk, February 14, 2017.
- Two historical talks on issues in mathematical historiography and the Conics of Apollonius, given June 21 and 22 in Clavius Group seminar at Holy Cross.
- Codes from surfaces with small Picard number, Fq12, Saratoga Springs, NY,
July 17, 2015.
- Codes from cubic surfaces, HC Faculty Seminar, November 12, 2014 (and a
somewhat later version at University of Illinois Algebraic Geometry Seminar, March 5, 2015)
- A historical talk on different interpretations of Book II of Euclid's Elements,
HC Math Summer research seminar, June 25, 2014.
- A historical talk on Archimedes' Quadrature of the Parabola, HC Math/CS Summer Research Seminar, June 12, 2013.
- Continua of central configurations
in the n-body problem, AMS Special Session on Celestial
Mechanics, JMM, San Diego, January 9, 2013.
- A historical talk on Babylonian roots of the Pythagorean
theorem, Amherst College Mathematics Colloquium, September 29, 2011.
- Observations on Toric Surface Codes -- HC Faculty Seminar,
September 8 and 15, 2011.
- A talk on mathematics courses in Holy Cross's Montserrat program of first year seminars, MAA MathFest, Lexington, KY, August
- Error Control Codes from Algebra -- SACNAS National
Meeting, Dallas TX, October 16, 2009.
- Order domains, Algebra Seminar, University
of South Alabama, April 6, 2007.
- Gr"obner bases and polynomial equations
Mathematics Department Colloquium, University of South Alabama, April 5, 2007.
- Mathematics and Music -- MAA NES meeting Sacred Heart
University, November 18, 2006.
- Workshop on coding theory at
TAGS, May 17 - 19, 2006
- Slides for a talk on Gr"obner bases for encoding
of AG Goppa codes and codes from order domains (Gr"obner Bases Semester,
D1 Workshop, Johann Kepler Universitaet, Linz), May 1, 2006
- Slides for talk in AMS Special
Session on Coding and Design-Theoretic Applications of Polynomials,
January 7, 2004.
Recent Publications, Preprints, etc.
- Toric Codes and Finite Geometries, preprint.
- (with Jonathan Gomez, Alex Gutierrez, Roberto Pelayo, and Jesse Robert) Cocircular
Relative Equilibria of Four Vortices, Involve 9, no. 3 (2016), 395-410.
- (with David Cox and Don O'Shea) Ideals, Varieties, and Algorithms, 4th ed., Springer, New York, 2015.
- Remarks on generalized toric codes, Finite Fields and Their Applications
24 (2013), 1-14.
- (with Julian Hachmeister, Jasmine McGhee, Roberto Pelayo, and Spencer Sasarita)
Continua of central configurations with a negative mass in the n-body problem,
Celest. Mech. Dyn. Astr. 115 (2013), 427-438,
- (with David Damiano), A Course In Linear Algebra, corrected reprint,
- (with David Cox and Hal Schenck) Toric Varieties, AMS Graduate Studies in Mathematics 124, 2011.
- Algebraic geometry codes from higher-dimensional varieties,
in Advances in Algebraic Geometry Codes, E. Martinez-Moro,
Carlos Munera, and D. Ruano, eds. World Scientific, 2009.
- Automorphisms and Encoding of AG
and Order Domain Codes, in: Gr"obner Bases, Coding Theory, and Cryptography, M. Sala,
T. Mora, L. Perret, S. Sakata, C. Traverso, eds. Springer RISC series, 2009.
- A key equation
and the computation of error values for codes from order domains
(a shorter version of this paper appears in ADVANCES IN CODING THEORY AND CRYPTOGRAPHY,
edited by T Shaska, W C Huffman, D Joyner, and V Ustimenko, World Scientific, 2007.)
- The Ubiquity
of Order Domains for the Construction of Error Control Codes,
Advances in Mathematics of Communications 1 (2007), 151-171;
Erratum for: The Ubiquity of Order Domains for the Construction of Error
Control Codes, Advances in Mathematics of Communications 2
- (with D. Cox and D. O'Shea), Ideals, Varieties, and Algorithms:
An Introduction to Computational Algebraic Geometry and Commutative
Algebra, 3nd edition, New York: Springer-Verlag, 2007.
Follow this link for the Ideals,
Varieties, and Algorithms homepage.
- (with Hal Schenck) Toric
surface codes and Minkowski sums, SIAM Journal of Discrete Mathematics
20 (2006), 999-1014.
- (with Ryan Schwarz) Toric codes
and Vandermonde determinants (new title) Applicable Algebra in Engineering,
Communications, and Computing 18 (2007), 349-367.
- (A Holy Cross Project with Cristina Ballantine, Sharon Frechette)
Associated to Zeta Matrices of Posets, Linear Algebra
and its Applications 411 (2005), 364-370.
- (with D. Cox and D. O'Shea), Using Algebraic Geometry, 2nd ed.,
Graduate Texts in Mathematics, v. 185. New York: Springer-Verlag, 2005.
This version contains several new sections on Gr"obner fans of ideals,
the Gr"obner Walk basis conversion algorithm, and a new chapter
on codes from order domains and the Berlekamp-Massey-Sakata
- (with Leah Gold and Hal Schenck)
Cayley-Bacharach and Evaluation Codes
on Complete Intersections, Journal of Pure
and Applied Algebra, 196 (2005), 91-99.
- (with G. Boros, V. Moll, E. Mosteig, R. Stanley)
A map on the space of rational functions,
Rocky Mountain Mathematical Journal 35 (2005), 1861-1880.
- On the Zeroes of Two Families of Polynomials Arising From
Certain Rational Integrals, Rocky Mountain Mathematical Journal
35 (2005), 1205 - 1216.
This note gives a proof of a conjecture of Boros, Moll and Shallit
on the locations of roots of two families of univariate
polynomials arising in the evaluation of certain rational integrals.
This problem was suggested to me by Victor Moll in June 2002
at SIMU at the University of Puerto Rico in Humacao.
See Victor's article
in the March 2002 issue of the Notices of the AMS for more on the
background of this story.
- "Solving the Selesnick-Burrus
Filter Design Equations Using Computational Algebra and Algebraic
Geometry", Advances in Applied Mathematics 31 (2003), 463-500.
- (with D. Ortiz, R. Ortiz-Rosado, R. Pablo, and K. Rios-Soto)
Some Remarks on Fitzpatrick and Flynn's Gr"obner Basis
Technique for Pade' Approximation, Journal of
Symbolic Computation 35 (2003), 451-461.
Last modified: February 13, 2017