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Research
I am interested in combinatorics, discrete
and computational geometry, theoretical computer science, and
computational biology. One
particular area in which I have published a number of papers is lattice
points in polytopes.
Preprints.
Parametric inference of
recombination with an application to HIV-1 circulating recombinant forms
(with Niko Beerenwinkel and Colin Dewey), preprint
(2006).
Publications, in roughly reverse chronological
order.
Maximal
periods of (Ehrhart)
quasi-polynomials (with Matthias Beck and Steven Sam),
Journal of Combinatorial Theory, Series A, to appear (2008).
Counting
with rational generating functions
(with Sven Verdoolaege), Journal of Symbolic Computation, 43 (2008), 75–91.
The
probability of choosing primitive sets (with Sergi Elizalde),
Journal of Number Theory, 125 (2007), 39-49.
Bounds on the number of
inference functions of a graphical model (with Sergi
Elizalde), Statistica Sinica, 17 (2007), 1395-1415.
Parametric alignment
of Drosophila genomes
(with Colin Dewey, Peter Huggins, Bernd Sturmfels, and Lior Pachter),
PLoS Computational Biology 2 (2006), 606-614.
Computing
the period of an Ehrhart
quasi-polynomial, The Electronic Journal
of
Combinatorics 12 (2005), #R34.
Short
rational generating functions and their applications to integer
programming
(with R. Yoshida), SIAG/OPT Views and
News, 16 (2005), 15-19.
Parametric Sequence Alignment
(with Colin Dewey), in Algebraic
Statistics for
Computational Biology, L.Pachter and
B.Sturmfels, eds,
Cambridge University Press (2005), 193-205.
Neighborhood
complexes, and generating functions for affine
semigroups (with Herbert Scarf), Discrete and Computational
Geometry 35 (2006), 385 - 403.
The
minimum period of the Ehrhart quasi-polynomial of a rational
polytope (with Tyrrell McAllister), Journal
of Combinatorial Theory, Series A, 109 (2005), 345-352.
Rational
Generating
Functions and Lattice
Point Sets, Ph.D. thesis, University
of Michigan
(2004).
Short
rational generating functions for lattice point problems
(with
Alexander Barvinok). Journal
of the
American
Mathematical Society, 16 (2003), 957-979.
Two unpublished papers from my college days
Our winning paper in the Mathematical Contest in Modeling:
My paper from the REU at Rose-Hulman:
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