My research
area is combinatorial optimization, specifically
optimization algorithms and modeling, and my advisor is Prof. Alan Goldman. Currently
my research has taken a more theoretical turn, and I am investigating
problems in stable matching. I've just posted two short papers on
stable matching, with hopefully more to come (geologically) soon.
In the mean time, please feel free to also look around my
earlier research endeavors.
Papers and Projects:
On the Computation of
Stable Many to Many Matchings: Written as a course project
for 550:750 this short paper's key result is an enumeration algorithm
for the set of all stable many to many matchings, using the "break
marriage" concept of McVitie and Wilson. This algorithm is similar to
the algorithm of Martinez et. al., but much better exposited. (pdf)
Fair Matchings with an
Application to Chess: Another course project, this time
for 550:457. This is another paper on matchings, this time a
modeling paper investigating how to find a minimum bias assignment of
partners from opposing teams in a chess match using the stable matching
polytope. As usual, the most interesting stuff is in the 'future
directions' part of the paper. (pdf)
[Note: Because the original
game is constant sum, one could considerably simplify the problem
presented in the introduction by replacing the simultaneous solution of
LPs with the solution of a single min max problem.
This fact was pointed out to me by Dr. Alan Goldman, and will
hopefully be incorporated into the above shortly.]
Talks Given:
Inequalities in Stochastic Linear
Programming (powerpoint)
(this presentation contains a
generalization of a theorem proven by Madansky, which I hope to write
up soon)
Equilibrium
Concepts in Two Player Games (abstract/powerpoint)
Optimal
Curriculum Generation via Clustering (abstract/powerpoint)
A
Survey of the Farkas Lemma (abstract/pdf)
Earlier/Ongoing Research:
Examining eBay
Auctions to Determine Optimal Pricing: (Joint with Eric Harley) This
work is just beginning, but attempts to examine historical eBay auction
data to determine the optimal pricing for sellers, in particular for
specialty markets. Potential applications (outside of eBay
itself) include small markets for commodities.