Published Papers
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- Tracy Grauman, Stephen G. Hartke, Adam Jobson, Bill Kinnersley, Douglas B. West, Lesley Wiglesworth, Pratik Worah, and Hehui Wu. "The Hub Number of a Graph." To appear in Information Processing Letters. (preprint pdf)
- Thanked in Daniel W. Cranston's paper "Nomadic Decompositions of Bidirected Complete Graphs", 2006.
Paper Folding - Fall 2006 to present [Advisor Jeff Erickson]
There has been a new wave of research on folding and unfolding problems, that is, problems which try to characterize how objects can be reconfigured subject to given constraints. One class of these problems deals with origami flat-foldability, where one is given a crease pattern on a piece of paper and is asked to determine if it is foldable into a flat origami using exactly those creases. One can think of this as receiving a map which has been opened and being asked to fold it back up again.
In particular, I have been working on the problem of flat-folding an
mx
n grid into a 1x1 square. The 1x
n case -- also called the "Postage Stamp Problem" -- already has a known polynomial time algorithm, but the problem still remains open for even the 2x
n case. I'm working on characterizing which grid crease patterns are flat-foldable down to the 1x1 square, and this will be the subject of my Master's Thesis. For more information, you may be interested in visiting Erik Demaine's
map folding website.
"REGS" stands for "Research Experiences for Graduate Students." I attended this program, run by UIUC Math Department, in which students and faculty collaborate on open problems in Combinatorics. We even published a paper on Hub Number (cited above). Here's a
picture of the lot of us, including some students from the combinatorics department in Louisville, Kentucky, who worked with us for couple weeks.
Summer Thinking - Summer 2006 [Advisor John Iacono]
Having some experience with the subject after an undergraduate summer research project, I read and thought about some recent papers on cache-oblivious data structures. I looked into the trade-off between cache-obliviously reading from and writing to arrays. I also worked with a few problems that had been discussed at a summer geometry workshop.
Spacetime Meshing - Fall 2005, Spring 2006 [Advisor Jeff Erickson]
Spacetime meshing is a technique employed for solving partial differential equations which model phenomena such as a wave traveling through a medium over time. The problem as considered previously kept all calculations confined to a rigid rectangular domain. I focused on the problem of moving boundaries: what happens if the medium being modeled changes in shape over time, like fuel being pushed out of its chamber by a piston? For more information, you may be interested to read either of the following papers:
Spacetime meshing with adaptive refinement and coarsening,
Building spacetime meshes over arbitrary spatial domains
