I am an NSF VIGRE postdoc in the mathematics department of the University of Georgia. My research combines elements of geometry, topology, group theory, combinatorics, and probability. I am especially pleased when these subjects have actual applications to actual objects in the actual world. Like robots.

More specifically, I am interested in:

configuration spaces and their compactifications; braid groups and their generalizations; state complexes in robotics; distances of Heegaard splittings; probability and combinatorics.

Here are some publications, projects, and press. First, my CV.

PUBLICATIONS: Life as we know it is apparently built out of things called G, T, A, and C. As far as I can tell, G stands for Geometry, T for Topology, A for Algebra, and C for Combinatorics. The biologists apparently haven't yet discovered P, which stands for Probability. Anyway I'm using this color coding to try to indicate what each of the following papers contains.

G T A C P	The number of possibilities for random dating      with Rod Canfield and Andrew Granville Submitted.	pdf
G T A C P	State complexes for metamorphic robots      with Rob Ghrist International Journal of Robotics Research, July, 2004.	pdf
G T A C P	Distances of Heegaard splittings      with Saul Schleimer To appear in Geometry & Topology.	pdf
G T A C P	Circles minimize most knot energies      with Jason Cantarella, Joe Fu, Mohammad Ghomi, and Ralph Howard Topology, vol. 42, no. 2 (2002), pp. 381-394.	pdf
G T A C P	Configuration spaces of colored graphs Geometriae Dedicata, vol. 92 (2002), pp. 185-194.	pdf
G T A C P	Finding topology in a factory: configuration spaces      with Rob Ghrist American Mathematical Monthly, vol. 109, no. 2 (2002), pp. 140-150.	pdf
G T A C P	Evasive random walks and the clairvoyant demon      with Henry Landau, Zeph Landau, Jamie Pommersheim, and Eric Zaslow Random Structures & Algorithms, vol. 20, no. 2 (2002), pp. 239-248.	pdf
G T A C P	An iterated random function with Lipschitz number one      with Henry Landau, Zeph Landau, Jamie Pommersheim, and Eric Zaslow Theory of Probability and Its Applications, vol. 47, no. 2 (2002), pp. 286-300.	pdf
G T A C P	Yet another species of forbidden-distances chromatic number      with Pete Johnson, Jr. Geombinatorics, vol. 10, no. 3 (2001), pp. 89-95.
G T A C P	Configuration spaces and braid groups of graphs Ph.D. thesis, UC Berkeley (2000).	ps (pdf coming)
G T A C P	Upper chromatic numbers: an update Geombinatorics, vol. 10, no. 1 (2000), pp. 4-11.	pdf
G T A C P	Evasive random walks In Paul Erdös and his Mathematics, Budapest, Hungary, July 1999.	pdf
G T A C P	The kth upper chromatic number of the line Discrete Mathematics, vol. 169 (1997), pp. 157-162.	pdf
G T A C P	The probability that (a,b)=1      with Matteo Paris College Mathematics Journal, vol. 23, no. 1 (1992), pg. 47.

 

PROJECTS:

The following are works in progress. I'll put up preprints when they're ready.

G T A C P	Topology of state complexes (with R. Ghrist)
G T A C P	Optimal estimators (with S. Ganzell, H. Landau, Z. Landau, J. Pommersheim, and E. Zaslow)
G T A C P	Hyperbolic manifolds arising as configuration spaces
G T A C P	Random elements of Z/2Z and other groups (with H. Landau, Z. Landau, J. Pommersheim, and E. Zaslow)

PRESS:

Recently an article in Science reported on my work with Rob Ghrist on metamorphic robots. If you subscribe to Science, you can go directly to these articles.

"Topologists and Roboticists Explore an `Inchoate World,'" by Dana Mackenzie. Science, 8 August 2003, page 756.

See also: "Shape Shifters Tread a Daunting Path Toward Reality," by Dana Mackenzie. Science, 8 August 2003, pp 754-756.

That's it.  Thanks for coming to my web site!
Last updated 4 October 2004.