Aaron Abrams: 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.


I. Research papers. (See table II. below for expository and other papers.)

G T A C P Sums of twisted circulants
     with Henry Landau, Zeph Landau, and Jamie Pommersheim
Submitted for publication.
G T A C P Group trisections and smooth 4-manifolds
     with David Gay and Rob Kirby
To appear in Geometry & Topology.
G T A C P Fixed-energy harmonic functions
     with Rick Kenyon
To appear in Discrete Analysis.
G T A C P Homological and homotopical Dehn functions are different
     with Noel Brady, Pallavi Dani, and Robert Young
Proceedings of the National Academy of Sciences, vol. 110 no. 48 (Nov. 26, 2013), pp. 19206-19212.
G T A C P Spaces of polygonal triangulations and Monsky polynomials
     with Jamie Pommersheim
Discrete and Computational Geometry, 51:132 (2014). DOI:10.1007/s00454-013-9553-6
G T A C P A central limit theorem for repeating patterns
     with Eric Babson, Henry Landau, Zeph Landau, and Jamie Pommersheim
arxiv:1204.2872
G T A C P Dull cut off for circulants
     with Eric Babson, Henry Landau, Zeph Landau, and Jamie Pommersheim
Submitted for publication.
G T A C P Discretized configurations and partial partitions
     with David Gay and Valerie Hower
Proceedings of the American Mathematical Society, vol. 141 (2013), pp. 1093-1104.
G T A C P Pushing fillings in right-angled Artin groups
     with Noel Brady, Pallavi Dani, Moon Duchin, and Robert Young
Journal of the London Mathematical Society, vol. 87 no. 3 (2013), pp. 663-688.
G T A C P Distributions of order pattern of interval maps
     with Eric Babson, Henry Landau, Zeph Landau, and Jamie Pommersheim
Combinatorics, Probability, & Computing, vol. 22 no. 1 (2013), pp. 319-341.
G T A C P Filling loops at infinity in the mapping class group
     with Noel Brady, Pallavi Dani, Moon Duchin, and Robert Young
Michigan Mathematics Journal, vol. 61 no. 4 (2012), pp. 867-874.
G T A C P Optimal estimators for threshold-based quality measures
     with Sandy Ganzell, Henry Landau, Zeph Landau, Jamie Pommersheim, and Eric Zaslow
Journal of Probability and Statistics, vol. 2010 (2010), Article ID 752750.
G T A C P The number of possibilities for random dating
     with Rod Canfield and Andrew Granville
Journal of Combinatorial Theory, Series A, vol. 115 (2008), pp. 1265-1271.
G T A C P Random multiplication approaches uniform measure in finite groups
     with Henry Landau, Zeph Landau, Jamie Pommersheim, and Eric Zaslow
Journal of Theoretical Probability, vol. 20 no. 1 (2007), pp. 107-118.
G T A C P Distances of Heegaard splittings
     with Saul Schleimer
Geometry & Topology, vol. 9 (2005), pp. 95-119.
G T A C P State complexes for metamorphic robots
     with Rob Ghrist
International Journal of Robotics Research,, vol. 23 no. 7-8 (July 2004), pp. 809-824.
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.
G T A C P Configuration spaces of colored graphs

Geometriae Dedicata, vol. 92 (2002), pp. 185-194.
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.
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.
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 (Postscript file)

Ph.D. thesis, UC Berkeley (2000).
G T A C P The kth upper chromatic number of the line

Discrete Mathematics, vol. 169 (1997), pp. 157-162.
G T A C P The probability that (a,b)=1
     with Matteo Paris
College Mathematics Journal, vol. 23, no. 1 (1992), pg. 47.




II. Expository articles, announcements, etc.

G T A C P Braids,
      a chapter in the book Office Hours with a Geometric Group Theorist,
eds. Matt Clay and Dan Margalit (Princeton University Press, 2017)
G T A C P Finding good bets in the lottery, and why you shouldn't take them
     with Skip Garibaldi
American Mathematical Monthly, vol. 117 no. 1 (2010), pp. 3-26.
G T A C P Why not buy lottery tickets? (A non-technical, locally published version of above. A .doc file.)
     with Skip Garibaldi
The Academic Exchange, vol. 10 no. 4 (2008), pp. 10-11.
G T A C P A million-dollar proof

The Mathematical Intelligencer, vol. 29 no. 4 (2007), pg. 8.
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.
G T A C P Upper chromatic numbers: an update

Geombinatorics, vol. 10, no. 1 (2000), pp. 4-11.
G T A C P Evasive random walks

In Paul Erdös and his Mathematics, Budapest, Hungary, July 1999.