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Moira Chas

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Office: 4-103 in the Math Tower
Phone: 632- 8266
The best way to contact me is by

Research

Interests:
Low dimensional topology, geometric topology, combinatorial group theory.

Current problems

Characterization of simple closed curves in terms of the Goldman Turaev Lie bialgebra. More generally, counting minimal intersection and self intersection numbers by means of this Lie bialgebra.
Configurations of curves on surfaces which have minimal intersection and self-intersection.
A presentation of the Goldman-Turaev Lie bialgebra of curves on closed surfaces.

Publications and Preprints

(with Fabiana Krongold) An algebraic characterization of simple closed curves on surfaces with boundary in Math Archives
Minimal intersection of curves on surfaces (preprint)
Combinatorial Lie Bialgebras of Curves on Surfaces. Topology 43 (2004), no3, 543--568. An improved version can be found here
(with Dennis Sullivan) Closed string operators in topology leading to Lie bialgebras and higher string algebra. The legacy of Niels Henrik Abel, 771-788, Springer, Verlin, 2004
(with Dennis Sullivan) String Topology (too appear in Annals of Mathematics)
(with Lluís Alsedà and Francesc Mañosas) Rotation sets for orbits of degree one circle maps. Internat. J. Bifur. Chaos Appl. Sci. Engrg. 12 (2002), no. 2, 429--437
(with Lluís Alsedà and Jaroslav Smítal), On the structure of the $\omega$-limit sets for continuous maps of the interval. Discrete dynamical systems. Internat. J. Bifur. Chaos Appl. Sci. Engrg. 9 (1999), no. 9, 1719--1729
PhD Thesis, Minimum periods of homeomorphisms of orientable surfaces. (I've beenplaning to submit it for publication since 1998, and I still did not loose hope)

Java applets for curves on surfaces

Algorithm to check whether two words in a closed surface group represent conjugate elements, following Birman-Series, 1987. (work in progress)
Goldman bracket and intersection number following Cohen-Lustig algorithm (Joint work with Fabiana Krongold).
Turaev cobracket and self intersection number following Cohen-Lustig algorithm. (Joint work with Fabiana Krongold.)
Programs to test bracket and cobracket conjectures (these are probably quite useless without explanations, but I'll be happy to explain if you email me about them.)

Past Teaching Webpages