Dror Bar-Natan:

Research Plan

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last updated: Oct. 19, 2002

The phrase ``research plan'' is almost an oxymoron, for if it can be planned, it ain't research. Or at least, if it can be planned it's already half done, and hence it isn't the best of research. Thus my primary plan of mathematical research for the next few years is to follow my nose. The scents that usually attract me most are

My backup plans are (in case I become anosmic, or if today's strong smells remain dominant in the future):


On the Vassiliev knot invariants, Topology 34 423-472 (1995).

Non-associative tangles, in Geometric topology (proceedings of the Georgia international topology conference), (W. H. Kazez, ed.), 139-183, Amer. Math. Soc. and International Press, Providence, 1997.

Polynomial invariants are polynomial, Mathematical Research Letters 2 (1995) 239-246.

(With S. Garoufalidis) On the Melvin-Morton-Rozansky conjecture, Inventiones Mathematica 125 (1996) 103-133.

Lie algebras and the Four Color Theorem, Combinatorica 17-1 (1997) 43-52.

(With A. Stoimenow) The fundamental theorem of Vassiliev invariants, in Proc. of the Århus Conf. Geometry and physics, (J. E. Andersen, J. Dupont, H. Pedersen, and A. Swann, eds.), lecture notes in pure and applied mathematics 184 (1997) 101-134, Marcel Dekker, New-York.

On Associators and the Grothendieck-Teichmuller Group I, Selecta Mathematica, New Series 4 (1998) 183-212.

(With S. Garoufalidis, L. Rozansky and D. P. Thurston) The Århus integral of rational homology 3-spheres I: A highly non trivial flat connection on $S^3$, Selecta Mathematica, to appear.

(With M. Bar-Hillel, G. Kalai and B. D. McKay) Solving the Bible Code Puzzle, Statistical Science 14-2 (1999) 150-173.

(With R. Lawrence) A Rational Surgery Formula for the LMO Invariant, Israel Journal of Mathematics, to appear.

On Khovanov's categorification of the Jones polynomial.

(With D. P. Thurston) Algebraic Structures on Knotted Objects and Universal Finite Type Invariants.

Other papers by Dror Bar-Natan.

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Dror Bar-Natan 2002-10-19