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9th Annual Cantrell Lectures

Joan Birman
Physics, Room 202
Joan Birman
Barnard College of Columbia University

Monday, March 31, 2003

4:00 p.m. Physics Bldg., Room 202

Scientific publication: a mathematician's viewpoint

Abstract: Digital computers have brought enormous changes in the way mathematicians work. One of them relates to an issue which sounds trivial, even though it is not: the art of mathematical typesetting died just as budget problems forced universities to cut back secretarial support. Mathematicians had to learn how to type their own papers! That lead to an interesting mathematical problem which was solved by Donald Knuth, the inventor of a new "language" called "Tex". In this talk I'll discuss Tex, how it works and how it has lead to a small revolution in mathematical publishing (which the commercial publishers are just beginning to appreciate). I'll describe the process by which math journals are created, and the multiple roles that mathematicians play in that process. I'll discuss the new economic pressures. In particular I'll tell you about two new professional journals which just may be winning a battle which has the potential to put the giants in the scientific publishing world out of business.


Tuesday, April 1, 2003

4:00 p.m., Physics Bldg., Room 202

Recognizing the Unknot

Abstract: The problem of recognizing the unknot is a rare mathematical problem because it can be explained in 30 seconds, yet 150 years after it was first understood as a serious mathematical problem it is still unclear whether a polynomial-time algorithm exists. We will review the literature, discuss how it was proved that the problem is both NP and co-NP, and discuss present efforts to find a polynomial-time algorithm.

Wednesday, April 2, 2003

4:00 p.m., Boyd Graduate Studies, Room 328

Stabilization in the braid groups

Abstract: Solved problems abound in topology where there is a notion of "stabilization". Examples:the Reidemeister-Singer Theorem relating any two Heegaard splittings of a 3-manifold, the Kirby Calculus relating any two surgery presentations of a 3-manifold,and Markov's Theorem, relating any two closed braid representatives of a knot. This talk will report on new joint work with William Menasco. Our main result is "Markov's Theorem Without Stabilization." We replace the stabilization move in the Markov theorem by finitely many moves which are strictly "complexity" reducing (and non-increasing on braid index). The statement of the theorem is too messy for this abstract, which is another way of saying that it's a very hard problem to decide when two knot diagrams determine the same knot type! As an application we solve a classical open problem about knots transverse to the standard contact structure.

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