**ODTÜ-B****Ý****LKENT
ALGEBRAIC GEOMETRY SEM****I****NAR**

**“Tait's conjectures”**

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by

**Deniz**** Kutluay**

**Abstract:
**P.G. Tait conjectured, in 1898, that a reduced
alternating diagram of a knot achieves the minimum possible number of crossings
for that knot (1), and writhe of such diagrams of the same knot is the same
(2). We will first give K. Murasugi's proof to (1)
which involves usage of Jones polynomial. We will then use the idea of taking
parallels of diagrams (due to R.A. Stong) to prove
(2).

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**Date:** 5 March 2010 Friday

**Time:** 15:40

**Place:** Bilkent,
Mathematics Seminar Room SA-141

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**Tea and cookies will be served before the
talk.**