Lecture (2004) /The 21st Century COE Program /Math of OCU(J)

The 21st Century COE Program

Constitution of wide-angle mathematical basis focused on knots

Department of Mathematics and Physics
Graduate School of Science
Osaka City University

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Lecture (2005)

Lecturer：	De Witt Sumners（Florida State University）



Title：	Scientific Applications of Knot Theory



Date：	Feb. 3(Friday)， Feb. 7, 14, 28 (Tuesdays)



Time：	13：30〜14：30



Place：	Dept. of Mathematics, Sci. Bldg., 3040

Abstracts
Knot theory is the study of entanglement of elastic curves in 3-space. Polymer chains (like DNA) can become entangled, and this entanglement has important chemical and biological consequences. This short course will provide an elementary introduction to knot theory and its uses in biology and chemistry. 2月3日　：　Introduction to Knots for Scientific Applications Topics: knots, knot equivalence, the Reidemeister moves, crossing number, prime and composite knots, unknotting number, linking number, twist, writhe, knot invariants, chirality, 2-string tangles. 2月7日　：　Knotting and Supercoiling of DNA Topics: DNA, supercoiling, analysis of topoisomerase experiments on circular DNA using knot theory 2月14日　：　DNA Site-Specific Recombination Topics: the tangle model for site-specific DNA recombination, analysis of Tn3 Resolvase and Xer recombination experiments on circular DNA substrates. 2月28日　：　Random Knotting Topics: proof that the probability of knotting goes to one exponentially rapidly with length for random curves; writhe of random curves, knotting of random arcs, random knots in confined volumes

Abstracts

Knot theory is the study of entanglement of elastic curves in 3-space. Polymer chains (like DNA) can become entangled, and this entanglement has important chemical and biological consequences. This short course will provide an elementary introduction to knot theory and its uses in biology and chemistry.

2月3日　：　Introduction to Knots for Scientific Applications

Topics: knots, knot equivalence, the Reidemeister moves, crossing number, prime and composite knots, unknotting number, linking number, twist, writhe, knot invariants, chirality, 2-string tangles.
2月7日　：　Knotting and Supercoiling of DNA

Topics: DNA, supercoiling, analysis of topoisomerase experiments on circular DNA using knot theory
2月14日　：　DNA Site-Specific Recombination

Topics: the tangle model for site-specific DNA recombination, analysis of Tn3 Resolvase and Xer recombination experiments on circular DNA substrates.
2月28日　：　Random Knotting

Topics: proof that the probability of knotting goes to one exponentially rapidly with length for random curves; writhe of random curves, knotting of random arcs, random knots in confined volumes

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