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.
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2月7日 : Knotting and Supercoiling of DNA
Topics: DNA, supercoiling, analysis of topoisomerase experiments on circular DNA
using knot theory
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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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