18.A13: Knots and Numbers

If someone gives you a loop of rope with an overhand knot in it, no amount of twisting and pulling (short of breaking the loop) will untie the knot. This looks obvious, but if the loop of rope is very long, are you really sure that some Houdini couldn't untie it? How can you be sure that nobody will ever find a way? Answers to this question lie in associating numerical invariants to knots, which can be used to distinguish them from each other. This seminar will investigate this active area of contemporary mathematical research. The only prerequisite is an interest in such questions.

Associate advisor:
Jillian Cairns, jillianc@mit.edu

The regular class meetings will occur on Wednesdays from 3:00 to 5:00 in 2-142. Students will lead discussions of relevant mathematical topics. The textbook for this course, Colin Adams's The Knot Book, will be available for free at the pre-registration meeting, so don't buy it!

Participants:

Sameer Deshpande sameerd@mit.edu
Vincent Lee vinitlee@mit.edu
Jelena Markovic markovic@mit.edu
Akin Morrison armorris@mit.edu
Daniel Ron dron@mit.edu
Liz Simon lizsimon@mit.edu
Justin Venezuela jven@mit.edu


Dan Ron found this Curves space flight simulator.

Schedule:

September 9: Haynes Miller: Reidemeister moves and 3-colorability.
September 16: Sameer Deshpande and Vincent Lee: Orientation and addition of knots; Linking number.
September 23: Daniel Ron and Liz Simon: Rational tangles.
September 30: Jelena Markovic and Akin Morrison: Crossing number, bridge number.
October 7: Jillian Cairns and Justin Venezuela: Genus.
October 14: Sameer Deshpande and Vincent Lee: Braids
October 21: Daniel Ron and Liz Simon: The bracket and Jones polynomials
October 28: Jelena Markovic and Akin Morrison: States and the Tait conjectures
November 5: Jillian Cairns and Justin Venezuela: Skein relations and the HOMFLYPT polynomial
November 12: Veterans Day, no meeting.
November 19: Sameer Deshpande and Vincent Lee: Curvature (See Precis of Milnor's work on this) and real knots.
November 26: Haynes Miller: Hyperbolic knots: the movie.

Professor Haynes Miller
Department of Mathematics 2-237
Massachusetts Institute of Technology
Cambridge, MA 02139
Phone: 617-253-7569
Fax: 617-253-4358
Email: hrm@math.mit.edu