Knot at Lunch on July 30 2008
Dear Knot at Lunch People,
Note the unusual time, place and content! Please let me know if you are planning to come (no need to respond otherwise).
On Wednesday July 30 2008 Jana Archibald and I will hold an "Alexander Relations Marathon", replacing our regular knot at lunch meeting.
There are many relations satisfied by the Alexander polynomial and its weight system; around 20 of them are on one blackboard, available for everybody's delight at. Some are well known, some are known but less well, some are known only to us (Jana and I), and some are not yet proven. Each one seems to have a different proof, and these proofs appear in many separate references.
Jana and I think we have a technique for proving all these identities cleanly and uniformly. The idea is to interpret all of them as certain computations that are carried out within certain exterior algebras: the exterior algebras and the descriptions of the computations fall under "conceptual mathematics"; the computations themselves are, well, just dull and brainless computations, that may well be delegated to a machine. So our hope is to write clean and elegant programs that clearly reflect the mathematics to carry out those computations, thus providing uniform verifications of all those relations.
As always, it is hard to plan math in advance; our "conceptual story" may collapse, or everything may be completed by Jana before we even start on July 30. Yet a realistic expectation and plan would be:
- Before July 30 Jana will already have a running program that does everything, perhaps with the exception of "clearly reflecting the mathematics". Thus we will be confident that the theory is right.
- Jana will start the marathon by briefly explaining the math (along with a nice handout?). She will also provide us with printouts of her program and the output of running it on all or most of the relations in .
- Strengthened by the confidence that the theory works, Jana and I will do our best to rewrite the program from scratch with two goals in mind:
- Our end result should clearly reflect the mathematics.
- Dror should also get the confidence one gets from explicitly applying a theory.
As with our previous marathon, the main beneficiaries will be the main participants - this time, Jana and Dror. But all are welcome to join, and all may have something to contribute.
We will meet at 9AM (July 30) either in small boardroom (Bahen 6290B) or in my house, depending on the number of people planning to come (so please let me know!!) and the availability of alternate company for my son, whose mother and brother will be out of town that week. The location will be emailed to those planning on coming around July 29.
Note that we will not have Knot at Lunch meetings on July 9, 16 and 23.
Further information about this Knot at Lunch meeting may be posted later at.
As always, if you know anyone I should add to this mailing list or if you wish to be removed from this mailing list please let me know. To prevent junk accumulation in mailboxes, I will actively remove inactive people unless they request otherwise.
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