Abstract. Everybody knows that nobody can solve the quintic. Indeed this insolubility is a well known hard theorem, the high point of a full-semester course on Galois theory, often taken in one's 3rd or 4th year of university mathematics. I'm not sure why so few know that the same theorem can be proven in about 15 minutes using *very* basic and easily understandable topology, accessible to practically anyone.
Handout: Quintic-Handout.pdf. Slides: Quintic-Slides.nb. Talk video: .
Abstract. It has long been known that there are knot invariants associated to semi-simple Lie algebras, and there has long been a dogma as for how to extract them: "quantize and use representation theory". We present an alternative and better procedure: "centrally extend, approximate by solvable, and learn how to re-order exponentials in a universal enveloping algebra". While equivalent to the old invariants via a complicated process, our invariants are in practice stronger, faster to compute (poly-time vs. exp-time), and clearly carry topological information.
This is joint work with Roland van der Veen and continues work by Rozansky and Overbay.
Handout: Dogma.html, Dogma.pdf, Dogma.png.
Talk Video (in Toulouse).
Handout: pre-talk (pdf, nb), post-talk (pdf, nb).