Talk I:
From the ax+b Lie Algebra to the Alexander Polynomial and Beyond
Abstract.
I will present the simplestever "quantum" formula for the Alexander
polynomial, using only the unique two dimensional noncommutative Lie algebra
(the one associated with the "ax+b" Lie group). After introducing
the "Euler technique" and some diagrammatic calculus I will sketch the
proof of the said formula, and following that, I will present a long
list of extensions, generalizations, and dreams.
Handout: axpb.html, axpb.pdf.
Source Files: axpb.zip.
Talk
Video.
See also Finite Type Invariants of
wKnotted Objects: From Alexander to Kashiwara and Vergne, and Talks: Toronto1005.


Talk II: 18 Conjectures
Abstract.
I will state 18=3x3x2 "fundamental" conjectures on finite type invariants of
various classes of virtual knots. This done, I will state a few further
conjectures about these conjectures and ask a few questions about how these 18
conjectures may or may not interact.
Handout: 18C.html, 18C.pdf.
Source Files: 18C.zip.
Talk
Video.
See also Some Dimensions of
Spaces of Finite Type Invariants of Virtual Knots, with Halacheva,
Leung, and Roukema, and Talks:
Goettingen1004.


Dancso's Talk: Pentagon and Hexagon Equations  Following
Furusho
Abstract.
In his beautiful paper 'Pentagon and hexagon equations' (Annals
Math., Vol 171 (2010), No.1, 545556), H. Furusho proves that of the
defining equations for associators, the pentagon equation implies the
hexagons. After a brief introduction to associators, we will sketch a
simplified proof. In particular, we replace the use of algebraic geometry
by the fact that associators up to a given degree can be extended to
the next degree, and eliminate the use of spherical braids.
Handout: furusho.pdf.
Talk
Video.
See also Zsuzsanna Dancso's home page.

