**Sources:** Quadraticity.zip.
**Pensieve:** Projects: Quadraticity.

Dear Friends and Potential Future Friends in Oregon,

I'd like to make use of a nice alignment of circumstances that is to occur this summer, and I wonder if you'd want to help (or, if you wish, also make use of that alignment).

[I will be in Oregon for a personal reason]. My student **
Peter Lee** has a math result that may interest some people in Oregon
(you) and he and I need a stage to motivate ourselves to sharpen it to
perfection. So it may be an excellent idea for **Peter** and for me to visit
Oregon and spend some time telling our story, right before [my personal
reason]. Here are the details:

[Timing details]

The math result is about groups and quadratic algebras. There is
a simple way to define functor *Q* that takes a group to "the
quadratic approximation to its unipotent completion". A famed example
is the pure braid group, which is taken by the functor *Q* to
the Drinfel'd-Kohno algebra (aka "horizontal chord diagrams").

We do not know how good is the functor *Q*. We do not know which
quadratic algebras occur in its image, and when a quadratic algebra does
occur, we don't know how well it approximates the unipotent completion
of the group it came from.

**Peter's** work is about a general methodology that allows one to
show that in certain cases the said quadratic approximation is "good"
(in some natural sense). Furthermore, in the case of the pure virtual
braid group the quadratic approximation is a well known algebra, the
one with generators *a _{ij}* (

Would any of you be around for the said dates (right before August 7th)? Would you be interested in hearing 2-4 lectures on the subject, or perhaps holding some sessions on the subject in the "Russian seminar" style?

My grant could cover all relevant expenses. We're really mostly looking for an audience to motivate us.

Best,

Dror.