Seminar: Polynomiality

• Non-commutative Geometry and Non-commutative Analysis Seminar
• Abstract:

  The question of polynomiality for maps and functors of abelian groups (not additive ones, obviously) was first addressed by Eilenberg and Mac Lane in 1954. We extend this notion to modules over numerical rings, which are rings equipped with binomial coefficients, presumably first discovered by Torsten Ekedahl in 2002. These rings turn out to present an array of rather pleasant properties, some of which may come somewhat as a surprise.

  After having discussed the elementary properties of numerical rings, we turn to different notions of polynomiality for maps and functors of modules. Strict and non-strict polynomiality are two concepts that have classically been rent asunder by their inherently different natures, but the setting of numerical rings allows for a beautiful unification of the two.

  An intricate design of ours is the labyrinth category, and we shall explain how it yields a complete combinatorial description of emph{all} module functors over an emph{arbitrary} base ring, as evidenced by the exquisite equation $$ mathfrak{Fun}(mathfrak{XMod},mathfrak{Mod}) sim mathfrak{Fun}(mathfrak{Laby},mathfrak{Mod}). $$

• Date: Friday, 12th February 2010
• Time: 17:00 to 17:45
• Room: MH:333
• Speaker: Qimh Xantcha, Stockholm University