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Current contacts: Vasily Dolgushev, Ed Letzter, Martin Lorenz or Chelsea Walton
The Seminar usually takes place on Mondays at 1:30 PM in Room 617 on the sixth floor of Wachman Hall. Click on title for abstract.
Angela Gibney, Rutgers University
TBA
Benjamin Collas, The University of Bayreuth
Following Grothendieck's "Esquisse d'un Programme", the moduli spaces of curves present remarkable arithmetic-geometry properties which translate to an elegant study of the absolute Galois group of rationals. This program results in the construction of Grothendieck-Teichmueller groups that express how the topological combinatoric of the compactification of spaces encaptures their arithmetic. In this duality, the arithmetic side is expressed through the deformation of curves and the notion of tangential structure, while the topological side recently found an elegant expression in terms of homotopy of the little 2-discs operad by Fresse, Horel et al. The goal of this talk is to present how these two sides intersect each other in the study of the absolute Galois group of rationals. We will thoroughly present both aspects in some recent work for genus 0 curves, and explain how it indicates some promising research lines in higher genus.
Martin Lorenz, Temple University
This time, the focus will be on affine algebraic groups, with some outlook/problems for "quantum groups" at the end. Again, the talk will be largely self-contained inasmuch as no details from the first two talks will be assumed. I will remind you of the general Nullstellensatz/Dixmier-Moeglin picture from the second lecture at the beginning of the talk.
Martin Lorenz, Temple University
Continuing with the theme of the first lecture, I will present some known results on group algebras and speculate on possible extensions to more general classes of Hopf algebras. Thus, much of the second lecture will again be concerned with groups and group algebras. It will be possible to understand this lecture even if you missed the first one.
Martin Lorenz, Temple University
This series of talks will be concerned with actions of Hopf algebras on other algebras ("quantum invariant theory"). I will present a few observations and then proceed to discuss some speculations and open questions. In the first talk, I plan to focus on "local finiteness."
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