Time: 13:00
Speaker: Emre Coskun (Western)
Title: "Gerbes from a Stack-Theoretic Perspective - Part II"
Room: MC 107

Abstract: In this talk, we will discuss some of the properties of gerbes from a stack-theoretic perspective. We will talk about the universal property of the structure morphism of a gerbe, define a neutral gerbe and prove that a neutral gerbe is of the form BG, where G is a sheaf of groups.

Time: 14:00
Speaker: Bahram Rangipour (New Brunswick)
Title: "Hopf algebras in Geometry without groups"
Room: MC 107

Abstract: It is now more than a decade that Hopf algebras established themselves as an integral part of Noncommutative Geometry via the work of Connes and Moscovici on the computation of the index of hypoelliptic operators on manifolds. The latest Hopf algebras constructed were those associated to Cartan-Lie pseudogroups. In this talk we canonically associate a Hopf algebra to any bicrossed sum Lie algebras. This construction covers all known cases in type II and also type III. The constructed Hopf algebra is naturally equipped with a modular pair in involution which is the coefficients for the Hopf cyclic cohomology of the Hopf algebra. At the end we show how to compute the Hopf cyclic cohomology of these Hopf algebras.

Time: 15:30
Speaker: Ivan Fesenko (Nottingham)
Title: "Higher fields and adeles associated to arithmetic surfaces, and a translation invariant integration on higher local fields and adeles"
Room: MC 107

Abstract: This is part 1 of the series "A generalization of the adelic analysis theory of Tate and Iwasawa to arithmetic surfaces"

On arithmetic surfaces one can work with refined structures which the classical algebraic geometry does not really see. Some of them come as higher global, local-global and local fields. The latter fields include power series over usual local fields. Their topology is very unusual. Remarkably, one can integrate over them.

Unlike the classical case of dimension one, arithmetic surfaces have two quite different adelic spaces associated to them: one which is good for geometric applications and another which is good for zeta functions and integration.

The apparent separation between geometry and analysis is a typical phenomenon in dimension two; the BSD conjecture shows that they are not unrelated.