Guest lectures and seminars - Page 161

Johanna Ridder (University of Oslo) will give a talk about

Analysis of a finite difference method for two-dimensional incompressible magnetohydrodynamics

Abstract: We consider the magnetohydrodynamics equations for a viscous incompressible resistive fluid in two dimensions. For these equations we analyse a semi-discrete finite difference scheme that is based on a staggered grid and is energy preserving. We show an a priori H^1-bound and the convergence of the scheme.

Professor B. Rajeev (India Statistical Institute, Bangalore) holder et seminar med tittelen: The Monotonicity Inequality on Hermite-Sobolev spaces.

In 1980 R. W. Thomason published a proof that CAT, the category of small categories, is a proper closed model category that is Quillen equivalent to SSet, the category of simplicial sets, with the standard model structure defined by Quillen. D-C Cisinski has since corrected the proof of left properness by replacing the central term of Dwyer morphism - a class of morphisms that Thomason believed to be the cofibrations - with a rough analogue in CAT of the NDR-pairs. The cofibrations, then, which are all retracts of Dwyer morphisms, are really the NDR-pair analogues. I will go through the main parts of Thomason's argument, incorporating Cisinski's adjustment, point out Thomason's mistake and here and there use more recent terminology from M. Hovey's book Model Categories. Towards the end I'll compare Thomason's method with modern, standardized ways of confirming a cofibrantly generated (closed) model structure, like the necessary and sufficient conditions listed in Hovey's Model Categories (thm. 2.1.19) and transferring a model structure across an adjunction by using Kan's lemma on transfer and similar results 

Antoine Julien (NTNU) will give a talk with title: Tiling spaces, groupoids and K-theory

Abstract:

 In this talk, I will describe how spaces, groupoids and C*-algebras can be associated with aperiodic tilings. In some cases, it is possible to describe the structure of the groupoid combinatorially in terms of augmented Bratteli diagrams. (joint work with Jean Savinien) Time permitting, I will expose a strategy for computing the K-theory of the tiling algebra in terms of the K-theory of AF-algebras (work in progress).