Guest lectures and seminars - Page 153

Jan Fredrik Bjørnstad (Statistics Norway and Dept. of Math.,UiO) gives a seminar in room 107, 1st floor N.H. Abels House at 14:15 November 18th: Survey sampling the way I see it.

This is a work we had done jointly with Garkusha (after Voevodsky) arXiv:1409.4372. Using the machinery of framed sheaves developed by Voevodsky, a triangulated category of framed motives is introduced and studied. To any smooth algebraic variety X in Sm/k, the framed motive M_fr(X) is associated in that category . Also, for any smooth scheme X in Sm/k an explicit quasi-fibrant motivic replacement of its suspension P1-spectrum is given. Moreover, it is shown that the bispectrum (M_fr(X),M_fr(X)(1),M_fr(X)(2), ... ), each term of which is a twisted framed motive of X, has motivic homotopy type of the suspension bispectrum of X. We also construct a compactly generated triangulated category of framed bispectra SH_fr(k) and show that it reconstructs the Morel-Voevodsky category SH(k). As a topological application, it is proved that the framed motive M_fr(pt)(pt) of the point pt = Speck evaluated at pt is a quasi-fibrant model of the classical sphere spectrum whenever the base field k is algebraically closed of characteristic zero.   

The goal of this talk is to present some recent computations of the Picard groups of several spectra of topological modular forms. The first part of the talk will introduce the toolbox, which consists of descent theory and a technical lemma allowing us to compare stable and unstable information in spectral sequences. This is joint work with Akhil Mathew.   

Tore Selland Kleppe (University of Stavanger) gives a seminar in room 107, 1st floor N.H. Abels House at 14:15 November 11th: Bandwidth Selection In Pre-Smoothed Particle Filters