Guest lectures and seminars - Page 182

Abstract: The Kolmogorov decomposition of positive scalar valued kernels has played an important role in applications of operator theory to function theory.  It has been vastly generalised, finding its apotheosis in the result of Baretto, Bhat, Liebscher and Skeide which states that a positive $L(A,B)$-valued kernel, $A$ and $B$ $C^*$-algebras, has a Kolmogorov decomposition if and only if it is completely positive; that is, the restriction of the kernel to any finite set of index points gives a completely positive map.  The result may be viewed as a generalisation of the Stinespring dilation theorem from single point to multi-point index sets.  This talk presents the analogue of the Haagerup-Paulsen-Wittstock decomposition theorem for $L(A,B)$-valued kernels (where now $B$ is assumed to be injective).  It happens that in general complete boundedness of the kernel (ie, complete boundedness of the map resulting from restriction of the kernel to any finite index set) is not quite enough to ensure a decomposition: a certain regularity condition must also hold.  This condition can be seen to be automatic if the kernel is completely positive or the index set is countable.  This is joint work with Tirthankar Bhattacharyya and Chris Todd.  

Abstract: In topology, there is a correspondence between generalized cohomology theories (in the sense of the Eilenberg-Steenrod axioms) on one hand and spectra on the other hand, the latter being objects in the stable homotopy category SH. In algebraic geometry and motivic homotopy theory, the situation is much more complicated in several ways. Firstly, there are many stable homotopy categories, one for each scheme, and various functors between them. Secondly, there are many sets of axioms for what a cohomology theory should be (Weil cohomology, Bloch-Ogus cohomology, oriented cohomology, ...) and a huge zoo of cohomology theories. The aim of the talk will be to give an overview of all generalized cohomology theories in algebraic geometry, using the language of motivic stable homotopy theory. 

Jukka Lempa, EMMOS/CMA, holder et seminar med tittelen: Some Properties of Harmonic Functions for Diffusion Processes

Øystein Sørensen (Department of Biostatistics, UiO) will talk about

Penalized Regression with Measurement Error