Guest lectures and seminars - Page 146

Prof. Dr. Alois Gisler (ETH Zurich, RiskLab Switzerland) holds a seminar with the title "On the Development of the Swiss Solvency Test"

Prof. Dr. Alois Gisler (ETH Zurich, RiskLab Switzerland) holds a seminar with the title "The Reserve Risk of the Chain-Ladder Reserving Method from a New Perspective"

Réamonn Ó Buachalla (IMPAN) will give a talk with title: Noncommutative Kähler structures on quantum homogeneous spaces

Abstract:

Building on the definition of a noncommutative complex structure for a general algebra A, I will introduce the notion of a noncommutative Kähler structure for A. In the special case where A is a quantum homogeneous space, I show that many of the fundamental results of classical Kähler geometry follow from the existence of such a structure: Hodge decomposition, Serre duality, the Hard Lefschetz theorem, the Kähler identities, and collapse of the Frölicher spectral sequence at the first page. We then apply these results to Heckenberger and Kolb's differential calculus for quantum projective space, and show that they have cohomology groups of at least classical dimension. Time permitting, I will also discuss the relationship of this work to Connes proposal to study positive Hochschild cocycles as a starting point for noncommutative complex geometry, and Fröchlich, Grandjean, and Recknagel's definition of a Kähler spectral tuple.

Eduard Ortega, NTNU, will give a talk with title: Cuntz-Krieger uniqueness theorems

Abstract: I will make a little survey about Cuntz-Krieger uniqueness theorems and how they help to the study of the ideal structure of the rings to which one can apply them. In certain classes of (C*-)algebras this is described as topologically freeness or condition (L). However they are important classes of rings for which are not known Cuntz-Krieger type theorems. I will present a class of rings, that generalize Leavitt path algebras and Passman crossed products, for which I can totally characterize the Cuntz-Krieger uniqueness theorem.