Seminars, for informal dissemination of research results, exploratory work by research teams, outreach activities, etc., constitute the simplest form of meetings at a Mathematics research centre.
CAMGSD has recorded the calendar of its seminars for a long time, this page serving both as a means of public announcement of forthcoming activities but also as a historic record.
It was observed in the 1980's that the entropy of an action by two or more commuting automorphisms on a compact abelian group is sometimes given by a zeta- or L-value. For example zeta(3) arises in this way. In the talk I will report on joint work with Thu Hà Trieu, which at least for expansive actions explains the deeper reason for these observations by a combination of operator algebra theory, in particular the theory of their determinants, K-theory and cyclic and Deligne cohomology. The talk is addressed to a general audience and will not go into technical details. Instead we will sketch the relevant theories and explain how to fit them together for our purpose.
We consider a class of Riesz transforms $R_V^a$ related to the Schrödinger operator $L = -\frac{1}{2}\Delta + V$ with $V$ being a non-negative potential. We will focus on $L^\infty$ boundedness of $R_V^a$ and give a specific integral condition on $V$ which provides the boundedness. We will also show that potentials with power or exponential growth satisfy this condition.
The Kerr de Sitter geometry models a rotating black hole in an expanding universe. I will review its stability properties in the context of the Einstein vacuum equations with positive cosmological constant, and present recent progress on the non-linear stability problem for the cosmological region.
