Seminários, para a disseminação informal de resultados de investigação, trabalho exploratório de equipas de investigação, actividades de difusão, etc., constituem a forma mais simples de encontros num centro de investigação de matemática.
O CAMGSD regista e publica o calendário dos seus seminários há bastante tempo, servindo páginas como esta não só como um método de anúncio dessas actividades mas também como um registo histórico.
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.
