14:00 - 15:00 Weekly Seminar
HEPCo Group
Symmetries at Null Boundaries: Two and Three Dimensional Gravity Cases
School PHYSICS
Abstract:
I will present in full generality and without ?xing speci?c boundary conditions, the symmetry and charge analysis near a generic null surface for two and three dimensional (2d and 3d) gravity theories. In 2d and 3d there are respectively two and three charges which are generic functions over the codimension one null surface. The integrability of charges and their algebra depend on the state-dependence of symmetry generators which is a priori not speci?ed. I will establish the existence of in?nitely many choices that render the surface charges integrable. I will show that there is a choice, the “fundamental basis”, whe ...
16:30 - 18:30 Geometry and Topology Weekly Seminar
Using invariant measures to understand the behavior of Lyapunov exponents of linear cocycles
School MATHEMATICS
In the first half of this talk we are going to give an overview of the basic theory of Lyapunov exponents of linear cocycles focusing on the relationship between them and the invariant skew-product measures. The idea is to understand how these measures can be used to give nice properties of the Lyapunov exponents such as positivity and continuity. In the second half, we are going to use these ideas to study the behavior of the Lyapunov exponents of linear cocycles when the base dynamics is a model of a partially hyperbolic skew-product.
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