Part 2 of this series of two talks focuses on properties of twisted Hilbert -modules, which are seen as representations of twisted -dynamical systems. I will introduce Ralf Meyer’s bra-ket operators and use them to define the notion of a ‘square-integrable representation’. A construction of generalized fixed-point algebras for twisted -dynamical systems will then be given. The highlight of the talk will be a classification (up to isomorphism) of Hilbert modules over a fixed non-commutative torus purely in terms of Hilbert spaces with certain special properties.
Generalized Fixed-Point Algebras for Twisted C*-Dynamical Systems (Part 2)
Sep. 29, 2016 3pm (MATH 350)
Probability
Hakima Bessaih (University of Wyoming)
X
We study some models with microscale properties that are highly heterogeneous in space and time. The time variations are controlled by a stochastic particle dynamics described by a stochastic ODE (SDE). Our main results include the derivation of macroscale equations and showing that the macroscale equations are deterministic. We use the asymptotic properties of the SDE. The macro scale equations are derived through an averaging principle of the slow motion (fluid velocity) with respect to the fast motion (particle dynamics). Our results can be extended to more general nonlinear diffusion equations with heterogeneous coefficients.
Homogenization of stochastic models in porous media