The main goal of this set of talks is to introduce twisted crossed products of Banach algebras by locally compact groups. Both talks will be accessible to anyone with basic Functional Analysis knowledge, but Part II will assume familiarity with Part I.
Classical crossed products of Banach algebras have been extensively studied for different classes of representations, including contractive representations on L^p-spaces.
Part I: We give a general formulation for Banach algebras associated with twisted dynamical systems. Recent developments in L^p-twisted crossed products have mostly focused on situations where either the algebra is the complex numbers or when the group is discrete (more generally for étale groupoids). We present a universal characterization of the twisted crossed product when the acting group is locally compact and the Banach algebra has a contractive approximate identity.
Part II: We now focus on the case when the representations are contractive ones acting on L^p spaces. We briefly discuss a reduced version for L^p-operator algebras. We present a generalization of the so called Packer–Raeburn trick to the L^p-setting, showing that the universal L^p twisted crossed product is ``stably'' isometrically isomorphic to an untwisted one.
This is joint work with Carla Farsi and Judith Packer.
Twisted Crossed Products of Banach Algebras (Part II)
Thu, Oct. 9 3:30pm (Math 3…
Probability
Ewan Davies (Colorado State University)
X
The hard-core model is a well-studied probability distribution in statistical physics and algorithms since it exhibits interesting behavior from probabilistic and algorithmic perspectives. We will survey the underlying mathematical phenomena that drive this interesting behavior and uncover some surprises.
A first-order phase transition in the hard-core model
TBA