Time: Wednesdays, 1pm, except where noted.
30-04-2014, Room MS.01.
Speaker: B. Mesland, Warwick.
"Noncommutative geometry and boundary actions"
Abstract: In this first talk of the seminar series, we will introduce some concepts of noncommutative geometry, such as C*-algebras, spectral triples and K-theory. We describe a certain "holographic principle" by which the geometry of classical objects is reflected in the quantum geometry on the boundary of this object. This idea has its origin in the physics of quantum systems, but can also be applied to situations in number theory and the dynamics of subshift of finite type. These topics will surface later in the seminar series, and this talk serves as an introduction of some of the main ideas.
- 07-05-2014, Room MS.01.
Speaker: X. Li, Queen Mary.
"Dynamical systems and C*-algebras"
Abstract: This talk is about the notions of Cartan pairs and continuous orbit equivalence and their relationship. We discuss the general picture as well as concrete examples.
14-05-2014, Room MS.01, meeting at 3pm.
Speaker: M.H. Sengun, Warwick.
"Noncommutative geometry and arithmetic manifolds"
Abstract: Consider a lattice L inside a connected semisimple Lie group G with associated global symmetric space X.
When L is "arithmetic" (that is, it arises from a certain number theoretic construction), the quotient L\X
has important extra features and in particular its cohomology plays a central role in a giant picture
(that goes by the name "Langlands Programme") that involves automorphic forms, Galois representations and many others.
From the above perspective, the action of L on the (whole) boundary of X has not been studied much by number theorists
as L acts with dense orbits. However, as exhibited by Manin and Marcolli, the study of this boundary action by means of
noncommutative geometry has potential to be of interest to number theory. I will discuss ongoing work with Bram Mesland,
and the questions inspired by this work, on the connections between the cohomology of the arithmetic manifolds L\X and
the K-theory of certain noncommutative C*-algebras that encode the action of L on the boundary of X.
21-05-2014, Room MS.02
Speakers: M. Fraczek, G. Cornelissen, B. Nica.
- 28-05-2014, Room B3.02.
Speaker: Robin Deeley, Clermond Ferrant.
"Correspondences for Smale spaces"
Abstract: We discuss some results of a joint project with Brady Killough and Michael Whittaker. The goal of the project is to better understand the functorial properties of the homology theory for Smale spaces introduced by Ian Putnam.
The fundamental objects of study are correspondences between Smale spaces; the precise definition will be given in the talk. However, the idea is to encode both types of functorial properties of Smale spaces (with respect to Putnam's homology theory) into a single object. The talk will be very much an introduction and will contain many examples (for the most part coming from the theory of shifts of finite type). No knowledge of Smale spaces or Putnam's homology theory are required for the talk.
04-06-2014. Room B3.02.
Speaker: M. Goffeng, Hannover.
"Finite summability on Cuntz-Krieger algebras"
Abstract: We present a way to (noncommutatively) geometrise the dynamics of a shift of finite type. In technical terms, it is carried out by means of Fredholm modules as well as spectral triples on the closely related Cuntz-Krieger algebras. The original motivation for considering such constructions was to find curiosities appearing for a certain regularity condition in noncommutative geometry. Curiosities do indeed appear. The talk is based on joint work with Bram Mesland.