Time: 13:00
Speaker: Asghar Ghorbanpour (Western)
Title: "Rationality of spectral action for Robertson-walker metrics and geometry of determinant line bundle for the nonocmmutative two torus"
Room: MC 107

Abstract: In nonocmmutative geometry, the geometry of a space is given via a spectral

triple $(\mathcal{A,H},D)$.

In this approach the geometric information is encoded in the spectrum of $D$.

To extract this spectral information, one should study the spectral action $\Tr f(D/\Lambda)$.

This function is very closely related to classical spectral functions such as the heat trace $\Tr (e^{-tD^2})$ and the spectral zeta function $\Tr(|D|^{-s})$.

The main focus of this talk is on the methods and tools that can be used to extract the spectral information.

Applying the pseudodifferential calculus and the heat trace techniques, in addition to computing the newer terms of the spectral action, we prove the rationality of this spectral action, which was conjectured by Chamseddine and Connes.

In the second part of the talk, we define the canonical trace for Connes' pseudodifferential calculus on the noncommutative torus and use it to compute the curvature of the determinant line bundle for the noncommutative torus.

At the end, the Euler-Maclaurin summation formula will be used to compute the spectral action of a Dirac operator (with torsion) on the Berger spheres $\mathbb{S}^3(T)$.

Time: 14:30
Speaker: Baris Ugurcan (Western)
Title: "Dilation Theorems and Non-commutative Stochastic Processes"
Room: MC 107

Abstract: We survey (including our results) the dilation theorems in operator algebras in various settings and in particular talk about their appearance in non-commutative stochastic processes. We talk about the well-known correspondence between semigroups and stochastic processes in the commutative case and survey how this correspondence can be generalized to non-commutative setting by using dilation theorems. We also mention how the correspondence (in the commutative case) arises in developing analysis on non-smooth spaces such as fractals.