## Evento

Quando: 21/12/2023 - 14:30

Dove: Palazzo Campana - TORINO

Aula: Aula C and webex

Relatore: G. Landi and M. Khalkhali

Afferenza: Università Trieste and University Western Ontario

Locandina:

## Descrizione:

For those who cannot attend onsite, there is also a link to participate online:

https://unito.webex.com/unito/

j.php?MTID= m1973fa6b4c7748efc1cebd926e5eb 1fa Meeting number (access code): 2783 674 4738

Titles and abstract

Giovanni Landi (U. Trieste)Title: On Atiyah sequences of braided Lie algebras and their splittingsAbstract: To an equivariant noncommutative principal bundle one associates an Atiyah sequence of braided derivations whose splittings give connections on the bundle. There is an explicit action of vertical braided derivations as infinitesimal gauge transformations on connections. From the sequence one derives a Chern—Weil homomorphism and braided Chern—Simons terms.

On the principal bundle of orthonormal frames over the quantum sphere S^{2n}_\theta, the splitting of the sequence leads to a Levi-Civita connection on the corresponding module of braided derivations. The connection is torsion free and compatible with the `round' metric. We work out the corresponding Riemannian geometry.

Masoud Khalkhali (U. Western Ontario)

Title: Introduction to Hopf cyclic cohomologyAbstract: Cyclic homology can be understood as a noncommutative analogue of de Rham cohomology of smooth manifolds. In the same vein, Hopf cyclic cohomology should be understood as the noncommutative analogue of group homology and Lie algebra homology. There is however no easy way to define either of these theories due to the noncommutativity of the algebra involved. In this lecture I shall give an introduction to the definition of Hopf cyclic cohomology and some of its applications to problems of index theory. I shall then sketch an extension of the theory using a variant of the so called Yetter-Drinfeld modules from the theory of quantum groups. They play the role of coefficients or local systems in the theory.