### University of Manchester

### Informal Research Seminar on Geometry and
Mathematical Physics

### Special programme:

## Double and Multiple
Structures in Standard and Super Geometry

## Meeting details, 2008 - 09

#### Monday May 11, 2009

Ted Voronov: "Non-Abelian Poincar� lemma and its application to Lie
algebroids."
I will speak about my recent work.
In particular I wish to explain how it can be applied to
transitive Lie algebroids in the language of Q-manifolds and to
their non-linear generalizations.
#### Monday April 27, 2009

Kirill Mackenzie: "Transitive Lie algebroids: local data,
obstruction class, and integration."
Kirill will introduce description of transitive Lie algebroids by
local data, leading to the obstruction class and solution of the
integration problem. (Possibly supplemented by T.V. using the
language of Q-manifolds.)
#### Monday March 30, 2009

Ted Voronov: "Transitive Lie algebroids from the viewpoint of
Q-manifolds".
I will try to start discussing local description of transitive
Lie algebroids in the language of Q-manifolds --- with an idea
in mind to interpret systematically "Strobl's algebroids" as
non-linear analogs of the former.
#### Monday March 16, 2009

Hovhannes Khudaverdian: "Second-order (and higher order) frames on
a manifold." I will discuss the bundle of second-order tangent frames and
canonical 1-forms on it, with view of an application to connection
theory.
#### Monday March 9, 2009

Hovhannes Khudaverdian: "Recollection of connection theory (continued)".
More will be said about projective and conformal transformations
and projective and conformal connections.
#### Monday March 2, 2009

Ted Voronov: "Cattaneo--Felder quantization again".
Ted will recall what we have learned so far about the
Cattaneo--Felder work from the viewpoint of Lie algebroids and
supermanifolds. A brief survey will include the construction of
action, its motivation and link with Lie algebroids, infinitesimal
symmetries, and the remarkable fact about the realization of the
"Batalin--Vilkovisky manifold" for this model as the
(super)manifold of *all* maps from TD ti T^* M (not only vector
bundle morphisms).
#### Monday February 23, 2009

Kirill will (do his best to) answer questions about connection theory in Lie groupoids
and Lie algebroids and its relationship to the integrability problem.

May 30, 2009