and

Geometry and Mathematical Physics Seminar

Thursdays 3.00pm (for the

The two seminars are run in combination/ alternation. Visit the **main page** to find more information, in particular, programmes of talks for previous years. For the Manchester Geometry Seminar, we meet about 3.50 for tea and biscuits; each lecture begins at 4.15pm in the seminar room FA 1. For the Geometry and Mathematical Physics Seminar, we start at 3pm in the seminar room FA 2; after a break around 4pm, we move to the seminar room FA 1.

**October 7: Manchester Geometry Seminar. 4.15pm, FA 1.**

Prof. Dmitry Talalaev, (Moscow State University): Quantum Gaudin model- October 14:
*No seminar* **October 21: Manchester Geometry Seminar. 4.15pm, FA 1.**

Prof. Dimitri Gourevitch, (Université de Valenciennes): Elements of braided geometry-
**October 28: Manchester Geometry Seminar. 4.15pm, FA 1.**

Mr Joel Haddley, (University of Liverpool): Symmetric singularities and complex hyperbolic reflection groups - November 4:
*No seminar*(reading week) **November 11: Geometry and Mathematical Physics Seminar. 3pm, FA 2.***Ted Voronov. Supermanifolds: from definition and Λ-points to supermanifolds of maps.***November 18: Geometry and Mathematical Physics Seminar. 3pm, FA 2.***Ted Voronov. Supermanifolds: from definition and Λ-points to supermanifolds of maps. II***November 25: Geometry and Mathematical Physics Seminar. 3pm, FA 2.***Special Programme on Double and Multiple Structures**Ted Voronov. From supermanifolds of maps to Q-groups and Q-categories.*

I will give a working definition of the infinite-dimensional supermanifold of maps between two supermanifolds. As an example of geometric constructions on it , I will consider the vector fields induced by a vector field on the target or on the source. In particular, in this way arises the "Q-category" of all Q-manifolds. Time permitting, I shall then discuss some constructions for Q-groups or an approach to integration of Lie algebras/ algebroids using Q-manifolds or the new algebraic structure arising from "non-linear" Lie algebroids.-
**December 2:****Manchester Geometry Seminar. 4.15pm, FA 1.**

Prof. Paul Bressler, (Université Paris 7): Formality for algebroids **December 9: Geometry and Mathematical Physics Seminar. 3pm, FA 2.***Ted Voronov. The Atiyah-Singer Index Theorem: an Informal Introduction*

I shall start by explaining the notion of index in an abstract setting and its relation with superalgebra. Then I shall introduce the Atiyah-Singer formula for the index of an elliptic operator, consider examples and discuss different ways of establishing it. Time permitting I will outline an "analytic" proof based on full symbol calculus and Berezin integration.- December 16:
*No seminar*

The seminar will resume its work in February 2011.

**
Merry Christmas!
**

*Ted Voronov. 8 (21) December 2010*