## Geometry in Representation Theory

### Autumn 2014

### Talks:

- 1st October,
**G-equivariant K-theory. ** (Vanessa Miemietz)

- 24th October,
**The cellular fibration of the Steinberg variety. ** (Vanessa Miemietz)

### Spring 2014

** In the spring semester, this study group will take place Fridays 2pm-3:30pm in S3.05.**

### Talks:

- 10th January,
**Lie-theoretic background and Bruhat decomposition. ** (Shaun Stevens)

- 17th January,
**The incidence variety of $\mathfrak{g}$ and $\mathcal{B}$. ** (Vanessa Miemietz)

- 24th January,
**The Chevalley restriction theorem. ** (Lewis Topley)

- 31st January,
**Grothendieck's simultaneous resolution. ** (Lewis Topley)

- 7th February,
**Springer resolution I. ** (Vanessa Miemietz)

- 14th February,
**Springer resolution II. ** (Vanessa Miemietz)

- 21st February,
**Stratified spaces. ** (Shaun Stevens)

- 28th February,
**Stratification of the nilpotent cone. ** (Shaun Stevens)

- 2nd June,
**Review session. ** (Vanessa Miemietz)

- 27th June,
**The Steinberg variety. ** (Vanessa Miemietz)

### Autumn 2013

** This study group takes place Fridays 1:30pm-3pm in S3.05. ****
I am giving all the talks, but it is nevertheless called a study group rather than a graduate lecture course, so as to not create any impression of me knowing what I am talking about!**

### Talks:

- 4th October,
**Motivation: Categorification. Flag variety, nilpotent cone and Steinberg variety. **

- 11th October,
**Manifolds and tangent spaces. **

- 18th October, no talk (Oxford conference).

- 25th October,
**Tangent and cotangent bundles, exterior derivative. **

- 1st November,
**Symplectic manifolds. **

- 8th November,
**Coadjoint orbits. **

- 18th November,
**Poisson algebras. **

- 22nd November,
**Coadjoint orbits revisited. **

- 29th November,
**Differential operators and regular functions on the cotangent bundle. **

- 6th December,
**(Co-)isotropic and lagrangian submanifolds. **

- 13th December,
**Hamiltonian group actions and the moment map. **

- 20th December,
**Explicit computations for the contangent bundle of G/P. **

### References

- Chriss, Neil; Ginzburg, Victor
*Representation theory and complex geometry.* Reprint of the 1997 edition. Modern Birkhäuser Classics. Birkhäuser Boston, Inc., Boston, MA, 2010.
- Broecker, Theodor; Jaenich, Klaus
* Introduction to differential topology.* Translated from the German by C. B. Thomas and M. J. Thomas. Cambridge University Press, Cambridge-New York, 1982.
- Taubes, Clifford Henry
* Differential Geometry.* Oxford Graduate Texts in Mathematics. Oxford University Press, Oxford, 2012.