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.