Everyone is welcome to attend. Refreshments will be served in the Math Lounge before the exam.
Tuesday, April 25, 2017
PhD Candidate: Yiannis Loizides
Supervisor: Eckhard Meinrenken
Thesis title: Norm-square localization for Hamiltonian LG-spaces
In this thesis we prove norm-square localization formulas for two invariants of Hamiltonian loop group spaces: twisted Duistermaat-Heckman measures and a K-theoretic `quantization’. The terms in the formulas are indexed by the components of the critical set of the norm-square of the moment map. These results are analogous to results proved by Paradan in the case of Hamiltonian G-spaces. An important application of the norm-square localization formula is to prove that the multiplicity of the fundamental level k representation in the quantization is a quasi-polynomial function of k. This is closely related to the [Q,R]=0 theorem of Alekseev-Meinrenken-Woodward for Hamiltonian loop group spaces.
A copy of the thesis can be found here: YLThesis