## Departmental PhD Thesis Exam – Yiannis Loizides

Everyone is welcome to attend.  Refreshments will be served in the Math Lounge before the exam.

Tuesday, April 25, 2017
2:10 p.m.
BA6183

PhD Candidate:  Yiannis Loizides
Supervisor:  Eckhard Meinrenken
Thesis title:  Norm-square localization for Hamiltonian LG-spaces

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Abstract:

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