Departmental PhD Thesis Exam – Selim Tawfik

Monday, January 11, 2021
1:00 p.m.

PhD Candidate:  Selim Tawfik
Supervisor:   Eckhard Meinrenken
Thesis title:  Fusion Product of D/G-Valued Moment Maps

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A fusion product is defined for Hamiltonian spaces with moment maps valued in a Lie group $D$ generalizing those of Alekseev-Malkin-Meinrenken. An analogous theory for these general Hamiltonian spaces is developed and, among other results, versions of symplectic reduction, duality and the shifting trick are derived. The Hamiltonian spaces with moment maps valued in a homogeneous space $D/G$ of Alekseev-Kosmann-Schwarzbach are shown to be equivalent to certain Hamiltonian spaces with group-valued moment maps. The aforementioned theory is consequently brought to bear on that of $D/G$-valued moment maps, thereby defining a fusion product for these. This fusion product affords many new examples of $D/G$-valued moment maps, of which there was hitherto a paucity. Among said examples are moduli spaces of flat principal bundles over certain surfaces with boundary.

A copy of the thesis can be found here: main