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

Monday, June 17, 2019

12:10 p.m.

BA6183

PhD Candidate: Jia Ji

Supervisor: Lisa Jeffrey

Thesis title: Volume Formula and Intersection Pairings of N-fold Reduced Products

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Let $ G $ be a semisimple compact connected Lie group. An $ N $-fold reduced product of $ G $ is the symplectic quotient of the Hamiltonian system of the Cartesian product of $ N $ coadjoint orbits of $ G $ under diagonal coadjoint action of $ G $. Under appropriate assumptions, it is a symplectic orbifold. Using the technique of nonabelian localization and the residue formula of Jeffrey and Kirwan, we investigate the symplectic volume and the intersection pairings of an $ N $-fold reduced product of $ G $. In 2008, Suzuki and Takakura gave a volume formula of $ N $-fold reduced products of $ \mathbf{SU}(3) $ via Riemann-Roch.

We compare our volume formula with theirs and prove that up to normalization constant, our volume formula completely matches theirs in the case of triple reduced products of $ \mathbf{SU}(3) $.

The draft of the thesis can be found here: ut-thesis_Ji_draft_v1_1

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