## Departmental PhD Thesis Exam – Jia Ji

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