## Departmental PhD Thesis Exam – Trefor Bazett

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

Wednesday, May 11, 2016
11:10 a.m.
BA6183

PhD Candidate:  Trefor Bazett
Co-Supervisors:  Lisa Jeffrey/Paul Selick
Thesis title: The equivariant K-theory of commuting 2-tuples in SU(2)

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Abstract:

In this thesis, we study the space of commuting n-tuples in SU(2), $Hom(\mathbb{Z}^n, SU(2))$. We describe this space geometrically via providing an explicit G-CW complex structure, an equivariant analog of familiar CW- complexes. For the n=2 case, this geometric description allows us to compute various cohomology theories of this space, in particular the G-equivariant K-Theory $K_G^*(Hom(\mathbb{Z}^2, SU(2)))$, both as an $R(SU(2))$-module and as an $R(SU(2))$-algebra. This space is of particular interest as $\phi^{-1}(e)$ in a quasi-Hamiltonian system $M\xrightarrow{\phi} G$ consisting of the G-space $SU(2)\times SU(2)$, together with a moment map $\phi$ given by the commutator map. Finite dimensional quasi-Hamiltonian spaces have a bijective correspondence with certain infinite dimensional Hamiltonian spaces, and we additionally compute relevant components of this larger picture in addition to $\phi^{-1}(e)=Hom(\mathbb{Z}^2, SU(2))$ for this example.

A copy of the thesis can be found here: TreforBazettThesis