Everyone is welcome to attend. Refreshments will be served in the Math Lounge before the exam.
Thursday, May 23, 2013
BA 6183, 40 St George St.
Ph.D. Candidate: Travis Li
Ph.D. Advisors: Marco Gualtieri, Lisa Jeffrey
Thesis Title: Constructions of Lie Groupoids
In this thesis, we develop two methods for constructing Lie groupoids.
The first method is a blow-up construction, corresponding to the elementary modification of a Lie algebroid along a subalgebroid over a hypersurface. This construction may be specialized to the Poisson groupoids and Lie bialgebroids. We then apply this method to the several cases. The first is the adjoint Lie groupoid integrating the Lie algebroid of vector fields tangent to a collection of normal crossing hypersurfaces. The second is the adjoint symplectic groupoid of a log symplectic manifold. The third is the adjoint Lie groupoid integrating the tangent algebroid of a Riemann surface twisted by a divisor.
The second method is a gluing construction, whereby Lie groupoids defined on the open sets of an appropriate cover may be combined to obtain global integrations. This allows us to construct and classify the Lie groupoids integrating a certain Lie algebroid. We apply this method to the aforementioned cases, albeit with slight differences. The first case is the cateogry of integrations of the Lie algebroid of vector fields tangent to a single smooth hypersurface.The second case is the category of Hausdorff symplectic groupoids of a log symplectic manifold. The third case is the category of integrations of the tangent algebroid of a Riemann surface twisted by a divisor.