Talk #1 (1:00-2:15pm)
Caleb Suan, University of British Columbia
"Conifold Transitions, Balanced Metrics, and Stability"
Conifold transitions are a general procedure for constructing new complex 3-folds from a compact Kähler Calabi-Yau 3-fold by contracting disjoint (-1,-1)-curves and smoothing the resulting ODP singularities. Though we begin with a Kähler manifold, the manifolds that we get may not stay Kähler, which may suggest that we should seek a more "general notion of Kähler". In this talk, we outline the geometry of conifold transitions and discuss results in this direction such as the balanced metrics of Fu-Li-Yau and the more recent stability results of Collins-Picard-Yau.
Talk #2 (2:30-4:00pm)
Aïssa Wade, Department of Pure Mathematics, University of Waterloo
"On the stability of symplectic leaves of Poisson manifolds"
A regular symplectic foliation on a smooth manifold M is a (regular) foliation $\mathfrak F$ on M together with a foliated 2-form $\omega$ whose restriction to each leaf S is a symplectic form $\omega_S$. Any regular symplectic foliation determines a regular Poisson structure on M. However a more interesting class of Poisson structures is that of Poisson structures corresponding to irregular symplectic foliations (i.e. the dimensions of the leaves vary). In this talk, I will present some results on the stability problem for compact leaves of Poisson manifolds. First I will review Poisson manifolds and their symplectic leaves. Then, I will explain the geometric data that encode the Poisson structure in a tubular neighborhood of a symplectic leaf S. Finally, I will explain some cohomology criterion for stability of symplectic leaves.
MC 5403