Special Year 2015-16: Geometric Structures on 3-manifolds

An interesting aspect of the classification of symplectic fillings of Seifert fibered spaces is the appearance of complex and symplectic line arrangements in CP2. Line arrangements have been studied classically for decades and have intricate...

A well known result of Eliashberg and Thurston states that smooth foliations can be approximated by contact structures. We discuss the uniqueness of this contact structure and applications.

I will discuss a Smith-type inequality for regular covering spaces in monopole Floer homology. Using the monopole Floer / Heegaard Floer correspondence, it follows that if a 3-manifold Y admits a p^n-sheeted regular cover that is a Z/p-L-space (for...

We obtain a simple topological and dynamical systems condition which is necessary and sufficient for an arbitrary pseudo-Anosov flow in a closed, hyperbolic three manifold to be quasigeodesic. Quasigeodesic means that orbits are efficient in...

The modern development of contact geometry in 3 dimensions has seen several (due to Giroux, Wendl, Latschev and Wendl, Hutchings, and others) invariants of contact structures meant in some sense to measure non-(Stein /symplectic)-fillability of the...

We give new constraints on the topology of symplectic four-manifolds using invariants from Heegaard Floer homology. In particular, we will prove that certain simply-connected four-manifolds with positive-definite intersection forms cannot admit...

We use contact deformations to study the topology of the space of taut foliations and group actions on the circle.

A bold conjecture of Boyer-Gorden-Watson and others posit that for any irreducible rational homology 3-sphere M the following three conditions are equivalent: (1) the fundamental group of M is left-orderable, (2) M has non-minimal Heegaard Floer...

A theorem of Borel's asserts that for any positive real number $V$, there are at most finitely many arithmetic lattices in ${\rm PSL}_2({\mathbb C})$ of covolume at most $V$, or equivalently at most finitely many arithmetic hyperbolid $3$-orbifolds...