Georgia Institute of Technology College of Sciences

This series will tie together algebraic, complex analytic, symplectic, and contact geometries together in one coherent story. This will be done via the study of a series of couplets from different fields of geometry:

Algebraic manifolds:
Affine and quasi-projective varieties (non-compact models)
Projective varieties (compact models)

Complex manifolds:
Stein manifolds
Stein compactifications

Symplectic manifolds:
Liouville/ Weinstein geometry
Compact Kahler manifolds 

Depending on how long it takes to discuss these items, I will also attempt to include discussions on:

• Biran-Giroux decompositions of symplectic manifolds • Boothby-Wang bundles and contact plumbings of these • Milnor's fibration theorem for isolated singularities and connections to open book decompositions and Lefschetz fibrations • Open questions and interesting avenues of research

Most of our discussion will, as a side effect, outline the topological structure behind Type IIA String theory (the "topological A-model") which requires a 6-dimensional Calabi-Yau (Kahler) background.

This series will tie together algebraic, complex analytic, symplectic, and contact geometries together in one coherent story. This will be done via the study of a series of couplets from different fields of geometry:

Algebraic manifolds:
Affine and quasi-projective varieties (non-compact models)
Projective varieties (compact models)

Complex manifolds:
Stein manifolds
Stein compactifications

Symplectic manifolds:
Liouville/ Weinstein geometry
Compact Kahler manifolds 

Depending on how long it takes to discuss these items, I will also attempt to include discussions on:

• Biran-Giroux decompositions of symplectic manifolds • Boothby-Wang bundles and contact plumbings of these • Milnor's fibration theorem for isolated singularities and connections to open book decompositions and Lefschetz fibrations • Open questions and interesting avenues of research

Most of our discussion will, as a side effect, outline the topological structure behind Type IIA String theory (the "topological A-model") which requires a 6-dimensional Calabi-Yau (Kahler) background.

This series of talks will introduce the immersed curve perspective of knot Floer homology and give applications to to 3-manifold topology.

This series of talks will discuss connections between Riemannian geometry and contact topology. Both structures have deep connections to the topology of 3-manifolds, but there has been little study of the interactions between them (at least the implications in contact topology). We will see that there are interesting connections between curvature and properties of contact structures. The talks will give a brief review of both Riemannian geometry and contact topology and then discuss various was one might try to connect them. There will be many open problems discussed (probably later in the series).