Georgia Institute of Technology College of Sciences

Algebraic torsion is a means of understanding the topological complexity of certain homomorphic curves counted in some Floer theories of contact manifolds.  This talk focuses on algebraic torsion and the contact invariant in embedded contact homology, useful for obstructing symplectic fillability and overtwistedness of the contact 3-manifold, but mostly left unexplored. We discuss results for concave linear plumbings of symplectic disk bundles over spheres admitting a concave contact boundary, whose boundaries are contact lens spaces.  We explain our curve counting methods in terms of the Reeb dynamics and their parallel with the topological contact toric description of these lens spaces. This talk is based on joint work with Aleksandra Marinkovic, Ana Rechtman, Laura Starkston, Shira Tanny, and Luya Wang.  Time permitting, we will discuss exploration of our methods to find nonfillable tight contact 3-manifolds obtained from more general plumbings.