Morning Talk by Jacob Russell

Title: Convex cocompactness: from Kleinian groups to surface bundles

Abstract: Farb and Mosher defined the convex cocompact subgroups of the mapping class group in analogy with convex cocompact groups of isometries of hyperbolic space. We will detail the remarkable robustness of this analogy and highlight the surprising role convex cocompact subgroups play in the geometry of surface bundles.

Afternoon Talk by Jacob Russell

Title: Geometric finiteness in the mapping class group

Abstract: Mosher proposed that the analogy between convex cocompactness in the isometries of hyperbolic space and the mapping class group should extend to the geometrically finite groups of isometries of the hyperbolic space. While no consensus definition of geometric finiteness in the mapping class group has emerged, there are several classes of subgroups that ought to be geometrically finite from several different points of view. We will survey these subgroups with a focus on the stabilizers of multicurves on the surface.

Morning Talk by Kristen Hendricks

Title: Equivariant cohomology and Lagrangian Floer cohomology

Abstract: In this talk we review some facts about the Borel equivariant cohomology of spaces, give a quick introduction to Lagrangian Floer cohomology, and discuss a little of the history of constructing equivariant versions of Lagrangian Floer cohomology, along with the consequences of these constructions for low-dimensional topology and symmetries of knots and three-manifolds.

Afternoon Talk by Kristen Hendricks

Title: Symplectic annular Khovanov homology and knot symmetry

Abstract: Khovanov homology is a combinatorially-defined invariant which has proved to contain a wealth of geometric information. In 2006 Seidel and Smith introduced a candidate analog of the theory in Lagrangian Floer analog cohomology, which has been shown by Abouzaid and Smith to be isomorphic to the original theory over fields of characteristic zero. The relationship between the theories is still unknown over other fields. In 2010 Seidel and Smith showed there is a spectral sequence relating the symplectic Khovanov homology of a two-periodic knot to the symplectic Khovanov homology of its quotient; in contrast, in 2018 Stoffregen and Zhang used the Khovanov homotopy type to show that there is a spectral sequence from the combinatorial Khovanov homology of a two-periodic knot to the annular Khovanov homology of its quotient. (An alternate proof of this result was subsequently given by Borodzik, Politarczyk, and Silvero.) These results necessarily use coefficients in the field of two elements. This inspired investigations of Mak and Seidel into an annular version of symplectic Khovanov homology, which they defined over characteristic zero. In this talk we introduce a new, conceptually straightforward, formulation of symplectic annular Khovanov homology, defined over any field. Using this theory, we show how to recover the Stoffregen-Zhang spectral sequence on the symplectic side. This is joint work with Cheuk Yu Mak and Sriram Raghunath.