Topology

Abstract: Exotic diffeomorphisms are those diffeomorphisms which are in the same path component as the identity of the homeomorphism group, but are not in the identity component in the diffeomorphism group. Several people have found the boundary Dehn twist is an exotic diffeomorphism…

Abstract: Webs are embedded trivalent graphs in the 3-sphere and foams are singular cobordisms between webs. I will talk about a construction of monopoleFloer homology for webs that is functorial under foam cobordisms.  The approach is based on Kronheimer and Mrowka’s monopole Floer…

Abstract: A famous unpublished theorem of Gabai and Mosher from the 90s states that every taut, finite depth foliation of a closed, oriented, atoroidal 3-manifold is almost transverse to a pseudo-Anosov flow. I will discuss the construction, and a slight refinement that is joint work in progress…

Abstract: Heegaard Floer homology and instanton Floer homology are packages of invariants in low dimensional topology constructed via symplectic topology and gauge theory respectively. Kronheimer and Mrowka conjecture that appropriate versions of the two invariants are equivalent. I will discuss…

Abstract: A slope p/q is characterizing for knot K if the resulting Dehn surgery determines K up to isotopy. Generalizing a question of Baker and Motegi, McCoy conjectured that for any knot, non-integral slopes p/q with |p|+|q| sufficiently large are characterizing. An advance towards this…

Abstract: In this talk, we define and state properties about a homological skein invariant constructed from Bar-Natan's deformation of Khovanov homology. We extend the notion of $H$-torsion order for Bar-Natan homology and corresponding results about internal stabilization distances of…

Abstract: In this talk, I will explain a recent result that pseudo-Anosov mapping classes are generic in every Cayley graph of mapping class groups. If time permits, I will also explain why this strategy goes well with quasi-isometries and implies genericity of Morse elements for groups…

Abstract: This talk will discuss an isomorphism between endomorphism algebras from the wrapped Fukaya category of a type of punctured surface, and a class of A-infinity algebras related to bordered knot Floer homology; see https://arxiv.org/abs/…

Abstract: There has been a great deal of interest in understanding which knots are characterized by which of their Dehn surgeries. We study a 4-dimensional version of this question: which knots are determined by which of their traces? We prove several results that are in stark contrast with what…

Abstract: Using a long-standing conjecture from combinatorial group theory, we explore, from multiple perspectives, the challenges of finding rare instances carrying disproportionately high rewards. Based on lessons learned in the context defined by the Andrews-Curtis conjecture, we propose…