Monday, November 5, 2018 - 13:00 , Location: Skiles 006 , Min Hoon Kim , Korea Institute for Advanced Study , Organizer: Jennifer Hom
In 1982, by using his celebrated disk embedding theorem, Freedman classified simply connected topological 4-manifolds up to homeomorphism. The disk embedding conjecture says that the disk embedding theorem holds for general 4-manifolds with arbitrary fundamental groups. The conjecture is a central open question in 4-manifold topology. In this introductory survey talk, I will briefly discuss Freedman's disk embedding conjecture and some related conjectures (the topological 4-dimensional surgery conjecture and the s-cobordism conjecture). I will also explain why the disk embedding conjecture implies that all good boundary links are freely slice.
Monday, October 15, 2018 - 00:45 , Location: Skiles 006 , Lev Tovstopyat-Nelip , Boston College , Organizer: John Etnyre
We explain the (classical) transverse Markov Theorem which relates transverse links in the tight three sphere to classical braid closures. We review an invariant of such transverse links coming from knot Floer homology and discuss some applications which appear in the literature.
Monday, September 24, 2018 - 13:00 , Location: Skiles 006 , Miriam Kuzbary , Rice University , Organizer: Jennifer Hom
In this introductory talk I will outline the general landscape of Milnor’s invariants for links. First introduced in Milnor’s master’s thesis in 1954, these invariants capture fundamental information about links and have remained a fascinating object of study throughout the past half century. In the early 80s, Turaev and Porter independently proved their long-conjectured correspondence with Massey products of the link complement and in 1990, Tim Cochran introduced a beautiful construction to compute them using intersection theory. I will give an overview of these constructions and motivate the importance of these invariants, particularly for the study of links considered up to concordance.