Seminars and Colloquia by Series

Monday, April 22, 2019 - 15:30 , Location: Skiles 006 , Eli Grigsby , Boston College , Organizer: Caitlin Leverson
Monday, April 22, 2019 - 14:00 , Location: Skiles 006 , Adam Levine , Duke University , Organizer: Caitlin Leverson
Given an m-dimensional manifold M that is homotopy equivalent to an n-dimensional manifold N (where n<m), a spine of M is a piecewise-linear embedding of N into M (not necessarily locally flat) realizing the homotopy equivalence. When m-n=2 and m>4, Cappell and Shaneson showed that if M is simply-connected or if m is odd, then it contains a spine. In contrast, I will show that there exist smooth, compact, simply-connected 4-manifolds which are homotopy equivalent to the 2-sphere but do not contain a spine (joint work with Tye Lidman). I will also discuss some related&nbsp;results about PL concordance of knots in homology spheres (joint with Lidman and Jen Hom).
Monday, April 15, 2019 - 14:00 , Location: Skiles 006 , Patrick Orson , Boston College , Organizer: JungHwan Park
Monday, April 8, 2019 - 14:00 , Location: Skiles 006 , Tye Lidman , NCSU , Organizer: Jennifer Hom
Wednesday, April 3, 2019 - 14:00 , Location: Skiles 006 , Peter Feller , ETH Zurich , Organizer: JungHwan Park
Monday, April 1, 2019 - 14:00 , Location: Skiles 006 , Ahmad Issa , University of Texas, Austin , Organizer: Jennifer Hom
Monday, March 25, 2019 - 16:00 , Location: Boyd , Christine Ruey Shan Lee , University of South Alabama , Organizer: Caitlin Leverson
Monday, March 25, 2019 - 14:30 , Location: Boyd , Nathan Dowlin , Dartmouth , Organizer: Caitlin Leverson
Khovanov homology and knot Floer homology are two knot invariants which are defined using very different techniques, with Khovanov homology having its roots in representation theory and knot Floer homology in symplectic geometry. However, they seem to contain a lot of the same topological data about knots. Rasmussen conjectured that this similarity stems from a spectral sequence from Khovanov homology to knot Floer homology. In this talk I will give a construction of this spectral sequence. The construction utilizes a recently defined knot homology theory HFK_2 which provides a framework in which the two theories can be related.
Monday, March 18, 2019 - 14:00 , Location: Skiles 006 , None , None , Organizer: John Etnyre
Monday, March 11, 2019 - 14:00 , Location: Skiles 154 , Hannah Schwartz , Bryn Mawr , Organizer: John Etnyre

It is well known that two knots in S^3 are ambiently isotopic if and only if there is an orientation preserving automorphism of S^3 carrying one knot to the other. In ;this talk, we will examine a family of smooth 4-manifolds in which the analogue of this fact does not hold, i.e. each manifold contains a pair of smoothly embedded, homotopic 2-spheres that are related by a diffeomorphism, but are not smoothly isotopic. In particular, the presence of 2-torsion in the fundamental groups of these 4-manifolds can be used to obstruct even a topological isotopy between the 2-spheres; this shows that Gabai's recent ``4D Lightbulb Theorem" does not hold without the 2-torsion hypothesis.