Seminars and Colloquia by Series

Monday, April 16, 2018 - 14:00 , Location: Skiles 006 , Ken Baker , University of Miami , Organizer: Caitlin Leverson
Based on the known examples, it had been conjectured that all L-space knots in S3 are strongly invertible.  We show this conjecture is false by constructing large families of asymmetric hyperbolic knots in S3 that admit a non-trivial surgery to the double branched cover of an alternating link.  The construction easily adapts to produce such knots in any lens space, including S1xS2.  This is joint work with John Luecke.
Monday, April 16, 2018 - 14:00 , Location: Skiles 006 , Ken Baker , University of Miami , Organizer: Caitlin Leverson
Based on the known examples, it had been conjectured that all L-space knots in S3 are strongly invertible.  We show this conjecture is false by constructing large families of asymmetric hyperbolic knots in S3 that admit a non-trivial surgery to the double branched cover of an alternating link.  The construction easily adapts to produce such knots in any lens space, including S1xS2.  This is joint work with John Luecke.
Monday, April 9, 2018 - 14:00 , Location: Skiles 006 , Bahar Acu , Northwestern University , Organizer: John Etnyre
Planar contact manifolds have been intensively studied to understand several aspects of 3-dimensional contact geometry. In this talk, we define "iterated planar contact manifolds", a higher-dimensional analog of planar contact manifolds, by using topological tools such as "open book decompositions" and "Lefschetz fibrations”. We provide some history on existing low-dimensional results regarding Reeb dynamics, symplectic fillings/caps of contact manifolds and explain some generalization of those results to higher dimensions via iterated planar structure. This is partly based on joint work in progress with J. Etnyre and B. Ozbagci.
Monday, April 9, 2018 - 14:00 , Location: Skiles 006 , Bahar Acu , Northwestern University , Organizer: John Etnyre
Planar contact manifolds have been intensively studied to understand several aspects of 3-dimensional contact geometry. In this talk, we define "iterated planar contact manifolds", a higher-dimensional analog of planar contact manifolds, by using topological tools such as "open book decompositions" and "Lefschetz fibrations”. We provide some history on existing low-dimensional results regarding Reeb dynamics, symplectic fillings/caps of contact manifolds and explain some generalization of those results to higher dimensions via iterated planar structure. This is partly based on joint work in progress with J. Etnyre and B. Ozbagci.
Monday, April 2, 2018 - 14:00 , Location: Skiles 006 , Linh Truong , Columbia University , Organizer: Jennifer Hom
Heegaard Floer homology has proven to be a useful tool in the study of knot concordance. Ozsvath and Szabo first constructed the tau invariant using the hat version of Heegaard Floer homology and showed it provides a lower bound on the slice genus. Later, Hom and Wu constructed a concordance invariant using the plus version of Heegaard Floer homology; this provides an even better lower-bound on the slice genus. In this talk, I discuss a sequence of concordance invariants that are derived from the truncated version of Heegaard Floer homology. These truncated Floer concordance invariants generalize the Ozsvath-Szabo and Hom-Wu invariants. 
Monday, April 2, 2018 - 14:00 , Location: Skiles 006 , Linh Truong , Columbia University , Organizer: Jennifer Hom
Heegaard Floer homology has proven to be a useful tool in the study of knot concordance. Ozsvath and Szabo first constructed the tau invariant using the hat version of Heegaard Floer homology and showed it provides a lower bound on the slice genus. Later, Hom and Wu constructed a concordance invariant using the plus version of Heegaard Floer homology; this provides an even better lower-bound on the slice genus. In this talk, I discuss a sequence of concordance invariants that are derived from the truncated version of Heegaard Floer homology. These truncated Floer concordance invariants generalize the Ozsvath-Szabo and Hom-Wu invariants. 
Monday, March 26, 2018 - 14:30 , Location: Room 304 , Bob Gompf and Sergei Gukov , UT Austin and Cal Tech , Organizer: Caitlin Leverson
For oriented manifolds of dimension at least 4 that are simply connected at infinity, it is known that end summing (the noncompact analogue of boundary summing) is a uniquely defined operation. Calcut and Haggerty showed that more complicated fundamental group behavior at infinity can lead to nonuniqueness. We will examine how and when uniqueness fails. There are examples in various categories (homotopy, TOP, PL and DIFF) of nonuniqueness that cannot be detected in a weaker category. In contrast, we will present a group-theoretic condition that guarantees uniqueness. As an application, the monoid of smooth manifolds homeomorphic to R^4 acts on the set of smoothings of any noncompact 4-manifold. (This work is joint with Jack Calcut.)
Monday, March 26, 2018 - 14:30 , Location: Room 304 , Bob Gompf and Sergei Gukov , UT Austin and Cal Tech , Organizer: Caitlin Leverson
For oriented manifolds of dimension at least 4 that are simply connected at infinity, it is known that end summing (the noncompact analogue of boundary summing) is a uniquely defined operation. Calcut and Haggerty showed that more complicated fundamental group behavior at infinity can lead to nonuniqueness. We will examine how and when uniqueness fails. There are examples in various categories (homotopy, TOP, PL and DIFF) of nonuniqueness that cannot be detected in a weaker category. In contrast, we will present a group-theoretic condition that guarantees uniqueness. As an application, the monoid of smooth manifolds homeomorphic to R^4 acts on the set of smoothings of any noncompact 4-manifold. (This work is joint with Jack Calcut.)
Monday, March 19, 2018 - 13:55 , Location: Skiles 006 , None , None , Organizer: Dan Margalit
Monday, March 19, 2018 - 13:55 , Location: Skiles 006 , None , None , Organizer: Dan Margalit

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