Robert Lipshitz's 2017-2018 Tour

Dates and venues

Sept. 14
Syracuse, NY
(Syracuse Geometry & Topology Seminar)
The Alexander polynomial and knot Floer homology: properties, applications, and questions
Sept. 15
Buffalo, NY
(U. Buffalo Topology Day)
Bordered Heegaard Floer homology and incompressible surfaces
Oct. 4
Los Angeles, CA
(USC Colloquium)
Trivial tangles and Floer homology
Nov. 17, 18, or 19
Austin, TX
(Texas Geometry and Topology Conference)
TBD

Abstracts

September 14, Syracuse Geometry & Topology Seminar.
The Alexander polynomial and knot Floer homology: properties, applications, and questions
Abstract. After recalling the definition of the Alexander polynomial, we will describe a refinement, knot Floer homology, introduced by Ozsváth-Szabó and Rasmussen. We will then discuss some properties of the Alexander polynomial which have been lifted to knot Floer homology, some properties that have not been lifted, and some properties of knot Floer homology that seem not to be visible from the Alexander polynomial. Some applications will be interspersed throughout. Most of this is due to other people, but part is joint work with Ozsváth-Thurston, Treumann, or Hendricks-Sarkar.

September 15, University of Buffalo Toplogy Day.
Bordered Heegaard Floer homology and incompressible surfaces
Abstract. Heegaard Floer homology is an invariant of closed 3-manifolds and 4-manifolds with boundary; bordered Heegaard Floer homology is an extension of one variant of Heegaard Floer homology to 3-manifolds with boundary. After sketching some of the formal structure of these theories and some of their basic definitions, we will deduce from a theorem of Ni’s that bordered Heegaard Floer homology detects homologically essential compressing disks. Time permitting, we will also give a version of this statement for tangles, and talk about what a computer implementation of this algorithm looks like. This is joint work with Akram Alishahi, and builds on earlier joint work with Peter Ozsváth and Dylan Thurston.

October 4, University of Southern California Departmental Colloquium.
Trivial tangles and Floer homology
Abstract. Tangles are pieces of knots. After introducing tangles, two notions of equivalence for them, and some examples and (knot-theoretic) uses of them, we will sketch an invariant which can be used to check if tangles are boundary parallel---one notion of triviality for tangles. This is joint work with A. Alishahi, building on earlier work with P. Ozsváth and D. Thurston.


Previous years: 2015-2016, 2016-2017.