Search Research Symposium Abstracts

Twist positivity, L-space knots, and concordance

In this talk, I’ll describe a braid word theoretic property, called “twist positivity”, which often puts strong restrictions on quantitative and geometric properties of a braid. I’ll describe some old and new results about twist positivity, as well as some new applications towards knot concordance. In particular, I’ll describe how using a suite of [Read More...]

Presenter: Siddhi Krishna, Columbia University
Authors: Hugh Morton, Siddhi Krishna
Symposium Year: 2023
Session: Progress in low-dimensional topology [Organized by Akram Alishahi, Jennifer Hom, Feride Ceren Kose, Gordana Matic, and Hannah Turner]
Presentation Time: October 1, 2023; 9:45 am

JSJ decomposition of knot exteriors, Dehn surgeries, and the L-space conjecture

In this talk, we study the properties of Dehn surgeries on satellite knots in the context of the L-space conjecture using slope detections. We show that if a satellite knot admits a Dehn surgery which produces an irreducible 3-manifold of non-left-orderable fundamental group, then the JSJ graph of its exterior must be homeomorphic to an interval. As a [Read More...]

Presenter: Ying Hu, University of Nebraska Omaha
Authors: Steve Boyer, Cameron Gordon, Ying Hu
Symposium Year: 2023
Session: Progress in low-dimensional topology [Organized by Akram Alishahi, Jennifer Hom, Feride Ceren Kose, Gordana Matic, and Hannah Turner]
Presentation Time: October 1, 2023; 10:10 am

Upsilon Torsion and barcode complexes

Recent work by a number of authors has found that torsion of a certain type in the homology of the curved Heegaard Floer knot complex provides a constraint on the number of maxima and minima in cobordisms between knots and, in particular, on the number of minima of slice disks for knots. One such invariant is Ord_v(K) described by Juhasz-Miller-Zemke. We [Read More...]

Presenter: Samantha Allen, Duquesne University
Authors: Samantha Allen, Charles Livingston, Misha Tyomkin, and C.M. Michael Wong
Symposium Year: 2023
Session: Progress in low-dimensional topology [Organized by Akram Alishahi, Jennifer Hom, Feride Ceren Kose, Gordana Matic, and Hannah Turner]
Presentation Time: October 1, 2023; 10:35 am

Four-ball genus bounds from the 11/8 Theorem

We give a new lower bound on the smooth 4-genus of knots, which we derive from the 10/8 + 4 theorem of Hopkins, Lin, Shi, and Xu. I'll state the result and show how it can be applied to bound the four-genus of certain satellite knots. Joint work with Gordana Matic and Linh [Read More...]

Presenter: Alexandra Kjuchukova, University of Notre Dame
Symposium Year: 2023
Session: Progress in low-dimensional topology [Organized by Akram Alishahi, Jennifer Hom, Feride Ceren Kose, Gordana Matic, and Hannah Turner]
Presentation Time: October 1, 2023; 11:00 am

Heegaard Floer homology and plane curves with non-cuspidal singularities

It is an interesting question to ask about the possible configurations of singular points occurring on general algebraic curves. In this talk, we use Heegaard Floer homology to study the singularity links and give some obstructions for the configurations. The main ingredient is to use the knot Floer complex of the knotification of the singularities links in [Read More...]

Presenter: Beibei Liu, The Ohio State university
Authors: Maciej Borodzik, Beibei Liu, Ian Zemke
Symposium Year: 2023
Session: Progress in low-dimensional topology [Organized by Akram Alishahi, Jennifer Hom, Feride Ceren Kose, Gordana Matic, and Hannah Turner]
Presentation Time: October 1, 2023; 2:00 pm

Branched double covers of links in the 3-sphere, involutions, and bordered Floer theory

Branched double covers $\Sigma_2(L)$ of links $L$ in the 3-sphere are a nice tractable class of 3-manifolds that can be studied using Heegaard Floer theory. In this talk, we will discuss recent work to compute the Heegaard Floer $d$-invariants of $\Sigma_2(L)$ for $L$ a 2-component plumbing link, using involutions and tools from bordered Floer theory. We [Read More...]

Presenter: Biji Wong, Duke University
Symposium Year: 2023
Session: Progress in low-dimensional topology [Organized by Akram Alishahi, Jennifer Hom, Feride Ceren Kose, Gordana Matic, and Hannah Turner]
Presentation Time: October 1, 2023; 2:25 pm

Singular fibers in algebraic fibrations of genus two and their monodromy factorizations

Kodaira classified all singular fibers that can arise in algebraic elliptic fibrations. Later, Ogg, Iitaka and then Namikawa and Ueno gave a classification for genus two fibrations. In this work, we split these algebraic genus two fibrations into Lefschetz fibrations and determine the monodromies. More specifically, we look at four families of hypersurface [Read More...]

Presenter: Sumeyra Sakalli, University of Arkansas
Authors: Sumeyra Sakalli and Jeremy Van Horn-Morris
Symposium Year: 2023
Session: Progress in low-dimensional topology [Organized by Akram Alishahi, Jennifer Hom, Feride Ceren Kose, Gordana Matic, and Hannah Turner]
Presentation Time: October 1, 2023; 2:50 pm

Algorithms for Computing Invariants of Trisected Branched Covers

We give diagrammatic algorithms for computing the group trisection, homology groups, and intersection form of a 4-manifold, presented as a branched cover of a bridge-trisected surface in S^4. The algorithm takes as input a tri-plane diagram, labelled with permutations according to the Wirtinger relations. We apply our algorithm to several examples, [Read More...]

Presenter: Patricia Cahn, Smith College
Authors: Akram Alishahi, Patricia Cahn, Gordana Matic, Juanita Pinzón-Caicedo, and Ben Ruppik
Symposium Year: 2023
Session: Progress in low-dimensional topology [Organized by Akram Alishahi, Jennifer Hom, Feride Ceren Kose, Gordana Matic, and Hannah Turner]
Presentation Time: October 1, 2023; 3:15 pm