Spring 2024 Schedule


Date Speaker Title and abstract
25-Jan Organizational Meeting
15-Feb Katherine Raoux (University of Arkansas) A 4-dimensional rational genus bound
The minimal genus question asks: “What is the minimum genus of a surface representing a particular 2-dimensional homology class?” Historically, minimal genus questions have focused on 2-dimensional homology with integer coefficients. In this talk, we study a minimal genus question for homology classes with Q mod Z coefficients. We define the rational 4-genus of knots and present a lower bound in terms of Heegaard Floer tau invariants. Our bound also leads to PL slice genus bounds. This is joint work with Matthew Hedden.
21-Mar No meeting (Spring Break)
28-Mar Steve Trettel (University of San Francisco) Informal geometry discussion followed by Colloquium at 3:30pm.
4-Apr Luya Wang* (Stanford University) Deformation inequivalent symplectic structures and Donaldson's four-six question (on Zoom)
Studying symplectic structures up to deformation equivalences is a fundamental question in symplectic geometry. Donaldson asked: given two homeomorphic closed symplectic four-manifolds, are they diffeomorphic if and only if their stabilized symplectic six-manifolds, obtained by taking products with CP^1 with the standard symplectic form, are deformation equivalent? I will discuss joint work with Amanda Hirschi on showing how deformation inequivalent symplectic forms remain deformation inequivalent when stabilized, under certain algebraic conditions. This gives the first counterexamples to one direction of Donaldson’s “four-six” question and the related Stabilizing Conjecture by Ruan. In the other direction, I will also discuss more supporting evidence via Gromov-Witten invariants.
11-Apr Jorge Robinson Arrieta (University of Arkansas) ** Special Time: 3:30-4:30 PM in SCEN 322**
An explicit section of the Laudenbach exact sequence of the mapping class group of connect sums of S2 x S1.
Laudenbach proved that the mapping class group of the connect sum of n copies of S2 x S1 is an extension of Out(Fn) by a finite group. Brendle-Broaddus-Putman proved that this exact sequence splits. We provide an explicit section s of this split exact sequence. In this talk, we will introduce mapping class groups and develop necessary background in order to show that this sequence splits.
18-Apr Marco Marengon (Alfréd Rényi Institute of Mathematics) Splitting Links by Integer Homology Spheres
For every n≥3, we construct links in Sn+1 which are split by an integer homology n-sphere, but not by the standard Sn. This is joint work with Marco Golla.
2-May Hyunki Min (University of California Los Angeles) Tight contact structures on hyperbolic L-spaces (on Zoom)
The classification of contact structures is one of the interesting problems in low-dimensional contact topology. In this talk, we will give an overview of the classification of tight contact structures. We will first discuss the general strategy and the classification of tight contact structures on Seifert fibered spaces. After that, we will talk about the classification of tight contact structures on hyperbolic 3-manifolds, particularly hyperbolic L-spaces. This is a joint work with Isacco Nonino.
3-May Agivna Roy (Louisiana State University) ** Special Day/Time: Friday 1pm **
Symplectic fillings of spinal open books with exotic fibers (on Zoom)
The technique of spinal open books, introduced by Lisi - Van Horn-Morris - Wendl, describes strong symplectic fillings of planar spinal manifolds in terms of foliations by pseudoholomorphic curves. These foliation descriptions, in the broadest generality, contain singular curves, similar to Lefschetz-type singularities, and also another type of singular object called exotic curves. In the Lefschetz-amenable setting, exotic curves disappear, and fillings can be classified as Lefschetz fibrations, depending on the number of singular curves. In this talk I will talk about ongoing work where we give a topological description of these exotic curves in terms of identifying them with a local model, give a count of exotic fibers in any filling, and use these to classify symplectic fillings of certain planar spinal open books that are not Lefschetz-amenable.


For Zoom access contact the organizers: Katherine Raoux or Sumeyra Sakalli .



Heegaard Floer Learning Seminar

We are reading Jen Hom's Lecture Notes from PCMI.

Date Speaker/Topic
1-Feb Watch Jen Hom's 2019 PCMI Lectures: Lecture 1.1 and Lecture 1.2
8-Feb Exercises and discussion -- Section 1 of Lecture Notes. .
22-Feb Watch Jen Hom's 2019 PCMI Lectures: Lecture 2.1 and Lecture 2.2
29-Feb Exercises and discussion -- Section 2 of Lecture Notes .
7-Mar Exercises and discussion -- Section 2 cont.
14-Mar
21-Mar No meeting (Spring Break)
4-Apr
11-Apr
25-Apr
2-May