Schedule
Abstracts are below.
Talks are in 201 Crow, and breakfast/coffee/tea are in the Math Lounge in Cupples I.
Friday, May 17
8:15-9:00 Bagels, coffee, etc.
9:00-10:00 Danny Calegari: Zippers
10:00-10:30 Coffee break
10:30-11:30 Lightning talk session
11:30-1:30 Lunch
1:30-2:30 David Gabai: Peeking into the heart of a pseudo-isotopy
2:45-3:45 Ying Hu: Foliations, flows, and detecting slopes
4:00-5:00 Early Career Panel
6:00-6:45 Cocktails/refreshments at the St. Louis Art Museum
6:45 Dinner at the St. Louis Art Museum (museum closes at 9)
Saturday, May 18
8:15-9:00 Bagels, coffee, etc.
9:00-10:00 Anna Parlak: Surfaces in 3-manifolds that are transverse to two topologically inequivalent flows
10:00-10:30 Coffee/tea break
10:30-11:30 Ian Agol: Chainmail links and L-spaces
11:30-1:30 Lunch break
1:30-2:30 Chi Cheuk Tsang: Pseudo-Anosov flows, finite depth foliations, and veering branched surfaces
2:45-3:45 Beibei Liu: Heegaard Floer homology of plumbed L-space links
4:00-5:00 Mehdi Yazdi: The algorithmic complexity of incompressible surfaces in 3-manifolds
Sunday, May 19
8:15-9:00 Bagels, coffee, etc.
9:00-10:00 Thomas Barthelmé: Promoting prelaminations
10:00-10:30 Coffee/tea
10:30-11:30 Samuel Taylor: Transverse surfaces and pseudo-Anosov flows
11:30-1:30 Lunch
1:30-2:30 Eriko Hironaka: Ferris Wheel Mapping Classes and the "shape" of small dilatation pA maps
2:45-3:45 Nathan Dunfield: Applications of the SL(2, R) Casson-Lin invariant to ordering 3-manifold groups
Abstracts (in order of schedule)
Danny Calegari: Zippers
Abstract: I will describe a new and streamlined approach to the construction of universal circles for various structures on hyperbolic 3-manifolds, together with some examples. This is joint work with Ino Loukidou.
David Gabai: Peeking into the heart of a pseudo-isotopy
Abstract: We start by giving a brief introduction to pseudo-isotopy theory. Then by examining a pseudo-isotopy of a 4-manifold presented as a Hatcher-Wagoner nested eye we see that the associated diffeomorphism is stably isotopic to id. Conversely a stable isotopy gives a recipe for constructing a nested eye presentation.
Ying Hu: Foliations, flows, and detecting slopes
Abstract: The idea of detecting slopes on the boundary of a knot manifold using foliations, left-orders, and Floer homologies was originally introduced by Boyer and Clay to study the L-space conjecture for toroidal 3-manifolds. In this talk, we will give a brief introduction to the topological and algebraic background related to slope detections. We will then focus our discussion on the applications of different universal circle actions derived from taut foliations and pseudo-Anosov flows in detecting slopes by orders. This is joint work with Steve Boyer and Cameron Gordon.
Anna Parlak: Surfaces in 3-manifolds that are transverse to two topologically inequivalent flows
Abstract: Veering triangulations are ideal triangulations of cusped hyperbolic 3-manifolds that are very closely connected to pseudo-Anosov flows. Namely, by the work of Agol-Gueritaud, one can construct a veering triangulation from any pseudo-Anosov flow and a suitable collection of closed orbits of that flow. Conversely, by the work of Agol-Tsang and Schleimer-Segerman, a pseudo-Anosov flow can be constructed from any veering triangulation and appropriate Dehn filling data.
Recently, I used veering triangulations to find surfaces embedded in 3-manifolds which are transverse to two topologically inequivalent (pseudo)-Anosov flows. Some of the examples are related by an operation called a veering mutation. In my talk, I will focus on explaining this construction and discuss a few examples of homeomorphic veering mutants and their underlying flows.
Ian Agol: Chainmail links and L-spaces
Abstract: We prove that alternating chainmail links are L-space links. The proof is inspired by corresponding proofs for double branched covers of alternating links which are surgeries on alternating chainmail links. We also (more generally) show that flat augmented chainmail links are generalized L-space links. This implies that every 3-manifold is surgery on a generalized L-space link, answering a question of Yajing Liu. Some other properties of these links are also considered.
Chi Cheuk Tsang: Pseudo-Anosov flows, finite depth foliations, and veering branched surfaces
Abstract: Gabai and Mosher showed that for every finite depth foliation on an orientable, irreducible, atoroidal 3-manifold, there is an almost transverse pseudo-Anosov flow. In this talk, we describe progress on a joint project with Michael Landry in upgrading this result to pseudo-Anosov flow without perfect fits. The motivation for this project comes from an attempt to understand the Thurston norm unit ball using pseudo-Anosov flows. The main part of the talk will be focused on explaining the motivation of the project, as well as our completed work on the 'base case' and its applications to foliation cones. If time permits, we will outline our goals for the next stage of the project --- the 'gluing step'.
Beibei Liu: Heegaard Floer homology of plumbed L-space links
Abstract: The well known L-space conjecture proposed a connection between Heegaard Floer homology of closed orient 3-manifolds, the left orderability of its fundamental group, and the existence of taut foliation. I will focus on the Heegaard Floer homology side of this conjecture. Every closed 3-manifold is obtained by Dehn surgeries on some links in S^3, so we will focus on the Heegaard Floer theory on links in S^3. The computation becomes very complicated when the number of components of links increases, however, we find for the plumbed L-space links, there is a simple and practical algorithm to compute the Heegaard Floer package. Part of this talk is joint work with Borodzik and Zemke.
Mehdi Yazdi: The algorithmic complexity of incompressible surfaces in 3-manifolds
Abstract: A two-sided properly embedded surface in a compact 3-manifold is called incompressible if its fundamental group is injectively included in that of the ambient 3-manifold. Irreducible 3-Manifolds that contain an incompressible surface are called Haken. Many important results in 3-manifold topology and geometry were first obtained for Haken 3-manifolds, such as solution to the homeomorphism problem and Thurston's hyperbolisation theorem. We consider the algorithmic complexity of the following decision problem: given a triangulated closed orientable 3-manifold M and an integer g in binary, does M contain a closed incompressible surface of genus g? We show that the above decision problem is NP-complete. This is joint work with Marc Lackenby and Eric Sedgwick.
Thomas Barthelmé: Promoting prelaminations
Abstract: Given a topological plane equipped with two transverse, possibly singular, foliations, one can build a natural, unique, circle boundary to the plane such that each (non singular) leaf of the foliations end at two distinct points on the boundary. In this talk, I'll present a characterization of which sets of pair of points on the circle can be completed into a bifoliation of the plane. This is joint work with C. Bonatti and K. Mann.
Samuel Taylor: Transverse surfaces and pseudo-Anosov flows
Abstract: I’ll discuss joint work with Michael Landry and Yair Minsky that characterizes the surfaces in a compact 3-manifold M that are (almost) transverse to a fixed transitive pseudo-Anosov flow. Our main tool is a general correspondence between surfaces that are almost transverse to the flow and those that are “relatively carried” by any associated veering triangulation. The correspondence also allows us to investigate the uniqueness of almost transverse position, to extend Mosher's Transverse Surface Theorem to the case with boundary, and more generally to characterize when relative homology classes represent Birkhoff surfaces of the flow.
Eriko Hironaka: Ferris Wheel Mapping Classes and the "shape" of small dilatation pA maps
Abstract: In this talk we discuss the question: what do small dilatation pseudo-Anosov mapping classes look like? More precisely we consider fully-punctured pseudo-Anosov mapping classes f : S —> S such that the dilatation raised to the absolute value of the Euler characteristic is bounded. The first sequence of such examples is due to Penner (1990s), and led to the (still open) question of whether up to a bounded distortion, small dilatation mapping classes look like "rotating wheels". In this talk we give an alternative construction of small dilatation mapping classes and some classical and recent results that support the conjecture that these Ferris Wheel maps provide a general picture of the "shape" of small dilatation pseudo-Anosov maps.
Nathan Dunfield: Applications of the SL(2, R) Casson-Lin invariant to ordering 3-manifold groups
Abstract: When M is the exterior of a knot K in the 3-sphere, Lin showed that the signature of K can be viewed as a Casson-style signed count of the SU(2) representations of pi_1(M) where the meridian has trace 0. This was later generalized to the fact that signature function of K on the unit circle counts SU(2) representations as a function of the trace of the meridan. I will define the SL(2, R) analog of these Casson-Lin invariants, and explain how it interacts with the original SU(2). I will use the new invariant to study left-orderability of Dehn fillings on M using the translation extension locus I introduced with Marc Culler, and also give a new proof of a theorem of Gordon’s on parabolic SL(2, R) representations of two-bridge knot groups. This is joint work with Jake Rasmussen. Based on https://arxiv.org/abs/2209.03382