Katie Mann: Codimension-1 Anosov flows on 4-manifolds

I will describe recent work with Sergio Fenley and Rafael Potrie to construct (infinitely many) new examples of smooth Anosov flows on 4-manifolds.  This will be essentially independent from Sergio's earlier talk on the subject (in particular that talk is not a prerequisite), focusing on the smooth setting rather than topological.  

Jonathan Zung: Obstructing transverse foliations

Given a pseudo-Anosov flow, one can ask whether or not there exists a codimension 1 foliation transverse to it. I'll try to explain the simplest obstruction I know, all without saying the V word.  

Qingfeng Lyu: Taut foliations from Heegaard splittings

The theory of constructing taut foliations from Heegaard splittings was initiated by Sarah Rasmussen and later developed by Tao Li using branched surfaces. This method has been proved successful for manifolds with small Heegaard genus. I’ll briefly sketch Li’s construction for manifolds with Heegaard genus 2, and show how we could apply the idea to (1,1) knots. In particular, we show that (1,1) non-L-space knots in the 3-sphere and lens spaces are persistently foliar.

Bojun Zhao: R-covered foliations from Dehn surgeries

R-covered foliations provide a natural geometric implication for the left-orderability of 3-manifold groups from taut foliations. In this talk, I will describe some constructions of R-covered foliations obtained by Dehn surgeries. I will focus on examples of such constructions in Dehn surgeries on the (-2,3,2q+1)-pretzel knot K with rational slopes less than 2g(K) - 1, for q greater than or equal to 3.

Sergio Fenley: Transverse pairs of foliations by Gromov hyperbolic leaves, part 2

This is the continuation of the talk of Rafael Potrie last week. We showed with him in https://arxiv.org/abs/2510.15176  that a pair of transverse foliations by Gromov hyperbolic leaves in a closed 3-manifold either intersects in a leafwise quasigeodesic manner, or it contains a (generalized) Reeb surface. I will talk about the case that if L, E are leaves of the two foliations in the universal cover, then their intersection is connected, that is a single bi-infinite properly embedded arc. This part of the proof at this point needs that leaves are Gromov hyperbolic. The analysis is pretty much independent of part 1, which did not need Gromov hyperbolicity at all, and part 2 uses much more geometric ideas. Translation: you can still understand most of it if you missed part 1.

Rafael Potrie: Transverse pairs of foliations by Gromov hyperbolic leaves, part 1

We showed with Fenley in https://arxiv.org/abs/2510.15176 (and with some additional work in progress j.w. Barthelme and Mann) that a pair of transverse foliations by Gromov hyperbolic leaves in a closed 3-manifold either intersects as a blow up of an Anosov flow, or it contains a (generalized) Reeb surface. I will present this result and show how the proof splits in two parts depending on how leaves intersect in the universal cover. I will explain some examples and the proof of one of the parts, showing that whenever a pair of leaves intersect in more than one connected component, then the intersection foliation must contain a Reeb annulus (and note that we do not know if this situation is actually possible in atoroidal manifolds). Sergio will explain the other case. 

Siddhi Krishna: Taut foliations in Dehn surgeries along positive braids: explicit constructions, examples, and strategies

Some of my past work has focused on constructing taut foliations in Dehn surgeries along positive braid knots; this work was motivated by the L-space conjecture. In this talk, I'll explain -- in a LOT of detail! -- how to construct taut foliations in r-surgery along P(-2,3,7)=K, where r <9 = 2g(K)-1. I'll explain why braids are a good tool in this setting, and also explain some implications of the construction. I will assume that you know what branched surfaces, train tracks, and taut foliations are, but I'll try not to assume much more.