Foliations learning seminar

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. 

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.