• November 13th

• 9:30-10:30 Sam Taylor - Talk 1 (E6-1, room 1401)

• 11:00-12:00 Chi Cheuk Tsang - Talk 1 (E6-1, room 1401)

• Lunch 

• 14:00-15:00 KyeongRo Kim (E6-1, room 1401)

• 15:45-16:15 Colloquium tea time (E6-1, room 1402)

• 16:15-17:15 Colloquium by Taylor (E6-1, room 1501)

• November 14th

• 9:30-10:30 Chi Cheuk Tsang - Talk 2 (E6-1, room 1401)

• 11:00-12:00 Minju Lee (E6-1, room 1401)

• Lunch 

• 14:00-15:00 Sam Taylor - Talk 2 (E6-1, room 1401)

• Chi Cheuk Tsang 

Title: Pseudo-Anosov flows and veering triangulations

Abstract: A pseudo-Anosov flow on a 3-manifold is a flow with the dynamical characteristics of the suspension flow of a pseudo-Anosov mapping torus. Despite having deep connections with other dynamical, topological, and geometric structures on 3-manifolds, many aspects of pseudo-Anosov flows have remained mysterious. In this sequence of talks, we will explain a recent tool, called veering triangulations, that has proved useful for studying pseudo-Anosov flows. In the first talk, we will go through some basic definitions and explain a construction of Agol-Guéritaud that constructs a veering triangulation from a pseudo-Anosov flow. In the second talk, we will explain how to recover the dynamical data of the pseudo-Anosov flow from the veering triangulation. Depending on time, we will also outline some recent applications.

• Samuel Taylor 

Title: Universal circles, flows, and foliations

Abstract: Let M be a connected, oriented, closed, irreducible, and atoroidal 3-manifold. Two structures of central importance in 3-manifold topology are taut foliations and pseudo-Anosov flows. Each structure determines an action of the fundamental group of M on a circle, and both types of actions are often referred to as universal circles. In the first talk, I’ll discuss joint work with Landry and Minsky that describes a precise relation between these: the circle action associated to a pseudo-Anosov flow on M is a universal circle for any taut foliation on M that is (almost) transverse to the flow. In the second talk, I’ll use this structure to outline some applications that are work in progress with Landry.

• Minju Lee 

Title: Counting totally geodesic submanifolds in infinite volume rank one spaces 

Abstract: In this talk, we focus on totally geodesic submanifolds (TGS) in geometrically finite rank one locally symmetric spaces of infinite volume. We first show that there are at most finitely many maximal TGS of finite volume of the given manifold. We then provide explicit upper bounds for the number of TGS with volume less than T. These bounds are polynomial in T, and are obtained by quantitative result accounting for the isolation of TGS. Our results extend previous work of Mohammadi-Oh on real hyperbolic 3-manifolds to the general rank-one locally symmetric spaces. This is ongoing joint work with Hee Oh.

• KyeongRo Kim

Title: Hyperbolic-like actions of Kleinian groups  

Abstract: In his study of the closed orbit conjecture for quasi-geodesic flows, Frankel showed a dichotomy: either a given quasi-geodesic flow admits a closed orbit, or the associated universal circle action is “hyperbolic-like.” In the follow-up work, he showed that the second case does not occur. Nonetheless, it remains an open question whether a closed hyperbolic 3-manifold group admits a hyperbolic-like action on the circle. This question is known as Frankel’s conjecture. In this talk, I will first review some of the background on one-dimensional group actions. Then, I will introduce the conjectures of Bonatti and Frankel and discuss related problems. Finally, I will present recent progress on hyperbolic-like actions. The talk is based on joint work with Michele Triestino.