Construction of countable coding for the geodesic flow on geometrically finite hyperbolic manifolds with cusps.

Abstract: Let $Gamma$ be a geometrically finite subgroup of $SO(n,1)$ with cusps. I will explain the construction of a countable coding of the geodesic flow on the unit tangent bundle $T^1(Gamma\ H^n)$. The problem can first be reduced to coding the dynamics on the limit set on the boundary. I will then explain a way to obtain a coding on the limit set and how to verify that this coding has a desired exponential tail property.

Zoom Link

For the first half-hour, I will give a tutorial on how to use the SnapPy program (https://snappy.computop.org/), a tool for understanding the topology of 3-manifolds with a focus on their hyperbolic geometry.  I will include some of the recent features related to knot concordance and verified length spectrum.   The second half-hour will be a combination of a question-answer session and a software installation party (bring your laptop if desired).

From the Space Sciences Laboratory at the University of California, Berkeley: 

We are thrilled to invite you all to a special colloquium featuring Francis Nimmo, Professor of Earth and Planetary Sciences at UC Santa Cruz, as he kicks off our new premier seminar series this year. SLMath members and visitors are welcome to join this event - RSVP below. 

Event Details

• Date: Friday, February 13, 2026

• Time: 1:00 PM – 2:00 PM

• In-Person Location: Simons Laufer Mathematical Sciences Institute (SLMath) Eisenbud Auditorium

• In-Person RSVP: If you plan to attend in person, please fill out the RSVP form here: https://docs.google.com/forms/d/e/1FAIpQLSdOKq6pPDyjthQ_WIRdaJtPEMEmJMkySP06mx7jOGrKLcpJJQ/viewform

• Virtual Participation: Join via Zoom

  • Link: https://berkeley.zoom.us/j/92310248808

  • Meeting ID: 923 1024 8808

• Shuttle: Take the Hill shuttle at 12:40 PM from Mining Circle.

• Networking (In-Person): Tea and cookies to follow at 2:00 PM on the SSL Patio.

Talk Title: Second thoughts about the Moon

Abstract: Some lunar theories developed in the immediate aftermath of the Apollo missions are getting a little threadbare. In this talk, I'll discuss three issues that are being re-addressed: how the Moon formed; when it formed; and how asymmetric it is. I'll also pay attention to how predictions might be tested with upcoming or active lunar missions.

About the Speaker: Francis Nimmo's interests are the interiors and evolution of solid solar system bodies. He received his BA in 1993 and PhD in 1996, both from Cambridge University. He joined the faculty at UC Santa Cruz in 2005 and received the Macelwane medal and Urey prize in 2007. He has served on the GRAIL, Cassini, New Horizons, and InSight missions and is currently a member of four teams on the Europa Clipper mission. He was elected to the National Academy of Sciences in 2020 and the Royal Society in 2024.

This colloquium is open to the wider Berkeley community. SSL particularly welcomes colleagues from Astronomy, Physics, and Earth & Planetary Science (EPS) to join this inaugural event.

Speaker: Maxwell Plummer

Title: Free-by-cyclic groups via expanding semiflows

Abstract: For a 3-manifold M, a pseudo-Anosov suspension flow determines a face of its Thurston norm ball, and describes many ways M fibers over the circle. In this talk, we study a similar picture for a free-by-cyclic group G: we will construct a 2-complex with an expanding semiflow whose cross sections will determine the ways that G can split as a semidirect product. Time permitting, we will discuss the growth rates of the first return maps of these semiflows and relationships to endperiodic maps of infinite graphs.

Speaker: Junmo Ryang

Title: Convex cocompact and purely pseudo-Anosov subgroups of mapping class groups

Abstract: In 2002, Farb and Mosher introduced the notion of convex cocompactness in the mapping class group to capture coarse geometric information of the associated surface group extensions. Convex cocompact subgroups are necessarily finitely generated and purely pseudo-Anosov, but it is an open question whether the converse is true. On the other hand, there are certain subgroups of mapping class groups for which the converse is known to be true, including some classes of surface group extensions. In this short talk, we present some known results and some open questions in this setting. 

Zoom Link

Let M be a hyperbolic 3-manifold. We say a sequence of distinct (non-commensurable) essential closed surfaces in M is asymptotically geodesic if their principal curvatures go uniformly to zero. When M is closed, these sequences exist abundantly by the Kahn-Markovic surface subgroup theorem, and we will discuss the fact that such surfaces are always asymptotically dense, even though they do not always equidistribute. We will also talk about the fact that such sequences do not exist when M has infinite volume and is geometrically finite. Finally, we will discuss some partial answers to the question: does the existence of asymptotically geodesic surfaces in a negatively-curved 3-manifold imply the manifold is hyperbolic? This is joint work with Ben Lowe.

Zoom Link

In this talk, I will compare a variety of contracting properties of group elements. Groups with contracting elements include word/relative/hierachically/acylindrically hyperbolic groups. I will describe the dynamics of generic elements of such groups. If time allows, I will explain how contracting property of group elements help understand the horospherical dynamics. The latter part is joint work with Dongryul M. Kim.

Yair Minsky has generously agreed to give us an introduction to the hierarchy structure in the mapping class group.

Construction of countable coding for the geodesic flow on geometrically finite hyperbolic manifolds with cusps.

Abstract: Let $Gamma$ be a geometrically finite subgroup of $SO(n,1)$ with cusps. I will explain the construction of a countable coding of the geodesic flow on the unit tangent bundle $T^1(Gamma\ H^n)$. The problem can first be reduced to coding the dynamics on the limit set on the boundary. I will then explain a way to obtain a coding on the limit set and how to verify that this coding has a desired exponential tail property.

The census of orientable cusped hyperbolic 3-manifolds, like the census of knots, enumerates all orientable cusped finite-volume hyperbolic 3-manifolds. Just as the census of knots is arranged by the minimal number of crossings in planar diagrams of knots, the census of orientable cusped hyperbolic 3-manifolds is typically arranged by the minimal number of tetrahedra in triangulations of 3-manifolds. The most widely used “SnapPea census” of orientable cusped hyperbolic 3-manifolds was created in 1989 and continuously expanded afterwards, while its completeness was left undetermined until 2014, when Burton expanded the census to 9 tetrahedra and proved that it is complete without repetition using algebraic tools. In this talk, I will talk about the expansion of the census to 10 and 11 tetrahedra using a more recently developed tool, the verified canonical triangulation, and various applications of the new censuses, including the precisely 439,898 and 1,340,930 exceptional Dehn fillings on them, the next 1849 and 4673 simplest hyperbolic knot exteriors in the 3-sphere, and the first three simplest examples of orientable cusped hyperbolic 3-manifolds containing a closed totally geodesic surface.

Based on your feedback, the date of the upcoming brunch potluck is Saturday, February 21, 2026. Thank you so much for your prompt review and responses.

Time: 10:00 - 11:30am 

Venue: Cedar Rose Park-  1300 Rose Street, Berkeley CA 94702 (Area #1- On the Rose Street side of the park (Northside) just off of the sidewalk, and across form the play structure. 

Potluck: Please bring a brunch themed dish for 4-6 people. SLMath will provide water, beverages, paper and plastic wares. 

Zoom Link

Zoom Link

This seminar series will take place on UC Berkeley campus, in Evans Hall room 939.

This seminar series will take place on UC Berkeley campus, in Evans Hall room 740.

Zoom Link

Zoom Link

Zoom Link

Mladen Bestvina has kindly agreed to give us an introduction to projection complex machinery.

Zoom Link

Zoom Link

This seminar series will take place on UC Berkeley campus, in Evans Hall room 939.

This seminar series will take place on UC Berkeley campus, in Evans Hall room 740.

Zoom Link

Zoom Link

Zoom Link

Zoom Link

This seminar series will take place on UC Berkeley campus, in Evans Hall room 939.

This seminar series will take place on UC Berkeley campus, in Evans Hall room 740.

Zoom Link

Zoom Link

Zoom Link

This seminar series will take place on UC Berkeley campus, in Evans Hall room 939.

This seminar series will take place on UC Berkeley campus, in Evans Hall room 740.

Zoom Link

Zoom Link

This seminar series will take place on UC Berkeley campus, in Evans Hall room 939.

Zoom Link

This seminar series will take place on UC Berkeley campus, in Evans Hall room 939.

This seminar series will take place on UC Berkeley campus, in Evans Hall room 740.

Zoom Link

Zoom Link

This seminar series will take place on UC Berkeley campus, in Evans Hall room 939.

This seminar series will take place on UC Berkeley campus, in Evans Hall room 740.

Zoom Link

Zoom Link

This seminar series will take place on UC Berkeley campus, in Evans Hall room 939.

This seminar series will take place on UC Berkeley campus, in Evans Hall room 740.

Zoom Link

Zoom Link

This seminar series will take place on UC Berkeley campus, in Evans Hall room 939.

This seminar series will take place on UC Berkeley campus, in Evans Hall room 740.

Zoom Link

This seminar series will take place on UC Berkeley campus, in Evans Hall room 939.

This seminar series will take place on UC Berkeley campus, in Evans Hall room 740.

Zoom Link

Zoom Link

This seminar series will take place on UC Berkeley campus, in Evans Hall room 939.

This seminar series will take place on UC Berkeley campus, in Evans Hall room 740.

Zoom Link

Zoom Link

Zoom Link

This seminar series will take place on UC Berkeley campus, in Evans Hall room 939.

This seminar series will take place on UC Berkeley campus, in Evans Hall room 740.

Zoom Link

Zoom Link

This seminar series will take place on UC Berkeley campus, in Evans Hall room 740.