Group Actions and Dynamics Seminar: Difference between revisions
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===Harrison Bray=== | ===Harrison Bray=== | ||
On the cusp of the 100 year anniversary, Khinchin's theorem implies a strong 0-1 law for the real line; namely, the set of real numbers within distance q^{-2-\epsilon} of infinitely many rationals p/q is Lebesgue measure 0 for \epsilon>0, and full measure for \epsilon=0. In these lectures, I will present an analogous result for horoball packings in Gromov hyperbolic metric spaces. As an application, we prove a logarithm law; that is, we prove asymptotics for the depth in the packing of a typical geodesic. This is joint work with Giulio Tiozzo. | |||
===Eliot Bongiovanni=== | ===Eliot Bongiovanni=== | ||
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===Caglar Uyanik=== | ===Caglar Uyanik=== | ||
Cannon and Thurston showed that a hyperbolic 3-manifold that fibers over the circle gives rise to a sphere-filling curve. The universal cover of the fiber surface is quasi-isometric to the hyperbolic plane, whose boundary is a circle, and the universal cover of the 3-manifold is 3-dimensional hyperbolic space, whose boundary is the 2-sphere. Cannon and Thurston showed that the inclusion map between the universal covers extends to a continuous map between their boundaries, whose image is dense. In particular, any measure on the circle pushes forward to a measure on the 2-sphere using this map. We compare several natural measures coming from this construction. | Cannon and Thurston showed that a hyperbolic 3-manifold that fibers over the circle gives rise to a sphere-filling curve. The universal cover of the fiber surface is quasi-isometric to the hyperbolic plane, whose boundary is a circle, and the universal cover of the 3-manifold is 3-dimensional hyperbolic space, whose boundary is the 2-sphere. Cannon and Thurston showed that the inclusion map between the universal covers extends to a continuous map between their boundaries, whose image is dense. In particular, any measure on the circle pushes forward to a measure on the 2-sphere using this map. We compare several natural measures coming from this construction. | ||
== Spring 2025 == | == Spring 2025 == | ||
Revision as of 14:43, 27 August 2024
During the Fall 2024 semester, RTG / Group Actions and Dynamics seminar meets in room B325 Van Vleck on Mondays from 2:25pm - 3:15pm. To sign up for the mailing list send an email from your wisc.edu address to dynamics+join@g-groups.wisc.edu. For more information, contact Paul Apisa, Marissa Loving, Caglar Uyanik, Chenxi Wu or Andy Zimmer.
Fall 2024
| date | speaker | title | host(s) |
|---|---|---|---|
| September 9 | Max Lahn (Michigan) | TBA | Uyanik and Zimmer |
| September 16 | Ben Lowe (Chicago) | TBA | Al Assal |
| September 23 | Harrison Bray (George Mason) | A 0-1 law for horoball packings of coarsely hyperbolic metric spaces and applications to cusp excursion | Zimmer |
| September 30 | Eliot Bongiovanni (Rice) | TBA | Uyanik |
| October 7 | Francis Bonahon (USC/Michigan State) | TBA | Loving |
| October 21 | Dongryul Kim (Yale) | TBA | Uyanik |
| October 28 | Matthew Durham (UC Riverside) | TBA | Loving |
| November 4 | Caglar Uyanik (UW) | Cannon-Thurston maps, random walks, and rigidity | local |
Fall Abstracts
Max Lahn
Ben Lowe
Harrison Bray
On the cusp of the 100 year anniversary, Khinchin's theorem implies a strong 0-1 law for the real line; namely, the set of real numbers within distance q^{-2-\epsilon} of infinitely many rationals p/q is Lebesgue measure 0 for \epsilon>0, and full measure for \epsilon=0. In these lectures, I will present an analogous result for horoball packings in Gromov hyperbolic metric spaces. As an application, we prove a logarithm law; that is, we prove asymptotics for the depth in the packing of a typical geodesic. This is joint work with Giulio Tiozzo.
Eliot Bongiovanni
Francis Bonahon
Dongryul Kim
Matthew Durham
Caglar Uyanik
Cannon and Thurston showed that a hyperbolic 3-manifold that fibers over the circle gives rise to a sphere-filling curve. The universal cover of the fiber surface is quasi-isometric to the hyperbolic plane, whose boundary is a circle, and the universal cover of the 3-manifold is 3-dimensional hyperbolic space, whose boundary is the 2-sphere. Cannon and Thurston showed that the inclusion map between the universal covers extends to a continuous map between their boundaries, whose image is dense. In particular, any measure on the circle pushes forward to a measure on the 2-sphere using this map. We compare several natural measures coming from this construction.
Spring 2025
| date | speaker | title | host(s) |
|---|---|---|---|
| January 27 | Ben Stucky (Beloit) | TBA | semi-local |
| April 21 | Mladen Bestvina (Utah) | Distinguished Lecture Series | Uyanik |
| April 28 | Inanc Baykur (UMass) | TBA | Uyanik |
Archive of past Dynamics seminars
2023-2024 Dynamics_Seminar_2023-2024
2022-2023 Dynamics_Seminar_2022-2023
2021-2022 Dynamics_Seminar_2021-2022
2020-2021 Dynamics_Seminar_2020-2021