Group Actions and Dynamics Seminar: Difference between revisions
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During the Fall 2025 semester, '''RTG / Group Actions and Dynamics''' seminar meets in room '''B123 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, Tullia Dymarz, Autumn Kent, Marissa Loving, Caglar Uyanik, Chenxi Wu or Andy Zimmer. | During the Fall 2025 semester, '''RTG / Group Actions and Dynamics''' seminar meets in room '''B123 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, Tullia Dymarz, Autumn Kent, Marissa Loving, Caglar Uyanik, Chenxi Wu or Andy Zimmer. | ||
== Fall | == Fall 2025 == | ||
{| cellpadding="8" | {| cellpadding="8" | ||
| Line 12: | Line 12: | ||
|September 8 | |September 8 | ||
|[https://sites.google.com/view/algebrandis/ Brandis Whitfield] (UW) | |[https://sites.google.com/view/algebrandis/ Brandis Whitfield] (UW) | ||
| | |Constructing reducibly geometrically finite subgroups of the mapping class group | ||
|local | |local | ||
|- | |- | ||
|September 15 | |September 15 | ||
|[https://sites.google.com/site/jhdezhdez/ Jesús Hernández Hernández] (UNAM) | |[https://sites.google.com/site/jhdezhdez/ Jesús Hernández Hernández] (UNAM) | ||
| | |Uncountably-many ways of cooking fibrations of handlebodies* | ||
|Loving | |Loving | ||
|- | |- | ||
|September 22 | |September 22 | ||
|[https://sites.google.com/view/junmo-ryang-math/home Junmo Ryang] (Rice) | |[https://sites.google.com/view/junmo-ryang-math/home Junmo Ryang] (Rice) | ||
| | |Pseudo-Anosov Subgroups of Surface Bundles over Tori | ||
|Loving and Uyanik | |Loving and Uyanik | ||
|- | |- | ||
|September 29 | |September 29 | ||
|[https://sites.google.com/view/jagerynn Jagerynn Verano] (UIC) | |[https://sites.google.com/view/jagerynn Jagerynn Verano] (UIC) | ||
| | |Locally convex immersions of complexes of groups | ||
|Loving | |Loving | ||
|- | |- | ||
|October 6 | |October 6 | ||
|[https://sites.google.com/wisc.edu/vickywen/ Vicky Wen] (UW) | |[https://sites.google.com/wisc.edu/vickywen/ Vicky Wen] (UW) | ||
| | |Sublinearly Morseness in Higher Rank Symmetric spaces | ||
|local | |local | ||
|- | |- | ||
|October 13 | |October 13 | ||
| | |[https://search.asu.edu/profile/1813459 Julien Paupert] (ASU) | ||
| | |Complex hyperbolic deformations of cusped hyperbolic lattices | ||
| | |Dymarz | ||
|- | |- | ||
|October 20 | |October 20 | ||
| | |[https://gauss.math.yale.edu/~dk929/ Dongryul Kim] (Yale) | ||
|TBA | |TBA | ||
| | |Zimmer | ||
|- | |- | ||
|October 27 | |October 27 | ||
| | |[https://sites.google.com/view/niclas-technaus-website Niclas Technau] (UW) | ||
|TBA | |TBA | ||
| | |local | ||
|- | |- | ||
|November 3 | |November 3 | ||
| Line 56: | Line 56: | ||
|- | |- | ||
|November 10 | |November 10 | ||
| | | [https://wuchenxi.github.io/ Chenxi Wu] (UW) | ||
|TBA | |TBA | ||
| | |local | ||
|- | |- | ||
|November 17 | |November 17 | ||
| Line 83: | Line 83: | ||
== Fall Abstracts == | == Fall Abstracts == | ||
===Brandis Whitfield=== | ===Brandis Whitfield=== | ||
A longstanding goal within low-dimensional geometry and topology is to establish parallels between the theory of Kleinian groups and subgroups of the mapping class group. Convex-cocompact subgroups of the mapping class group have been well studied in the past few decades; current research aims to extend this analogy to the more general class of geometric finiteness. Dowdall–Durham–Leininger–Sisto introduce parabolically geometrically finite (PGF) subgroups of the mapping class group whose coned-off Cayley graphs, with respect to a collection of twist subgroups, quasi-isometrically embed into the curve complex. In joint work with Aougab, Bray, Dowdall, Hoganson and Maloni, we extend this definition to allow the coned-off subgroups to be more generally reducible, and produce plentiful examples of this behavior. Our examples include free products of reducible subgroups and the beloved right-angled Artin constructions of Clay–Mangahas–Leininger. | |||
=== Jesús Hernández Hernández=== | === Jesús Hernández Hernández=== | ||
In this talk we introduce a Denjoy homeomorphisms of the circle, which can be thought as "irrational rotations of the circle that leave an invariant Cantor set". Using these homeomorphisms we create uncountably-many homeomorphisms of the Cantor-tree surface, all of which have mapping torus homeomorphic to (the interior of) a genus 2 handlebody. Finally, we show some variations of this construction to a) fiber any genus g > 1 handlebody with Cantor-tree surfaces, and b) how can we modify the construction of the homeomorphisms for this result to be applied to different surfaces. This is joint work with Christopher J. Leininger and Ferrán Valdez. | |||
===Junmo Ryang=== | ===Junmo Ryang=== | ||
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. Several partial results are known in certain settings, however. For example, work of Dowdall, Kent, Leininger, Russell, and Schleimer give a positive answer for subgroups of fibered 3-manifold groups (aka surface-by-cyclic extensions) naturally embedded in punctured mapping class groups via the Birman exact sequence. We present a generalization of this in the setting of surface-by-abelian extensions. | |||
=== Jagerynn Verano === | === Jagerynn Verano === | ||
The theory of complexes of groups was introduced to describe group actions on simply connected polyhedral complexes. In this talk, we discuss the motivations of the theory, including applications to recent work by Groves—Manning and Einstein—Groves to extend Agol’s theorem beyond the setting of geometric actions. We define a new notion of an immersion and state our main result on locally convex immersions into non-positively curved complexes of groups. Lastly, we define a local complex of groups and offer a functorial perspective on the statement that every complex of groups is locally developable. | |||
===Vicky Wen=== | ===Vicky Wen === | ||
The Morse property of geodesics in hyperbolic spaces has always been a useful tool in proving many rigidity results. People in the past decade have tried to generalize this property in many different ways. I will present to you some of those generalizations and explain why they are still somewhat restrictive in the setting of higher rank symmetric spaces, which in turn motivates my definition of “sublinear Morseness”. | |||
===Julien Paupert=== | |||
After reviewing some classical results about rigidity and flexibility of lattices in semisimple Lie groups and known results in dimension 2, we will discuss the existence and potential discreteness/faithfulness ofdeformations of cusped lattices of SO(3,1) into SU(3,1). We will focus on the cases of small Bianchi groups (joint with M. Thistlethwaite) and the figure-eight knot group (joint with S. Ballas and P. Will), as well as the general behavior of bending deformations in all dimensions. | |||
===Dongryul Kim=== | |||
===Niclas Technau=== | |||
===Neil Hoffman=== | ===Neil Hoffman=== | ||
===Chenxi Wu=== | |||
===Marissa Loving=== | ===Marissa Loving=== | ||
Latest revision as of 18:37, 30 September 2025
During the Fall 2025 semester, RTG / Group Actions and Dynamics seminar meets in room B123 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, Tullia Dymarz, Autumn Kent, Marissa Loving, Caglar Uyanik, Chenxi Wu or Andy Zimmer.
Fall 2025
| date | speaker | title | host(s) |
|---|---|---|---|
| September 8 | Brandis Whitfield (UW) | Constructing reducibly geometrically finite subgroups of the mapping class group | local |
| September 15 | Jesús Hernández Hernández (UNAM) | Uncountably-many ways of cooking fibrations of handlebodies* | Loving |
| September 22 | Junmo Ryang (Rice) | Pseudo-Anosov Subgroups of Surface Bundles over Tori | Loving and Uyanik |
| September 29 | Jagerynn Verano (UIC) | Locally convex immersions of complexes of groups | Loving |
| October 6 | Vicky Wen (UW) | Sublinearly Morseness in Higher Rank Symmetric spaces | local |
| October 13 | Julien Paupert (ASU) | Complex hyperbolic deformations of cusped hyperbolic lattices | Dymarz |
| October 20 | Dongryul Kim (Yale) | TBA | Zimmer |
| October 27 | Niclas Technau (UW) | TBA | local |
| November 3 | Neil Hoffman (UMN-Duluth) | TBA | Uyanik |
| November 10 | Chenxi Wu (UW) | TBA | local |
| November 17 | Marissa Loving (UW) | TBA | local |
| November 24 | Andrew Zimmer (UW) | TBA | local |
| December 1 | Caglar Uyanik (UW) | TBA | local |
| December 8 | reserved | TBA |
Fall Abstracts
Brandis Whitfield
A longstanding goal within low-dimensional geometry and topology is to establish parallels between the theory of Kleinian groups and subgroups of the mapping class group. Convex-cocompact subgroups of the mapping class group have been well studied in the past few decades; current research aims to extend this analogy to the more general class of geometric finiteness. Dowdall–Durham–Leininger–Sisto introduce parabolically geometrically finite (PGF) subgroups of the mapping class group whose coned-off Cayley graphs, with respect to a collection of twist subgroups, quasi-isometrically embed into the curve complex. In joint work with Aougab, Bray, Dowdall, Hoganson and Maloni, we extend this definition to allow the coned-off subgroups to be more generally reducible, and produce plentiful examples of this behavior. Our examples include free products of reducible subgroups and the beloved right-angled Artin constructions of Clay–Mangahas–Leininger.
Jesús Hernández Hernández
In this talk we introduce a Denjoy homeomorphisms of the circle, which can be thought as "irrational rotations of the circle that leave an invariant Cantor set". Using these homeomorphisms we create uncountably-many homeomorphisms of the Cantor-tree surface, all of which have mapping torus homeomorphic to (the interior of) a genus 2 handlebody. Finally, we show some variations of this construction to a) fiber any genus g > 1 handlebody with Cantor-tree surfaces, and b) how can we modify the construction of the homeomorphisms for this result to be applied to different surfaces. This is joint work with Christopher J. Leininger and Ferrán Valdez.
Junmo Ryang
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. Several partial results are known in certain settings, however. For example, work of Dowdall, Kent, Leininger, Russell, and Schleimer give a positive answer for subgroups of fibered 3-manifold groups (aka surface-by-cyclic extensions) naturally embedded in punctured mapping class groups via the Birman exact sequence. We present a generalization of this in the setting of surface-by-abelian extensions.
Jagerynn Verano
The theory of complexes of groups was introduced to describe group actions on simply connected polyhedral complexes. In this talk, we discuss the motivations of the theory, including applications to recent work by Groves—Manning and Einstein—Groves to extend Agol’s theorem beyond the setting of geometric actions. We define a new notion of an immersion and state our main result on locally convex immersions into non-positively curved complexes of groups. Lastly, we define a local complex of groups and offer a functorial perspective on the statement that every complex of groups is locally developable.
Vicky Wen
The Morse property of geodesics in hyperbolic spaces has always been a useful tool in proving many rigidity results. People in the past decade have tried to generalize this property in many different ways. I will present to you some of those generalizations and explain why they are still somewhat restrictive in the setting of higher rank symmetric spaces, which in turn motivates my definition of “sublinear Morseness”.
Julien Paupert
After reviewing some classical results about rigidity and flexibility of lattices in semisimple Lie groups and known results in dimension 2, we will discuss the existence and potential discreteness/faithfulness ofdeformations of cusped lattices of SO(3,1) into SU(3,1). We will focus on the cases of small Bianchi groups (joint with M. Thistlethwaite) and the figure-eight knot group (joint with S. Ballas and P. Will), as well as the general behavior of bending deformations in all dimensions.
Dongryul Kim
Niclas Technau
Neil Hoffman
Chenxi Wu
Marissa Loving
Andrew Zimmer
Caglar Uyanik
Archive of past Dynamics seminars
2024-2025 Dynamics_Seminar_2024-2025
2023-2024 Dynamics_Seminar_2023-2024
2022-2023 Dynamics_Seminar_2022-2023
2021-2022 Dynamics_Seminar_2021-2022
2020-2021 Dynamics_Seminar_2020-2021