Geometry and Topology Seminar 2019-2020: Difference between revisions
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In my presentation, I introduce three new invariants for pairs $(G;H)$ consisting of a finitely generated group $G$ and a subgroup $H$. The first invariant is the upper relative divergence which generalizes Gersten's notion of divergence. The second invariant is the lower relative divergence which generalizes a definition of Cooper-Mihalik. The third invariant is the lower subgroup distortion which parallels the standard notion | In my presentation, I introduce three new invariants for pairs $(G;H)$ consisting of a finitely generated group $G$ and a subgroup $H$. The first invariant is the upper relative divergence which generalizes Gersten's notion of divergence. The second invariant is the lower relative divergence which generalizes a definition of Cooper-Mihalik. The third invariant is the lower subgroup distortion which parallels the standard notion | ||
of subgroup distortion. We examine the relative divergence (both upper and lower) of a group with respect to a normal subgroup or a cyclic subgroup. We also explore relative divergence of $CAT(0)$ groups and relatively hyperbolic groups with respect to various subgroups to better understand geometric properties of these groups. We answer the question of Behrstock and | of subgroup distortion. We examine the relative divergence (both upper and lower) of a group with respect to a normal subgroup or a cyclic subgroup. We also explore relative divergence of $CAT(0)$ groups and relatively hyperbolic groups with respect to various subgroups to better understand geometric properties of these groups. We answer the question of Behrstock and Drutu about the existence of Morse geodesics in $CAT(0)$ spaces with divergence function strictly greater than $r^n$ and strictly less than $r^{n+1}$, where $n$ is an integer greater than $1$. More precisely, we show that for each real number $s>2$, there is a $CAT(0)$ space $X$ with a proper and cocompact action of some finitely generated group such that $X$ contains a Morse bi-infinite geodesic with the divergence equivalent to $r^s$. | ||
===Anton Izosimov=== | ===Anton Izosimov=== | ||
Revision as of 03:14, 5 September 2015
The Geometry and Topology seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.
For more information, contact Tullia Dymarz.
Summer 2015
| date | speaker | title | host(s) |
|---|---|---|---|
| June 23 at 2pm in Van Vleck 901 | David Epstein (Warwick) | Splines and manifolds. | Hirsch |
Summer Abstracts
David Epstein (Warwick)
Splines and manifolds.
Fall 2015
| date | speaker | title | host(s) |
|---|---|---|---|
| September 4 | |||
| September 11 | [Hung Tran] (UW Milwaukee) | Relative divergence, subgroup distortion, and geodesic divergence | T. Dymarz |
| September 18 | |||
| September 25 | |||
| October 2 | |||
| October 9 | |||
| October 16 | Jacob Bernstein (Johns Hopkins University) | TBA | L. Wang |
| October 23 | Anton Izosimov (University of Toronto) | TBA | Mari-Beffa |
| October 30 | |||
| November 6 | |||
| November 13 | |||
| November 20 | |||
| Thanksgiving Recess | |||
| December 4 | |||
| December 11 | |||
Fall Abstracts
Hung Tran
Relative divergence, subgroup distortion, and geodesic divergence
In my presentation, I introduce three new invariants for pairs $(G;H)$ consisting of a finitely generated group $G$ and a subgroup $H$. The first invariant is the upper relative divergence which generalizes Gersten's notion of divergence. The second invariant is the lower relative divergence which generalizes a definition of Cooper-Mihalik. The third invariant is the lower subgroup distortion which parallels the standard notion of subgroup distortion. We examine the relative divergence (both upper and lower) of a group with respect to a normal subgroup or a cyclic subgroup. We also explore relative divergence of $CAT(0)$ groups and relatively hyperbolic groups with respect to various subgroups to better understand geometric properties of these groups. We answer the question of Behrstock and Drutu about the existence of Morse geodesics in $CAT(0)$ spaces with divergence function strictly greater than $r^n$ and strictly less than $r^{n+1}$, where $n$ is an integer greater than $1$. More precisely, we show that for each real number $s>2$, there is a $CAT(0)$ space $X$ with a proper and cocompact action of some finitely generated group such that $X$ contains a Morse bi-infinite geodesic with the divergence equivalent to $r^s$.
Anton Izosimov
TBA
Jacob Bernstein
TBA
Archive of past Geometry seminars
2014-2015: Geometry_and_Topology_Seminar_2014-2015
2013-2014: Geometry_and_Topology_Seminar_2013-2014
2012-2013: Geometry_and_Topology_Seminar_2012-2013
2011-2012: Geometry_and_Topology_Seminar_2011-2012
2010: Fall-2010-Geometry-Topology