Geometry and Topology Seminar
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.
Contents
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 | Tullia Dymarz (UW Madison) | Non-rectifiable Delone sets in amenable groups | (local) | |
September 25 | ||||
October 2 | Jose Ignacio Cogolludo Agustín (University of Zaragoza, Spain) | TBA | L. Maxim | |
October 9 | Matthew Cordes (Brandeis) | TBA | T. Dymarz | |
October 16 | Jacob Bernstein (Johns Hopkins University) | TBA | L. Wang | |
October 23 | ||||
October 30 | Yun Su (UW Madison) | Higher-order degrees of hypersurface complements. | (local) | |
November 6 | ||||
November 13 | Danny Ruberman (Brandeis) | TBA | Kjuchukova | |
November 20 | Anton Izosimov (University of Toronto) | TBA | Mari-Beffa | |
Thanksgiving Recess | ||||
December 4 | ||||
December 11 | Tommy Wong (UW Madison) | Milnor Fiber of Complex Hyperplane Arrangement. | (local) | |
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 $r^s$.
Tullia Dymarz
Non-rectifiable Delone sets in amenable groups
In 1998 Burago-Kleiner and McMullen constructed the first examples of coarsely dense and uniformly discrete subsets of R^n that are not biLipschitz equivalent to the standard lattice Z^n. Similarly we find subsets inside the three dimensional solvable Lie group SOL that are not bilipschitz to any lattice in SOL. The techniques involve combining ideas from Burago-Kleiner with quasi-isometric rigidity results from geometric group theory.
Matthew Cordes
TBA
Anton Izosimov
TBA
Jacob Bernstein
TBA
Yun Su
Higher-order degrees of hypersurface complements.
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