Geometry and Topology Seminar 2019-2020

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.

Abstract (pdf)

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
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
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