Geometry and Topology Seminar 2019-2020

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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 or Alexandra Kjuchukova.

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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 Jesse Wolfson (Uchicago) Counting Problems and Homological Stability M. Matchett Wood
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 Yun Su (UW Madison) Higher-order degrees of hypersurface complements. (local)
October 30 Gao Chen (Stony Brook University) TBA B.Wang
November 6 Dan Cristofaro-Gardiner (Harvard) TBA Kjuchukova
November 13 Danny Ruberman (Brandeis) TBA Kjuchukova
November 20 Anton Izosimov (University of Toronto) TBA Mari-Beffa
Thanksgiving Recess
December 4 Quinton Westrich (UW Madison) Harmonic Chern Forms on Polarized Kähler Manifolds (local)
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.

Jesse Wolfson

Counting Problems and Homological Stability

In 1969, Arnold showed that the i^{th} homology of the space of un-ordered configurations of n points in the plane becomes independent of n for n>>i. A decade later, Segal extended Arnold's method to show that the i^{th} homology of the space of degree n holomorphic maps from \mathbb{P}^1 to itself also becomes independent of n for large n, and, moreover, that both sequences of spaces have the same limiting homology. We explain how, using Weil's number field/function field dictionary, one might have predicted this topological coincidence from easily verifiable statements about specific counting problems. We then discuss ongoing joint work with Benson Farb and Melanie Wood in which we use other counting problems to predict and discover new instances of homological stability in the topology of complex manifolds.


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