Jingyin Huang
Nathan Broaddus
Mike Davis

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OSU Topology Seminar
OSU Math Department

Participating Faculty

Hannah Alpert
Dan Boros
Sergei Chmutov
Dan Burghelea
Jim Fowler
Matthew Kahle
Thomas Kerler
Facundo Mémoli
Jingyin Huang
Guido Mislin
Crichton Ogle
Bobby Ramsey

Previous Years


Autumn 2018
Tuesday, August 28, 2018 at 1:50pm in Math Tower (MW) 154

Mark Pengitore, Ohio State University

Unipotent translation-like actions on lattices on lattices in rank 1 simple Lie groups


The Gersten conjecture says that a group being hyperbolic is equivalent to having no Baumslag-Solitar subgroups. This is known to be false due to work of Brady. While there are some weaker versions still open, we are interested in a geometric reformulation of the Gersten conjecture using translation-like actions. To be more specific, the geometric Gersten conjecture asks whether hyperbolicity is equivalent to having no translation-like action by any Baumslag-solitar group. In work in progress, we show that cocompact lattices in real rank 1 simple Lie groups admit translation-like actions by cocompact lattices in the unipotent part of the Iwasawa decomposition of the original Lie group. In particular, we demonstrate that Zn acts translation-like on the fundamental group of any closed hyperbolic n+1 manifold which provides counterexamples to the geometric Gersten conjecture. This is joint work with David Bruce Cohen and Ben McReynolds.

Tuesday, September 11, 2018 at 1:50pm in Math Tower (MW) 154

Jingyin Huang, Ohio State University

Uniform lattices acting on RAAG complexes


It is a classical result by Bieberbach that uniform lattices acting on Euclidean spaces are virtually free abelian. On the other hand, uniform lattices acting on trees are virtually free. This motivates the study of commensurability classification of uniform lattices acting on RAAG complexes, which are cube complexes that "interpolate" between Euclidean spaces and trees. We show the tree times tree obstruction is the only obstruction for commmensurability of label-preserving lattices acting on RAAG complexes.

This seminar is supported by the OSU Mathematics Research Institute (MRI).