Simplicial Complex

Wednesday, June 26, 2019 - 9:00am - 10:00am
Jennifer Schultens (University of California, Davis)
Seifert fibered spaces are 3-dimensional manifolds with a 2-dimensional quotient space. Surfaces in Seifert fibered spaces fall into two categories: Compressible and incompressible. The structure of Seifert fibered spaces allows for a complete description of essential surfaces in Seifert fibered spaces in terms of a simplicial complex derived from their positioning.
Monday, April 28, 2014 - 10:15am - 11:05am
Sayan Mukherjee (Duke University)
We state some results on Cheeger Inequalities for the combinatorial
Laplacian and random walks on simplicial complexes.

Specifically, for the combinatorial Laplacian we prove that a Cheeger
type inequality holds on the highest dimension, or for the boundary
operator with Dirichlet boundary conditions. We also show that
coboundary expanders do not satisfy natural Buser or Cheeger
inequalities. We provide some statements about middle dimensions.

We also introduce random walks with absorbing states on simplicial
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