Geometric Analysis seminar series.
https://sites.google.com/math.iitb.ac.in/geometric-analysis/home
Speaker: Samir Shukla (IIT Mandi)
Time: March 17, Thursday, 5:00 pm (Indian Standard Time)
Title: Spectral gap bounds for the simplicial Laplacian and an application
to random complexes
Abstract: Let L(G) denotes the Laplacian of a graph G. The second smallest
eigenvalue of L(G) is called the spectral gap. In this talk, we discuss
two spectral gap bounds for the reduced Laplacian of a simplicial complex.
As an application we prove that, if the spectral gap of the Laplacian of
skeleton of a simplicial complex is enough large, then its co-homology
vanishes up to certain dimensions. We also see an application of these
results in certain random complexes. This is a joint work with D.
Yogeshwaran.
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