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Cheeger constants, exponential growth and spectrum of planar graphs

GFM seminar

CIUL, A2-25

2009-11-13 16:00 .. 17:00

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by Matthias Keller (Mathematical Institute, FSU Jena, Germany)

We will discuss relations between local geometry of infinité planar graphs and global invariants. Namely we give estimates for Cheeger's constant (a.k.a. the isoperimetric constant) and exponential growth in terms of combinatorial curvature. These invariants are of importance since they yield estimates for the bottom of the spectrum of the combinatorial Laplacian on the graph. (This is joint work with Norbert Peyerimhoff).

Past conference highlights: Symmetries in Quantum Physics 2017; Advances in Mathematical Fluid Mechanics, Stochastic & Deterministic Methods; Quantum Integrable Systems and Geometry; Chern-Simons Gauge Theory: 20 years after; Second Workshop on Quantum Gravity and Noncommutative Geometry; Infinite Dimensional Algebras and Quantum Integrable Systems II; Stochastic Analysis in Mathematical Physics; Mathematics in Chemistry; Geometric Aspects of Integrable Systems; ICMP 2003