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Symmetry, heat kernels, and spectrum of infinite weighted graphs

GFM seminar

IIIUL, B2-01

2011-07-05 14:30 .. 15:30

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by Radoslaw Wojciechowski (City University of New York, USA)

We will discuss how the symmetry of the geometry of a weighted graph can be characterized by the symmetry of the heat semigroup. We will then present some heat kernel comparisons and use these to study spectral properties of graphs. In particular, we will prove some estimates for the bottom of the spectrum and a condition for discreteness of the spectrum. Time permitting, we will illustrate our results with examples for the usual graph Laplacians. This is joint work with Matthias Keller and Daniel Lenz.

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