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Title:
Laplacians on Infinite Graphs
Speaker:
Abstract:
There are two different notions of a Laplacian operator associated with infinitegraphs: discrete Laplacians and quantum graphs. Both objects have a venerable history and their spectral theory relates to several diverse branches ofmathematics (random walks, combinatorics, geometric group theory, ...).In our talk we explore connections between these two types of operators (spectral, parabolic and geometric properties), and exploit these relations to prove anumber of new results in spectral theory for both settings.Based on joint work with Aleksey Kostenko (Ljubljana&Vienna) and MarkMalamud (Moscow).
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