Graphs play an important role in many disciplines of study in the natural and exact
sciences. Of particular interest is the understanding of various flows on graphs, including
the flows of information and heat, and the dynamics of a quantum particle.
These flows are associated to various linear operators acting on function spaces defined
over these graphs. The purpose of the proposed research group is to study the connection
between the geometry of the graphs, spectral properties of these operators and
properties of the flows associated with them.
We want to bring together world leaders and promising young researchers studying
spectral theory, dynamics, eigenfunctions and heat kernels on graphs to study problems
in several directions associated with the general goal. These include spectral and
dynamical effects of symmetries, spectral estimates, asymptotics of eigenfunctions and
eigenvalue spacings, and the heat flow and functional inequalities.
There are exceptionally strong mathematicians working in Israel (and particularly at
the Hebrew University) in areas related to the aims of the program and we plan to
interact with them through seminars and informal meetings.
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Mathematics