Lecturer: Prof. Robert Adler
Affiliation: Electrical Engineering,
Technion - Israel Institute of Technology
Abstract:
The Gaussian kinematic formula - or GKF -
is a fundamental result in the theory of
smooth Gaussian processes, and is mainly
about the topological properties of many of
the random sets that they generate.
Its genesis lies in the geometry of the 19-th
century, its main growth was part of the
development of the probability theory of the
second half of the 20-th century, but its real
beauty and mathematical importance were
only realized as 21-st century phenomena.
All well and good - but what does this have
to do with Physics, and why should the GKF
appear as the topic of a Nonlinear Physics
seminar?
It turns out that smooth random Gaussian
processes appear in many places in Physics,
including areas of astronomy - particularly
cosmology - and quantum chaos (areas from
which I will bring examples). It also turns out
that specific versions of the GKF also get
used by physicists very often, although
without realizing that there is something
generic behind the specific.
The aim of this talk is to try to paint the
“bigger picture”, at least as far as it relates to
the GKF, and thus make a small contribution
to closing the language gap between
mathematicians and physicists.