Pure Maths Colloquium: Topologies of nodal sets of random band limited functions
9 February 2015 16:00 in CM221
In the beginning I will introduce the audience to my main motivation
coming from mathematical physics: Chladni Plates and Chladni Patterns.
I will present the main questions in this area. Then I will define the band-limited
limited function, their random Gaussian ensembles, and how to measure
the topology of their zero sets ("nodal patterns").
Then I will discuss a recent work, joint with Peter Sarnak, where
it is shown that the topologies and nestings of the zero and nodal
sets of random (Gaussian) band limited functions have universal
laws of distribution. Qualitative features of the
supports of these distributions are determined. In
particular the results apply to random monochromatic waves and to
random real algebraic hyper-surfaces in projective space.
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