Drummed up for maths : spectra and geometry

International Centre for Mathematical Sciences

A talk by Walter van Suijlekom (Prof of Noncommutative Geometry)

International Centre for Mathematical Sciences (ICMS) G.03

Can you hear the shape of a drum? This question was asked some 60 years ago by mathematician Mark Kac, trying to reconstruct the shape of a vibrating membrane (the drum) from its (audible) vibrational spectrum. In the first part of the lecture we will study this spectral approach to geometry, while illustrating it using drums of different shapes. We will then turn to the applications of spectral geometry in physics and astrophysics. We come to the conclusion that actually all our information about, say, the universe comes to us through spectra: instead of sound waves, the observed spectrum now ranges from radio waves, to electromagnetic waves, to gravitational waves. This means that the mathematical question of whether you can reconstruct the shape (of, say, the universe) from a spectrum is directly applicable in physics and astronomy. We end with a brief impression of current research, which deals with the question of how geometry is an emergent phenomenon, when an increasing part of the vibrational spectrum becomes available. Speaker: Walter van Suijlekom (Prof of Noncommutative Geometry)After studying physics at the University of Amsterdam, Walter van Suijlekom did his PhD in mathematics in Trieste (Italy) from 2002 to 2005. He spent a year as a postdoc at the Max Planck Institute in Bonn and since 2007 he has been working at Radboud University Nijmegen. From 2021, he is a professor of noncommutative geometry, a field in mathematics where functional analysis, (operator) algebra, (partial) differential equations and (Riemannian) geometry come together. In his research, Walter focuses on its applications in physics. In his spare time, he plays percussion in Symphony Orchestra Nijmegen.

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