Mark Agranovsky: Spherical Waves, Nodal Sets and Thermoacoustic Tomography

14:00-15:00
The three different ( at least for the first glance), problems:
approximation of functions by linear combinations of shifted radial functions (spherical waves), geometry of the zero sets of solutions of the wave and Helmholtz equation (nodal sets) and mathematics involved in a modern trend in medical imaging (thermo- and photoacoustic tomography) have the same common root :
reconstruction of functions from their spherical means. In spite of
the spherical mean operator being a very classical object, the novelty of the problem is due to nonstandard complexes of spheres in question.
I will give a survey of the development of the subject and, if time allows, will discuss problems which still remain open.