The talk will contain a sruvey of mathematical problems and results of the
so called Thermoacoustic Tomography (TAT) and its sibling Photoacoustic
Tomography (PAT). These are among novel methods of medical imaging that
have been emerging recently. The main feature of these new methods is
combining different physical types of waves for creating and for measuring a
signal. In the case of TAT, the signal is triggered by irradiation of an
object by a MW or RF pulse, while the measured signal itself is an
ultrasound wave.

Mathematics of these new methods is very interesting and often hard. The
mathematical model of TAT/PAT boils down to an inverse problem for the wave
equation, or to an equivalent problem of recovering a function from its spherical
means with a restricted set of centers. Significant breakthroughs in this
area have been made very recently, e.g. in the last few months.

No prior knowledge of the subject will be assumed.