Photoacoustic tomography (PAT) is an emerging soft-tissue imaging modality that has great potential for a wide range of biomedical imaging applications.  It can be viewed as a hybrid imaging modality in the sense that it utilizes an optical contrast mechanism combined with ultrasonic detection principles, thereby combining the advantages of optical and ultrasonic imaging while circumventing their primary limitations. The goal of PAT is to reconstruct the distribution of an object's absorbed optical energy density from measurements of pressure wavefields that are induced via the thermoacoustic effect.  In this talk, we review our recent advancements in practical image reconstruction approaches for PAT in heterogeneous acoustic media.  Such advancements include physics-based models of the measurement process and associated inversion methods for reconstructing images from limited data sets.  Applications of PAT to transcranial brain imaging are presented.

Advisor:  Jack Xin

In this talk, we study Cauchy-Riemann equation on some smooth convex domains of innite type in
C2. In detail, we show that supnorm estimates hold for those infinite exponential type
domains provided the exponent is less than 1. This is a joint work with John Erik Fornaess
and Lina Lee.

Starting from a supercompact, we construct a model in which SCH fails at $\aleph_\omega$ and there is a bad scale at $\aleph_\omega$. The existence of a bad scale implies the failure of weak square. The construction uses two Prikry type forcings defined in different ground models and a suitably defined projection between them. This is joint work with Spencer Unger.