Week 15.02.2009 – 21.02.2009

Two different types of inverse problems will be discussed: (a) The inversion of certain integral transforms arising in medical imaging. (b) The generalized Dirichlet to Neumann map for certain physically significant boundary value problems, including the biharmonic equation in a semi strip and the Helmholtz equation in the interior of a canonical polygon.

The AdS4/Chern-Simons theory duality, recently conjectured by Aharony, Bergman, Jafferis and Maldacena, provides not only a new testing ground for the gauge theory/gravity correspondence, but also a possible way to access M-theoretic degrees of freedom. In this talk, I shall discuss some of our recent results on the open string sector of the type IIA string theory in AdS4xCP3, with emphasis on D-branes and giant gravitons in particular. Specifically, I shall focus on the so-called dual giant, a D2-brane extended on an S2 in AdS4, its spectrum of small fluctuations and open strings attached to it.

I will discuss the Hopf algebraic (quantum symmetry) structures underlying certain four-dimensional finite quantum field theories which are related to the N=4 SYM theory by marginal deformations. The motivation is to understand why these theories, despite being finite (like N=4 SYM), are generically not integrable in the planar limit (unlike N=4 SYM). Apart from a better understanding of integrability, these hidden symmetries might eventually provide insight into the construction of the (still unknown) dual AdS/CFT geometries for these field theories.