Talks

After reviewing recent developments in the study of the AdS/CFT correspondence between the IR gauge theory living on a stack of D3-branes placed at a Calabi-Yau singularity and type IIB string theory on the near horizon geometry, we focus on the problem of counting chiral BPS operators in this class of CFTs and we match them with the dual string states in the general case of toric CY. Partition functions can be explicitly written in all sectors with fixed baryonic charge using localization over fixed points of the toric actions. These partition functions are related to the volume functions of the Sasaki-Einstein manifold and of its divisors.

We propose an extended quantum theory, in which the number of degrees of freedom K behaves as FOURTH power the number N of distinguishable states. As the simplex of classical N--point probability distributions can be embedded inside a higher dimensional convex body of mixed quantum states, one can further increase the dimensionality constructing the set of extended quantum states. The embedding proposed corresponds to an assumption that the physical system described in N dimensional Hilbert space is coupled with an auxiliary subsystem of the same dimensionality. The extended theory is shown to be a non-trivial generalisation of the standard quantum theory for which K=N^2. Imposing certain restrictions on initial conditions and dynamics allowed in the quartic theory one obtains quadratic theory as a special case. We discuss the question, how the theory of information processing looks like in the framework of the generalised quantum theory. In particular we propose a scheme of extended dense coding, in which one transmits two qubits by sending one extended bit, provided it was initially entangled with the extended bit of the receiver.

Neural circuits exhibit complex patterns of spontaneous activity. I will discuss how neural network models can reproduce this activity and how it interacts with responses evoked by sensory stimuli. This work involves analytic, mean-field and computer analyses of large systems of nonlinear differential equations with random parameters.

The general relativity has been tested from mm scales to solar system scales. The discovery of cosmic acceleration motivates the study of infrared modification of gravity at horizon scales. The cosmic expansion can be accelerated by dark energy without any correction to GR, but alternatively it can be explained by the modified gravity at large scales without introducing the unknown exotic energy. We introduce the linear structure formation theory of DGP and f(R) gravity, and present what it the strategy to test general relativity at cosmological scales.