We show the existence of an N=1 supersymmetric vacuum in string theory whose observable sector has exactly the matter content of the MSSM without exotic particles and vector-like pairs of any type. This is done so by compactifying the E_8 x E_8 heterotic string on a Calabi-Yau threefold endowed with an SU(4) vector bundle which has been constructed after extensive search. In addition, we discuss the Yukawa couplings and Higgs mu-terms in this model.

In the moduli stabilization program a la KKLT, the dilaton and the complex structure moduli are fixed via background 3-form fluxes, whereas the Kaehler moduli are fixed through non-perturbative effects such as Euclidean D3-brane instantons and gaugino condensation. After briefly introducing toroidal orbifolds, I will discuss some issues of stability and then turn to moduli stabilization in resolved toroidal type IIB orientifolds. The main emphasis will be on the resolution of the singularities via blow-ups, gluing together the local patches to obtain a smooth Calabi-Yau, and the topologies of the exceptional divisors.

I review what one has learned about SU(N) gauge theories from lattice calculations. I will discuss the mass spectrum, finite T phase transitions, k-strings, topology and strong-to-weak coupling transitions as well as the basic question of how close N=3 is to N=infinity.

We study a stationary black brane in M-superstring theory. Assuming BPS-type relations between the first-order derivatives of metric functions, we present general stationary black brane solutions with a traveling wave for the Einstein equations in D-dimensions. The solutions are given by a few independent harmonic equations (and plus the Poisson equation). General solutions are constructed by superposition of a complete set of those harmonic functions. Using the hyperspherical coordinate system for a conformally flat base space, we explicitly give the solutions in 11-dimensional M-theory for the case with M2-M5 intersecting branes and a traveling wave. Compactifying these solutions into five dimensions, we show that these solutions include the BMPV black hole and the Brinkmann wave solution, and those extension to non-BPS ones. We also find new solutions similar to the Brinkmann wave. We prove that the solutions preserve the one eigth supersymmetry if the gravi-electromagnetic field, which is a rotational part of gravity, is self-dual. We also discuss non-spherical black objects (e.g., a ring topology and an elliptical shape) by use of other curvilinear coordinates.

I will discuss the dynamics of Nambu--Goto strings with junctions at which three strings meet, in particular, the process of intercommuting of two straight strings, in which they exchange partners but become joined by a third string. I shall show that there are important kinematical constraints on this process. The exchange cannot occur if the strings meet with very large relative velocity. In the case of non-abelian strings, there is also a possibility that they can get locked, unable to separate in any direction. This may have important implications for the evolution of cosmic superstring networks and non-abelian string networks.

TBA

TBA

After a brief introduction to the basic concepts of entanglement in discrete and continuous systems I will outline various results of our recent work in these areas. In particular, I will present a scaling relation for the entanglement of a subsystem with respect to the rest of the lattice in the size of the regions.

Based on the observation that classical strings only couple to area, we study the generalized geometry of manifolds equipped with an area measure but not a metric length measure. This in particular includes geometries combined from a metric and a two-form. We discuss the equation of stationary surfaces on these backgrounds which leads to the identification of differential geometric structures appropriate for area geometry. This work is expected to be of relevance for the study of the gravitational sector of strings and branes.

Evidence for the existence of some form of dark energy -- a smooth component that causes the accelerated expansion of the universe and contributes about 70 percent of the total energy density -- is by now very solid. However, very little progress has been made in understanding its nature and the underlying physical mechanism. In this talk I describe the prospects of several promising methods to improve the measurements of dark energy properties within the next decade. In addition to type Ia supernovae, these include weak gravitational lensing, counts of clusters of galaxies, and cosmic microwave background anisotropies. I comment on specific upcoming surveys, and challenges in controlling the systematic errors so that these probes can achieve their full potential and help us understand the nature of dark energy.

I review the structure of higher spin gauge theories in various dimensions, with some emphasize on the infinite-dimensional higher spin symmetries and unfolded dynamics approach. If I have time, I would also discuss how this approach works in the standard field theories like Yang-Mills and Einstein gravity.

One main reason to quantize gravity is the hope that the singularities of classical General Relativity will be absent within the framework of a quantum theory of gravity. One candidate for such a theory is the well developed framework of Loop Quantum Gravity. During the last years remarkable results concerning the big bang singularity have been achieved within symmetry reduced cosmological models of Loop Quantum Cosmology. In this talk we will address the question whether these results are characteristic also for the full, unreduced theory. As a first step towards answering that question we will present an explicit analysis of the geometric operator corresponding to the classical inverse scale factor occurring in cosmological models which has been performed within the full theory. The results will be discussed.