• L. Bonora (SISSA, Triest, Italy)
  • E. Elizalde  (ICREA, Barcelona, Spain) 
  • J. P. Gazeau (Université Paris, France)
  • J. Helayel (CBPF, Rio de Janeiro, Brazil)
  • G. M. Marugán (IEM - CSIC- Madrid, Spain)
  • C. M. Mendes (USP, Brazil)
  • B. M. R. Santos (UEL, Londrina, Brazil)
  • E. Sharpe (Virginia Tech., Blacksburg, USA)
  • R. J. Szabo  (Heriot-Watt Univ. and Maxwell Inst. for Math. Science, Edinburg, Scotland)


     * to be confirmed


L. Bonora

"Overview and prospects of field theories of strings"


I will review the recent research concerning second quantized string theories, the results and the mathematical problems behind them. The purpose of the talk is to illustrate the possibility of defining a full-fledged string field theory as a useful tool to investigate quantum gravity and the fundamental interactions.



Emilio Elizalde

“Mathematics and Cosmology: on the Universe acceleration and the zeta function as a regularization tool”


The knowledge of the Universe as a whole, its origin, size and shape, its evolution and future, has always intrigued the human mind. Galileo wrote: "Nature's great book is written in mathematical language." In the talk some explicit examples to confirm this statement will be presented. Main issue will be the nowadays hot question: What drives the acceleration of the Universe expansion? Dark energy, of course, but what is it? Beautiful mathematics, involving the zeta function of pseudo differential operators, describe, mathematically modellize) the Universe we live in.



J. P. Gazeau

"Physical examples of integral quantizations with Weyl-Heisenberg and affine groups"


We explain the powerful role that coherent states (CS), or more generally operator-valued measure, can play in quantizing any set equipped with a measure. Integral quantizations based on the Weyl-Heisenberg group and on the affine group are compared. An interesting application in quantum cosmology will be presented.



J. Helayel

"A Possible Scenario for the Interconnection between SUSY Breaking and Lorentz-Symmetry Violation"


By assuming that Lorentz-symmetry violation (LSV) takes place in a region not far from the SUSY scale, we set up a scenario where fermions in supersymmetric multiplets condensate and yield LSV. Goldstone fermionic modes are excited so that we conclude that, in our specific approach, LSV also triggers SUSY breaking.



C. M. Mendes

"Black holes and wormholes in a Randall-Sundrum brane"


Randall-Sundrum models provide concrete scenarios where extra dimensions are made compatible with the observed four dimensional universe. Nevertheless, the treatment of compact objects within this approach is still a challenge. In the present work we derive families of exact solutions in a Randall-Sundrum brane. We use the effective gravitational field equations proposed by Shiromizu, Maeda and Sasaki to construct exact solutions that are locally deformable to the usual general relativity vacuum geometries. The derived spacetimes describe black holes and wormholes in a Randall-Sundrum brane model.



G. M. Marugán

"Combining Loop and Fock Quantizations for Cosmological Universes with Perturbations"


A complete quantization of an approximately homogeneous and isotropic universe with small scalar perturbations is carried out by means of an hybrid approach in Loop Quantum Cosmology. The matter content is provided by a minimally coupled massive scalar field. The homogenous sector of the geometry degrees of freedom is polymerically quantized, while the inhomogeneities are quantized employing Fock techniques. The Fock quantization adopted is a privileged one, picked out in a unique way by criteria of dynamical unitarity and symmetry invariance in the context of quantum field theory in curved spacetimes. We characterize the physical states of this quantum theory and investigate some aspects of the resulting physics, including the connection with standard cosmological perturbation theory.



B. M. R. Santos

"Rotational Submanifolds of Pseudo-Euclidian Spaces"


We define rotational submanifolds in pseudo euclidean spaces R^n_t. We use the rotational imersion to classify all rotational submanifolds of L^n and we also generalize a result showing suficient conditions for a riemannian submanifold of R^n_t be a rotational submanifold.



E. Sharpe

"Some new advances in gauged linear sigma models"


Gauged linear sigma models (GLSM's) are simple generalizations of the supersymmetric CP^n model which have played a surprisingly important role in string compactifications over the last twenty years. The last six years have seen a resurgence of interest in GLSM's and some new technologies that have significantly advanced our understanding of these tools. In this talk, we will first review the basic properties of GLSM's, and then briefly discuss a few of the recent advances in their understanding.


R. J. Szabo

"Quantization of non-geometric flux backgrounds"


We describe the emergence of nonassociative geometries probed by closed strings in non-geometric flux compactifications of string theory. We show that these non-geometric backgrounds can be geometrised through the dynamics of membranes propagating in the phase space of the target space compactification. Quantization of the membrane sigma-model leads to a proper quantization of the nonassociative background, which we relate to Kontsevich's formalism of global deformation quantization. We construct Seiberg-Witten type maps between associative and nonassociative backgrounds, and show how they may realise a nonassociative deformation of gravity. We also explain how this approach is related to the quantization of certain Lie 2-algebras and cochain twist quantization using suitable quasi-Hopf algebras.