Minkowski superspaces and superstrings as almost real-complex supermanifolds

In 1996/7, J. Bernstein observed that smooth or analytic supermanifolds that mathematicians study are real or (almost) complex ones, while Minkowski superspaces are completely different objects. They are what we call almost real-complex supermanifolds, i.e., real supermanifolds with a non-integrable distribution, the collection of subspaces of the tangent space, and in every subspace a complex structure is given. An almost complex structure on a real supermanifold can be given by an even or odd operator; it is complex (without "always") if the suitable superization of the Nijenhuis tensor vanishes. On almost real-complex supermanifolds, we define the circumcised analog of the Nijenhuis tensor. We compute it for the Minkowski superspaces and superstrings. The space of values of the circumcised Nijenhuis tensor splits into (indecomposable, generally) components whose irreducible constituents are similar to those of Riemann or Penrose tensors. The Nijenhuis tensor vanishes identically only on superstrings of superdimension 1|1 and, besides, the superstring is endowed with a contact structure. We also prove that all real forms of complex Grassmann algebras are isomorphic although singled out by manifestly different anti-involutions.Comment: Exposition of the same results as in v.1 is more lucid. Reference to related recent work by Witten is adde

Topology Change in Canonical Quantum Cosmology

We develop the canonical quantization of a midisuperspace model which contains, as a subspace, a minisuperspace constituted of a Friedman-Lema\^{\i}tre-Robertson-Walker Universe filled with homogeneous scalar and dust fields, where the sign of the intrinsic curvature of the spacelike hypersurfaces of homogeneity is not specified, allowing the study of topology change in these hypersurfaces. We solve the Wheeler-DeWitt equation of the midisuperspace model restricted to this minisuperspace subspace in the semi-classical approximation. Adopting the conditional probability interpretation, we find that some of the solutions present change of topology of the homogeneous hypersurfaces. However, this result depends crucially on the interpretation we adopt: using the usual probabilistic interpretation, we find selection rules which forbid some of these topology changes.Comment: 23 pages, LaTex file. We added in the conclusion some comments about path integral formalism and corrected litle misprinting

Notes on Stein-Sahi representations and some problems of non L2L^2 harmonic analysis

We discuss one natural class of kernels on pseudo-Riemannian symmetric spaces.Comment: 40p

Immunological Mechanisms Mediating Hantavirus Persistence in Rodent Reservoirs

Hantaviruses, similar to several emerging zoonotic viruses, persistently infect their natural reservoir hosts, without causing overt signs of disease. Spillover to incidental human hosts results in morbidity and mortality mediated by excessive proinflammatory and cellular immune responses. The mechanisms mediating the persistence of hantaviruses and the absence of clinical symptoms in rodent reservoirs are only starting to be uncovered. Recent studies indicate that during hantavirus infection, proinflammatory and antiviral responses are reduced and regulatory responses are elevated at sites of increased virus replication in rodents. The recent discovery of structural and non-structural proteins that suppress type I interferon responses in humans suggests that immune responses in rodent hosts could be mediated directly by the virus. Alternatively, several host factors, including sex steroids, glucocorticoids, and genetic factors, are reported to alter host susceptibility and may contribute to persistence of hantaviruses in rodents. Humans and reservoir hosts differ in infection outcomes and in immune responses to hantavirus infection; thus, understanding the mechanisms mediating viral persistence and the absence of disease in rodents may provide insight into the prevention and treatment of disease in humans. Consideration of the coevolutionary mechanisms mediating hantaviral persistence and rodent host survival is providing insight into the mechanisms by which zoonotic viruses have remained in the environment for millions of years and continue to be transmitted to humans