A support theorem for the Hitchin fibration: the case of GLnGL_n and KCK_C

We compute the supports of the perverse cohomology sheaves of the Hitchin fibration for $GL_n$ over the locus of reduced spectral curves. In contrast to the case of meromorphic Higgs fields we find additional supports at the loci of reducible spectral curves. Their contribution to the global cohomology is governed by a finite twist of Hitchin fibrations for Levi subgroups. The corresponding summands give non-trivial contributions to the cohomology of the moduli spaces for every $n \geq 3$. A key ingredient is a restriction result for intersection cohomology sheaves that allows us to compare the fibration to the one defined over the versal deformations of spectral curves

A support theorem for\break the Hitchin fibration: The case of GLnand KC

We compute the supports of the perverse cohomology sheaves of the Hitchin fibration for GLn{\mathrm{GL}_{n}} over the locus of reduced spectral curves. In contrast to the case of meromorphic Higgs fields we find additional supports at the loci of reducible spectral curves. Their contribution to the global cohomology is governed by a finite twist of Hitchin fibrations for Levi subgroups. The corresponding summands give non-trivial contributions to the cohomology of the moduli spaces for every n≥2{n\geq{2}}. A key ingredient is a restriction result for intersection cohomology sheaves that allows us to compare the fibration to the one defined over versal deformations of spectral curves

The Hodge numbers of O'Grady 10 via Ngô strings

We determine the Hodge numbers of the hyper-Kähler manifold known as O'Grady 10 by studying some related modular Lagrangian fibrations by means of Nĝo strings, which we introduce via a refinement of the Ngô Support Theorem

Towards a social robot as interface for tourism recommendations

The popularity of social robots is steadily increasing, mainly due to the interesting impact they have in several application domains. In this paper, we propose the use of Pepper Robot as an interface of a recommender system for tourism. In particular, we used the robot to interact with the users and to provide them with personalized recommendations about hotels, restaurants, and points of interest in the area. The personalization mechanism encoded in the social robot relies on soft biometrics traits automatically recognized by the robot, as age and gender, user interests and personal facets. All these data are used to feed a neural network that returns as output the most suitable recommendations for the target user. To evaluate the effectiveness of the interaction driven by a social robot, we carried out a user study whose goal was to evaluate: (1) how the robot affects the perceived accuracy of the recommendations; (2) how the user experience and the engagement vary by interacting with a social robot instead of a classic web application. Even if there is a large room for improvement, mainly due to the poor speech recognizer integrated in the Pepper, the results showed that the robot can strongly attract people, thanks to its presence and interaction capabilities. These findings encouraged us in performing a larger field study to test the approach in the wild and to understand whether it can increase the acceptance of recommendations in real environments

Cohomological Hall algebras and character varieties

In this paper we investigate the relationship between twisted and untwisted character varieties via a specific instance of the Cohomological Hall algebra for moduli of objects in 3-Calabi-Yau categories introduced by Kontsevich and Soibelman. In terms of Donaldson--Thomas theory, this relationship is completely understood via the calculations of Hausel and Villegas of the E polynomials of twisted character varieties and untwisted character stacks. We present a conjectural lift of this relationship to the cohomological Hall algebra setting.Comment: Slight improvements picked up while editing for publication. To appear in IJM special volume for proceedings of VBAC 201

Interacting Kasner-type cosmologies

It is well known that Kasner-type cosmologies provide a useful framework for analyzing the three-dimensional anisotropic expansion because of the simplification of the anisotropic dynamics. In this paper relativistic multi-fluid Kasner-type scenarios are studied. We first consider the general case of a superposition of two ideal cosmic fluids, as well as the particular cases of non-interacting and interacting ones, by introducing a phenomenological coupling function $q(t)$. For two-fluid cosmological scenarios there exist only cosmological scaling solutions, while for three-fluid configurations there exist not only cosmological scaling ones, but also more general solutions. In the case of triply interacting cosmic fluids we can have energy transfer from two fluids to a third one, or energy transfer from one cosmic fluid to the other two. It is shown that by requiring the positivity of energy densities there always is a matter component which violates the dominant energy condition in this kind of anisotropic cosmological scenarios.Comment: Accepted for publication in Astrophysics &Space Science, 8 page

The current progress of the ALICE Ring Imaging Cherenkov Detector

Recently, the last two modules (out of seven) of the ALICE High Momentum Particle Identification detector (HMPID) were assembled and tested. The full detector, after a pre-commissioning phase, has been installed in the experimental area, inside the ALICE solenoid, at the end of September 2006. In this paper we review the status of the ALICE/HMPID project and we present a summary of the series production of the CsI photo-cathodes. We describe the key features of the production procedure which ensures high quality photo-cathodes as well as the results of the quality assessment performed by means of a specially developed 2D scanner system able to produce a detailed map of the CsI photo-current over the entire photo-cathode surface. Finally we present our recent R&D efforts toward the development of a novel generation of imaging Cherenkov detectors with the aim to identify, in heavy ions collisions, hadrons up to 30 GeV/c.Comment: Presented at the Imaging-2006 Conference, Stockholm, Sweden, June 200