Uniformization, Unipotent Flows and the Riemann Hypothesis

We prove equidistribution of certain multidimensional unipotent flows in the moduli space of genus $g$ principally polarized abelian varieties (ppav). This is done by studying asymptotics of $\pmb{\Gamma}_{g} \sim Sp(2g,\mathbb{Z})$-automorphic forms averaged along unipotent flows, toward the codimension-one component of the boundary of the ppav moduli space. We prove a link between the error estimate and the Riemann hypothesis. Further, we prove $\pmb{\Gamma}_{g - r}$ modularity of the function obtained by iterating the unipotent average process $r$ times. This shows uniformization of modular integrals of automorphic functions via unipotent flows

Eluding SUSY at every genus on stable closed string vacua

In closed string vacua, ergodicity of unipotent flows provide a key for relating vacuum stability to the UV behavior of spectra and interactions. Infrared finiteness at all genera in perturbation theory can be rephrased in terms of cancelations involving only tree-level closed strings scattering amplitudes. This provides quantitative results on the allowed deviations from supersymmetry on perturbative stable vacua. From a mathematical perspective, diagrammatic relations involving closed string amplitudes suggest a relevance of unipotent flows dynamics for the Schottky problem and for the construction of the superstring measure.Comment: v2, 17 pages, 8 figures, typos corrected, new figure added with 3 modular images of long horocycles,(obtained with Mathematica

Equidistribution Rates, Closed String Amplitudes, and the Riemann Hypothesis

We study asymptotic relations connecting unipotent averages of $Sp(2g,\mathbb{Z})$ automorphic forms to their integrals over the moduli space of principally polarized abelian varieties. We obtain reformulations of the Riemann hypothesis as a class of problems concerning the computation of the equidistribution convergence rate in those asymptotic relations. We discuss applications of our results to closed string amplitudes. Remarkably, the Riemann hypothesis can be rephrased in terms of ultraviolet relations occurring in perturbative closed string theory.Comment: 15 page

Noncommutative deformation of four dimensional Einstein gravity

We construct a model for noncommutative gravity in four dimensions, which reduces to the Einstein-Hilbert action in the commutative limit. Our proposal is based on a gauge formulation of gravity with constraints. While the action is metric independent, the constraints insure that it is not topological. We find that the choice of the gauge group and of the constraints are crucial to recover a correct deformation of standard gravity. Using the Seiberg-Witten map the whole theory is described in terms of the vierbeins and of the Lorentz transformations of its commutative counterpart. We solve explicitly the constraints and exhibit the first order noncommutative corrections to the Einstein-Hilbert action.Comment: LaTex, 11 pages, comments added, to appear in Classical and Quantum Gravit

An overview of the Italian forest biodiversity and its conservation level, based on the first outcomes of the 4th Habitat Report ex-Art. 17

In 2019 the 4th Report ex-Art. 17 on the conservation status (CS) of Annex I Habitats of the 92/43/EEC Directive was expected by every EU/28 country, with reference to the period 2013-18. In Italy, the process was in charge to the Italian Institute for Environmental Protection and Research (ISPRA), on behalf of the Ministry for Environment, Land and Sea Protection (MATTM), with the scientific support of the Italian Botanical Society (SBI). A large group of thematic and territorial experts elaborated the available data concerning the 124 types of terrestrial and inland water Habitats present in Italy, 39 of which are represented by Forest Habitats (Group 9),. The main aim of the work was the evaluation of the overall CS of each Habitat by Biogeographic Region (Mediterranean, Continental and Alpine), for a total amount of 294 assessments. A high proportion of these (92, corresponding to 31% of the total) referred to Forest Habitats, including 20 marginal types for which the CS was not requested. The analysis was carried out at different scales: a) administrative territory, through the data contained in the ISPRA database, whose compilation was in charge to the Regions and Autonomous Provinces; b) Natura 2000 site, with the latest updates available (Standard Data Forms updated to 2018); c) national scale, implementing the distribution maps for each Habitat based on the European grid ETRS89-LAEA5210 (10x10 km2 mesh); d) Biogeographic Region, scale of the final assessment. Cartographic outcomes, associated databases and additional data used for the assessments will be available online on the ISPRA Portal as soon as the validation process by the European Commission will be completed. A dedicated archive named "HAB_IT" has been created in the national database "VegItaly" (1), managed by the Italian Society of Vegetation Science, where the phytosociological relevés representative of the various Annex I Habitats in Italy will be archived and freely accessible. An overview of the results regarding the Forest habitats is here provided, including a comparison with the outcomes of the former reporting cycle, the 3rd Report ex-Art. 17 (2). In several cases (e.g. 9120, 91L0), the distribution maps have been remarkably improved due to better knowledge and more fitful interpretation. The conservation status resulted as Favourable (FV) for 6,7%, Inadequate (U1) for 58,7% and Bad (U1) for 32,0% of the 72 assessed forest Habitat types. In no case there was an improvement of the conservation status, while in 6 cases a worsening of the conditions resulted from the data analysis, pointing out the Habitats types with a higher need of action. Similarly to other projects carried out as a team by the network of Annex I Habitat experts of the Italian Botanical Society and the Italian Society for Vegetation Science (e.g. 3, 4), this is another step in the direction of supporting the implementation of the 92/43/EEC "Habitat" Directive in Italy and Europe. On this ground, the high biodiversity of the Italian forest Habitats could be emphasized, however results pointed out that some rare or endemic types (e.g. Alnus cordata or Betula aetnensis-dominated forests) are still scarcely acknowledged by the most prominent EU conservation tools such as the Annex I to the "Habitat" Directive. 1) F. Landucci et al. (2012) Plant Biosyst., 146(4), 756-763 2) P. Genovesi et al. (2014) ISPRA, Serie Rapporti, 194/2014 3) E. Biondi et al. (2009) Società Botanica Italiana, MATTM, D.P.N., http://vnr.unipg.it/habitat/ 4) D. Gigante et al. (2016) Plant Sociology, 53(2), 77-8

What is the role of the placebo effect for pain relief in neurorehabilitation? Clinical implications from the Italian Consensus Conference on Pain in Neurorehabilitation

Background: It is increasingly acknowledged that the outcomes of medical treatments are influenced by the context of the clinical encounter through the mechanisms of the placebo effect. The phenomenon of placebo analgesia might be exploited to maximize the efficacy of neurorehabilitation treatments. Since its intensity varies across neurological disorders, the Italian Consensus Conference on Pain in Neurorehabilitation (ICCP) summarized the studies on this field to provide guidance on its use. Methods: A review of the existing reviews and meta-analyses was performed to assess the magnitude of the placebo effect in disorders that may undergo neurorehabilitation treatment. The search was performed on Pubmed using placebo, pain, and the names of neurological disorders as keywords. Methodological quality was assessed using a pre-existing checklist. Data about the magnitude of the placebo effect were extracted from the included reviews and were commented in a narrative form. Results: 11 articles were included in this review. Placebo treatments showed weak effects in central neuropathic pain (pain reduction from 0.44 to 0.66 on a 0-10 scale) and moderate effects in postherpetic neuralgia (1.16), in diabetic peripheral neuropathy (1.45), and in pain associated to HIV (1.82). Moderate effects were also found on pain due to fibromyalgia and migraine; only weak short-term effects were found in complex regional pain syndrome. Confounding variables might have influenced these results. Clinical implications: These estimates should be interpreted with caution, but underscore that the placebo effect can be exploited in neurorehabilitation programs. It is not necessary to conceal its use from the patient. Knowledge of placebo mechanisms can be used to shape the doctor-patient relationship, to reduce the use of analgesic drugs and to train the patient to become an active agent of the therapy