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

Characteristics of Feedback that Influence Student Confidence and Performance during Mathematical Modeling

This study focuses on characteristics of written feedback that influence students’ performance and confidence in addressing the mathematical complexity embedded in a Model-Eliciting Activity (MEA). MEAs are authentic mathematical modeling problems that facilitate students’ iterative development of solutions in a realistic context. We analyzed 132 first-year engineering students’ confidence levels and mathematical model scores on aMEA(pre and post feedback), along with teaching assistant feedback given to the students. The findings show several examples of affective and cognitive feedback that students reported that they used to revise their models. Students’ performance and confidence in developing mathematical models can be increased when they are in an environment where they iteratively develop models based on effective feedback

Integrazione. Le barriere della comunicazione

L'importanza ormai ampiamente riconosciuta, della comunicazione interculturale come strumento di integrazione sociale e culturale degli stranieri e, dunque, come obiettivo delle politiche pubbliche. L'idea di integrazione cui si fa riferimento in questo contesto, rimanda ad una interazione positiva, sostenuta da una adeguata strategia comunicativa , con l\u2019obiettivo di favorire percorsi di inclusione e partecipazione alla vita pubblica locale. Alla base di questa idea di integrazione vi \ue8 la consapevolezza che il riconoscimento di taluni diritti di per s\ue9 non \ue8 sufficiente a garantirne il rispetto e la possibilit\ue0 di esercizio da parte dei soggetti titolari, se non accompagnato dalla messa in atto di strumenti di informazione e facilitazione adeguati ed efficaci a rendere effettivo tale esercizio. Realizzare condizioni di pari opportunit\ue0 di accesso ai servizi, compresi quelli informativi, \ue8 dunque un obiettivo ineludibile di una politica impegnata a promuovere la rimozione di ostacoli di ordine linguistico, sociale e culturale che impediscono alle persone straniere o a particolari porzioni della popolazione straniera (es. donne, richiedenti asilo e rifugiati, nomadi) la reale fruizione del \u201csistema dei servizi pubblici\u201d

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

Alpha-particle clustering in excited expanding self-conjugate nuclei

The fragmentation of quasi-projectiles from the nuclear reaction 40Ca + 12C at 25 MeV/nucleon was used to produce alpha-emission sources. From a careful selection of these sources provided by a complete detection and from comparisons with models of sequential and simultaneous decays, strong indications in favour of $\alpha$-particle clustering in excited 16O, 20Ne and 24}Mg are reported.Comment: 8 pages, 4 figures, 12th International Conference on Nucleus-Nucleus collisions (NN2015), 21-26 June 2015, Catania, Ital

Emergent Gravity from Noncommutative Gauge Theory

We show that the matrix-model action for noncommutative U(n) gauge theory actually describes SU(n) gauge theory coupled to gravity. This is elaborated in the 4-dimensional case. The SU(n) gauge fields as well as additional scalar fields couple to an effective metric G_{ab}, which is determined by a dynamical Poisson structure. The emergent gravity is intimately related to noncommutativity, encoding those degrees of freedom which are usually interpreted as U(1) gauge fields. This leads to a class of metrics which contains the physical degrees of freedom of gravitational waves, and allows to recover e.g. the Newtonian limit with arbitrary mass distribution. It also suggests a consistent picture of UV/IR mixing in terms of an induced gravity action. This should provide a suitable framework for quantizing gravity.Comment: 28 pages + 11 pages appendix. V2: references and discussion added. V3: minor correctio

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

Noncommutative Symmetries and Gravity

Spacetime geometry is twisted (deformed) into noncommutative spacetime geometry, where functions and tensors are now star-multiplied. Consistently, spacetime diffeomorhisms are twisted into noncommutative diffeomorphisms. Their deformed Lie algebra structure and that of infinitesimal Poincare' transformations is defined and explicitly constructed. This allows to construct a noncommutative theory of gravity.Comment: 26 pages. Lectures given at the workshop `Noncommutative Geometry in Field and String Theories', Corfu Summer Institute on EPP, September 2005, Corfu, Greece. Version 2: Marie Curie European Reintegration Grant MERG-CT-2004-006374 acknowledge