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Verbalització multilingüística del llenguatge simbòlic, una eina d'aprenentatge

Mon, 13 May 2013 14:46:06 GMT

Title: Verbalització multilingüística del llenguatge simbòlic, una eina d'aprenentatge Authors: Alsina Aubach, Montserrat; Soler Lorente, Mónica

Improving symbolic language comprehension

Mon, 08 Apr 2013 13:31:02 GMT

Title: Improving symbolic language comprehension Authors: Alsina Aubach, Montserrat; Bonet Dalmau, Jordi Abstract: We focus on the goal of “Handling mathematical symbols and formalism” through the methodology of Content and Language Integrated Learning. The use of foreign language highlights, and possibly increases, the difficulties in the point of mathematical competence, but it can also be used to fix them. That is, making explicit the equivalence between formal and verbal language could improve symbolic language comprehension. Multilingual Formulae, an on -line resource at http://mformulae.epsem.upc.edu, is designed to give support in that direction, as equivalence is not found explicitly in textbooks or research papers. It contains sets of formulas with the corresponding written and oral version in several languages. The project, conducted by professors at the UPC Engineering School at Manresa Campus, is addressed to lecturers and students as a support to ensure effective communication when both Symbolic and Foreign language are used.

Computation of ATR Darmon points on nongeometrically modular elliptic curves

Fri, 05 Apr 2013 13:25:08 GMT

Title: Computation of ATR Darmon points on nongeometrically modular elliptic curves Authors: Guitart Morales, Xavier; Masdeu, Marc Abstract: ATR points were introduced by Darmon as a conjectural con- struction of algebraic points on certain elliptic curves for which the Heegner-point method is not in general available. So far, the only numerical evidence, provided by Darmon–Logan and G ̈ artner,concernedcurvesarisingasquotientsofShimuracurves. In those special cases, the ATR points can be obtained from the already existing Heegner points, thanks to results from Zhang and Darmon–Rotger–Zhao. In this paper, we compute for the first time an algebraic ATR point on a curve that is not uniformizable by any Shimura curve, thus providing the first piece of numerical evidence that Darmon’s construction works beyond geometric modularity. To this pur- pose, we improve the method proposed by Darmon and Logan by removing the requirement that the real quadratic base field be norm-Euclidean and accelerating the numerical integration of Hilbert modular forms.

Sato-Tate distributions and Galois endomorphism modules in genus 2

Fri, 01 Mar 2013 10:38:57 GMT

Title: Sato-Tate distributions and Galois endomorphism modules in genus 2 Authors: Fité, Francesc; Kedlaya, Kiran; Rotger Cerdà, Víctor; Sutherland, Andrew Abstract: For an abelian surface A over a number eld k, we study the limit- ing distribution of the normalized Euler factors of the L-function of A. This distribution is expected to correspond to taking characteristic poly- nomials of a uniform random matrix in some closed subgroup of USp(4); this Sato-Tate group may be obtained from the Galois action on any Tate module of A. We show that the Sato-Tate group is limited to a particular list of 55 groups up to conjugacy. We then classify A according to the Galois module structure on the R-algebra generated by endomorphisms of AQ (the Galois type), and establish a matching with the classi cation of Sato-Tate groups; this shows that there are at most 52 groups up to con- jugacy which occur as Sato-Tate groups for suitable A and k, of which 34 can occur for k = Q. Finally, we exhibit examples of Jacobians of hyperel- liptic curves exhibiting each Galois type (over Q whenever possible), and observe numerical agreement with the expected Sato-Tate distribution by comparing moment statistics.

Elaboració de recursos multimèdia per a l'ensenyament/aprenentatge en anglès en graus tecnològics

Wed, 13 Feb 2013 15:43:37 GMT

Title: Elaboració de recursos multimèdia per a l'ensenyament/aprenentatge en anglès en graus tecnològics Authors: Alsina Aubach, Montserrat; Fortuny Santos, Jordi; Giralt Mas, Ma. Rosa Abstract: En aquest article es presenta el procés d'elaboració de recursos per a la impartició d'assignatures en anglès a l'ensenyament superior. Els principals resultats són les aplicacions Class-Talk i Multilingual Formulae, obertes a la comunitat educativa interessada en AICLE. Class-talk (http://www.upc.edu/slt/classtalk) conté la fraseologia docent d'us habitual. Multilingual Formulae (https://mformulae.epsem.upc.edu) conté la verbalització, oral i escrita, de fórmules i símbols matemàtics. Ambdós recursos s'adrecen a professorat i alumnat, d'origen català o internacional, involucrat en programes de millora de la competència lingüística; innovació docent al servei de la internacionalització de la universitat.

Teaching symbolic language to non-native speakers

Thu, 15 Nov 2012 11:42:22 GMT

Title: Teaching symbolic language to non-native speakers Authors: Bonet Dalmau, Jordi; Alsina Aubach, Montserrat Abstract: In this paper, we describe how an on-line resource, primarily intended to improve the proficiency in a foreign language, can also facilitate the understanding of the symbolic language in an engineering degree course. We think that thanks to the use of this resource, a course in an engineering degree can tackle both the challenge of teaching symbolic language to non-native speakers and the challenge of doing this without losing insight into the concepts that appear in the course.

Single-factor lifting and factorization of polynomials over local fields

Tue, 18 Sep 2012 16:54:18 GMT

Title: Single-factor lifting and factorization of polynomials over local fields Authors: Guàrdia Rubies, Jordi; Nart, Enric; Pauli, S. Abstract: Let f (x) be a separable polynomial over a local field. The Montes algorithm computes certain approximations to the different irreducible factors of f (x), with strong arithmetic properties. In this paper, we develop an algorithm to improve any one of these approximations, till a prescribed precision is attained. The most natural application of this ‘‘single-factor lifting’’ routine is to combine it with the Montes algorithm to provide a fast polynomial factorization algorithm. Moreover, the single-factor lifting algorithm may be applied as well to accelerate the computational resolution of several global arithmetic problems in which the improvement of an approximation to a single local irreducible factor of a polynomial is required

Abelian varieties with many endomorphisms and their absolutely simple factors

Mon, 09 Jul 2012 07:36:39 GMT

Title: Abelian varieties with many endomorphisms and their absolutely simple factors Authors: Guitart Morales, Xavier Abstract: We characterize the abelian varieties arising as absolutely simple factors of GL2-type varieties over a number field k. In order to obtain this result, we study a wider class of abelian varieties: the k-varieties A/k satisfying that End0 k(A) is a maximal subfield of End0 ¯k (A). We call them Ribet–Pyle varieties over k. We see that every Ribet–Pyle variety over k is isogenous over ¯k to a power of an abelian k-variety and, conversely, that every abelian k-variety occurs as the absolutely simple factor of some Ribet–Pyle variety over k. We deduce from this correspondence a precise description of the absolutely simple factors of the varieties over k of GL2-type.

Higher Newton polygons in the computation of discriminants and prime ideal decomposition in number fields

Wed, 25 Jan 2012 15:10:02 GMT

Title: Higher Newton polygons in the computation of discriminants and prime ideal decomposition in number fields Authors: Guàrdia Rubies, Jordi; Montes Peral, Jesús; Nart, Enric Abstract: We present an algorithm for computing discriminants and prime ideal decomposition in number fields. The algorithm is a refinement of a p-adic factorization method based on Newton polygons of higher order. The running-time and memory requirements of the algorithm appear to be very good: for a given prime number p, it computes the p-valuation of the discriminant and the factorization of p in a number field of degree 1000 in a few seconds, in a personal computer.

Newton polygons of higher order in algebraic number theory

Wed, 25 Jan 2012 15:03:12 GMT

Title: Newton polygons of higher order in algebraic number theory Authors: Guàrdia Rubies, Jordi; Montes Peral, Jesús; Nart, Enric Abstract: We develop a theory of arithmetic Newton polygons of higher order, that provides the factorization of a separable polynomial over a p-adic eld, together with relevant arithmetic information about the elds generated by the irreducible factors. This carries out a program suggested by . Ore. As an application, we obtain fast algorithms to compute discriminants, prime ideal decomposition and integral bases of number elds.

Exposició "Les matemàtiques i la vida"

Wed, 16 Mar 2011 17:02:24 GMT

Title: Exposició "Les matemàtiques i la vida" Authors: Alsina Aubach, Montserrat

Tipus de reduccions de corbes

Fri, 08 Oct 2010 13:18:39 GMT

Title: Tipus de reduccions de corbes Authors: Guitart Morales, Xavier Editor: Rotjer, V. Description: Publicat originalment dins la col·lecció "Notes del Seminari de Teoria de Nombres (UB-UAB-UPC)". Disponible a:

On the modularity level of modular abelian varieties over number fields

Fri, 30 Jul 2010 10:16:08 GMT

Title: On the modularity level of modular abelian varieties over number fields Authors: Gonzalez Jimenez, Enrique; Guitart Morales, Xavier Abstract: Let f be a weight two newform for Γ1(N) without complex multiplication. In this article we study the conductor of the absolutely simple factors B of the variety A f over certain number fields L. The strategy we follow is to compute the restriction of scalars ResL/Q(B), and then to apply Milne’s formula for the conductor of the restriction of scalars. In this way we obtain an expression for the local exponents of the conductor NL (B). Under some hypothesis it is possible to give global formulas relating this conductor with N. For instance, if N is squarefree, we find that NL (B) belongs to Z and NL (B)f dim B L = N dim B, where fL is the conductor of L Description: Electronic version of an article published as "Journal of number theory", vol. 130, no 7, p. 1560-1570. DOI no 10.1016/j.jnt.2010.03.003.

Parametrization of Abelian K-surfaces with quaternionic multiplication

Wed, 02 Jun 2010 15:06:27 GMT

Title: Parametrization of Abelian K-surfaces with quaternionic multiplication Authors: Guitart Morales, Xavier; Molina Blanco, Santiago Abstract: We prove that the Abelian K-surfaces whose endomorphism algebra is a rational quaternion algebra are parametrized, up to isogeny, by the K-rational points of the quotient of certain Shimura curves by the group of their Atkin–Lehner involutions.

On the Torelli problem and Jacobian Nullwerte in genus three

Thu, 29 Jan 2009 13:25:35 GMT

Title: On the Torelli problem and Jacobian Nullwerte in genus three Authors: Guàrdia Rubies, Jordi Abstract: We give a closed formula for recovering a non-hyperelliptic genus three curve from its period matrix, and derive some identities between Jacobian Nullwerte in dimension three.