In a recent paper, Fortin, Jacob and Mathieu [5] found congruences modulo powers of 2 for the values of the overpartition function p(n) in arithmetic progressions. The moduli for these congruences ranged as high as 64. This note shows that p(n) ≡ 0 (mod 64) for a set of integers of arithmetic density 1.

— In the moduli space Pd of degree d polynomials, the set Pern(w) of classes [f ] for which f admits a cycle of exact period n and multiplier multiplier w is known to be an algebraic hypersurface. We prove that, given w ∈ C, these hypersurfaces equidistribute towards the bifurcation current as n tends to infinity.

We consider principally polarized abelian varieties with quaternionic multiplication over number fields and we study the field of moduli of their endomorphisms in relation to the set of rational points on suitable Shimura varieties. Published in Intern. J. Math. M. Sc. 52 (2004), 2795-2808.

We study the moduli spaces and compute the fundamental groups of plane sextics of torus type with the set of inner singularities 2A8 or A17. We also compute the fundamental groups of a number of other sextics, both of and not of torus type. The groups found are simplest possible, i.e., Z2 ∗Z3 and Z6, respectively.

In the moduli space of quadratic differentials over complex structures on a surface, we construct a set of full Hausdorff dimension of points with bounded Teichmüller geodesic trajectories. The main tool is quantitative nondivergence of Teichmüller horocycles, due to Minsky and Weiss. This has an application to billiards in rational polygons.

This paper, motivated from complex dynamics and algebraic geometry, studies the moduli space of polynomial maps of C, from the standpoint of their fixed-point eigenvalues. We denote by e Pd the set of affine conjugacy classes of f(z) ∈ C[z] with degC = d, and define the map Φd : e Pd → e Λd := n (λ1, . . . , λd) ∈ C d ̨

By using an exact method to impose unitarity on the neutrino data we show that around the central values of the moduli of the PMNS matrix there is a continuous approximate unitary set of matrices, all of them being consistent with a maximal CP violation in the lepton sector, i.e. δ ≈ 90◦, over a wide range for Ve3 values.

Successful synthesis of the stable metal-free two-dimensional polymer graphitic carbon-nitride with remarkable properties has made it as one of the most promising nanostructures in many novel nanodevices, especially photocatalytic ones. Understanding the mechanical properties of nanostructures is of crucial importance. Thus, this study employs density functional theory (DFT) to obtain the mecha...

In this paper we study the geometry of 14 families K3 surfaces Picard number four with finite automorphism group, whose Neron—Severi lattices have been classified by È. B. Vinberg. We provide projective models, identify degrees a generating set Cox ring and in some cases prove unirationality associated moduli space.

In [17], we considered the local classification of plane curves on the symplectic plane. In particular, we introduced the number “symplectic defect”, which represents the difference of two natural equivalence relations on plane curves, the equivalence by diffeomorphisms and that by symplectomorphisms. For an immersion, two equivalence relations coincide, so the symplectic defect is null. For co...