From Out of Sight to \u27Outta Sight!\u27 Collaborative Art Projects that Empower Children with At-Risk Tendencies

Children with at-risk tendencies are often left out of sight/ site/ cite because of their potential for academic and social failure. Like all children, children with at-risk tendencies have something of value to contribute to society and yearn for opportunities to show of their talents. This article discusses how three different groups of children with at-risk tendencies in Florida and Tennessee participated in site specific community art projects that targeted their needs. Although each student population worked a different theme, the children expressed similar learning outcomes when describing their involvement with the project. This study demonstrates how collaborative community art projects engage students in constructive behaviors that help prepare them for life. The success they gain from their participation in these projects can be transferred to other areas of their lives and show society that they are truly outta sight individuals

On computing Belyi maps

We survey methods to compute three-point branched covers of the projective line, also known as Belyi maps. These methods include a direct approach, involving the solution of a system of polynomial equations, as well as complex analytic methods, modular forms methods, and p-adic methods. Along the way, we pose several questions and provide numerous examples.Comment: 57 pages, 3 figures, extensive bibliography; English and French abstract; revised according to referee's suggestion

On nondegeneracy of curves

A curve is called nondegenerate if it can be modeled by a Laurent polynomial that is nondegenerate with respect to its Newton polytope. We show that up to genus 4, every curve is nondegenerate. We also prove that the locus of nondegenerate curves inside the moduli space of curves of fixed genus g > 1 is min(2g+1,3g-3)-dimensional, except in case g=7 where it is 16-dimensional

On explicit descent of marked curves and maps

We revisit a statement of Birch that the field of moduli for a marked three-point ramified cover is a field of definition. Classical criteria due to D\`ebes and Emsalem can be used to prove this statement in the presence of a smooth point, and in fact these results imply more generally that a marked curve descends to its field of moduli. We give a constructive version of their results, based on an algebraic version of the notion of branches of a morphism and allowing us to extend the aforementioned results to the wildly ramified case. Moreover, we give explicit counterexamples for singular curves.Comment: 35 page

Nondegenerate curves of low genus over small finite fields

In a previous paper, we proved that over a finite field $k$ of sufficiently large cardinality, all curves of genus at most 3 over k can be modeled by a bivariate Laurent polynomial that is nondegenerate with respect to its Newton polytope. In this paper, we prove that there are exactly two curves of genus at most 3 over a finite field that are not nondegenerate, one over F_2 and one over F_3. Both of these curves have remarkable extremal properties concerning the number of rational points over various extension fields.Comment: 8 pages; uses pstrick

Explicit methods for Hilbert modular forms

We exhibit algorithms to compute systems of Hecke eigenvalues for spaces of Hilbert modular forms over a totally real field. We provide many explicit examples as well as applications to modularity and Galois representations.Comment: 52 pages, 10 figures, many table