Abstract:
Let C be a smooth projective curve over the field of the complex numbers. We consider Brill-Noether loci over the moduli of maps from C to the Grassmannian G(m,n) and the corresponding Quot schemes of quotients of a trivial vector bundle on C compactifying the spaces of morphisms. We study in detail the case in which m=2, n=4. We prove results on the irreducibility and dimension of these Brill-Noether loci and we address explicit formulas for their cohomology classes. We study the existence problem of these spaces which is closely related with the problem of classification of vector bundles over curves.

Abstract:
We consider the Quot scheme, R_{d}, compactifying the space of degree d maps from the projective line to the Grassmannian of lines. We give an algorithm for computing the degree of R_{d} under a "generalized Pl\"ucker embedding", this is a certain Gromov-Witten invariant. The approach is to apply the Atiyah-Bott localization formula for the natural C^{*}-action on R_{d}. These numbers can be obtained directly from Vafa-Intriligator formula.

Abstract:
We compute the degree of the variety parametrizing rational ruled surfaces of degree d in the projective space by relating the problem to Gromov-Witten invariants and Quantum cohomology.

Abstract:
We prove a non abelian Torelli type result for smooth projective curves by working in the derived category of some associated polarized Quot schemes and defining Brill-Noether loci and Abel-Jacobi maps on them.

Abstract:
We study the geometry of the Kontsevich compactification of stable maps to the Grassmannian of lines in the projective space. We consider a stratification of this space. As an application we compute the degree of the variety parametrizing rational ruled surfaces with a minimal directix of degree d/2-1 by intersecting divisors in the moduli space of stable maps. For example, there are 128054031872040 rational ruled sextics passing through 25 points in $\mathbb{P}^{3}$ with a minimal directrix of degree 2.

Abstract:
We consider fibrations by abelian surfaces and K3 surfaces over a one dimensional base that are Calabi-Yau and we obtain dual fibrations that are derived equivalent to the original fibration. Finally, we relate the problem to mirror symmetry.

Abstract:
We study cyclic finite Galois extensions of the rational function field of the projective line P^{1}(F_q) over a finite field F_q with q elements defined by considering quotient curves by finite subgroups of the projective linear group PGL(2,q), and we enumerate them expressing the count in terms of Stirling numbers.

A sample of 80 secondary students was required to take an information integration
theory study to explore judgment formation toward health risk behavior
regarding obesity. Here, twelve social scenarios containing a simulated
actor were implemented (vignettes) having in mind a three factor experimental
factor design (diet, weight and physical activity). Subjects had to read each
vignette and provide an answer by marking ten points anchored scale to provide
judgment on actors’ possible health risk outcome. Results showed that
study participants valuated diet as the most relevant factor, followed by the
description of weight and finally followed by the factor of physical activity.
They impose systematic thinking to integrate different sources of information
provided by factor manipulation in the vignettes by using a cognitive summative
rule. Implications of this study result to clinical intervention in obesity as
well as for theoretical considerations of cognitive models of health risk behavior
are discussed in the present article.

Single particle
characterization can provide information on the evolution of size distribution
and chemical composition of pollution aerosol. The work described the use of
Scanning Electron Microscopy (SEM) combined with X-ray Dispersive Energy
Spectrometry (EDS) to characterize inorganic atmospheric particles samples
collected on PM10 filters from January 2013 to October 2013 from three zones
within the city of Hermosillo, Sonora. Specimens were initially processed by separating
the collected particles from the filters by means of submersing a 2 cm^{2} section of each filter into isopropilic alcohol within a test tube for 5
minutes. Then, an aliquot of
the suspension was placed over a sample holder and into the SEM. The different
elements found amongst
individual particles were Al, Ba, Ca, Cl, Cr, Cu, Fe, K, Mg, Mn, Na, Pb, S, Si,
Ti and U. The predominant elements are Al (17.10 At%), Si (10.17 At%), Ba (5.90
At%), Fe (5.45 At%) and U (2.32 At%). The particles were classified into groups
based on morphology and elemental composition: particles of aluminosilicate,
salts of sodium chloride, sulfates, metal particles, barium and uranium. These
particles morphology and chemical composition, illustrate an abundance of
natural elements within the zone. However, some of the elements presented are
directly related with human activities, and are of much interest from the
public health and environmental perspectives.

Abstract:
We study the Horn problem in the context of algebraic codes on a smooth projective curve defined over a finite field, reducing the problem to the representation theory of the special linear group $SL(2,F_q)$. We characterize the coefficients that appear in the Kronecker product of symmetric functions in terms of Gromov-Witten invariants of the Hilbert scheme of points in the plane. In addition we classify all the algebraic codes defined over the rational normal curve.