Harder-Narasimhan filtration for rank 2 tensors and stable coverings

We construct a Harder-Narasimhan filtration for rank $2$ tensors, where there does not exist any such notion a priori, as coming from a GIT notion of maximal unstability. The filtration associated to the 1-parameter subgroup of Kempf giving the maximal way to destabilize, in the GIT sense, a point in the parameter space of the construction of the moduli space of rank $2$ tensors over a smooth projective complex variety, does not depend on certain integer used in the construction of the moduli space, for large values of the integer. Hence, this filtration is unique and we define the Harder-Narasimhan filtration for rank $2$ tensors as this unique filtration coming from GIT. Symmetric rank $2$ tensors over smooth projective complex curves define curve coverings lying on a ruled surface, hence we can translate the stability condition to define stable coverings and characterize the Harder-Narasimhan filtration in terms of intersection theory.Comment: 22 pages; Minor changes suggested by the referee; To appear on Proc. Indian Acad. Sci. (Math. Sci.

On the Operator Product Expansion in Noncommutative Quantum Field Theory

Motivated by the mixing of UV and IR effects, we test the OPE formula in noncommutative field theory. First we look at the renormalization of local composite operators, identifying some of their characteristic IR/UV singularities. Then we find that the product of two fields in general cannot be described by a series expansion of single local operator insertions.Comment: 15 pages, six figures. LaTeX, JHEP class. Minor improvements, typos corrected. To be published in JHE

Separation of analytic sets by rectangles of low complexity

We provide Hurewicz tests for the separation of disjoint analytic sets by rectangles of the form $\Gamma\times\Gamma'$ for $\Gamma,\Gamma'\in {\mathbf\Sigma^0_1 , \mathbf\Pi^0_1 , \mathbf\Pi^0_2 }$

"Low-Income Students of Color in the U.S. Neoliberal Public Education System: An Examination of Federal and State Intervention Policies”

In this thesis I will use a critical policy analysis approach to examine US education reform and its effects on social inequality. I situate my analysis within the rise of neoliberal ideology which prioritizes market-driven values, champions individualism, diminishes social responsibility, and promotes deregulation. I seek to answer research questions such as: how does the United States’ neoliberal agenda create, maintain, and reproduce the marginalization of low-income students of color? How is the neoliberal agenda embedded in US education policy and law at state and federal levels? And, how might students of color conceptualize themselves within the larger framework of neoliberalism? As evidence I draw on theory, policy analysis, and existing empirical data on one of the most underperforming public schools in San Diego, California, with most of the students being minorities and low-income: Abraham Lincoln High School