Regularization of Discontinuous Foliations: Blowing up and Sliding Conditions via Fenichel Theory

We study the regularization of an oriented 1-foliation $\mathcal{F}$ on $M \setminus \Sigma$ where $M$ is a smooth manifold and $\Sigma \subset M$ is a closed subset, which can be interpreted as the discontinuity locus of $\mathcal{F}$. In the spirit of Filippov's work, we define a sliding and sewing dynamics on the discontinuity locus $\Sigma$ as some sort of limit of the dynamics of a nearby smooth 1-foliation and obtain conditions to identify whether a point belongs to the sliding or sewing regions.Comment: 32 page

Global Analytic Solutions for the Nonlinear Schr\"odinger Equation

We prove the existence of global analytic solutions to the nonlinear Schr\"odinger equation in one dimension for a certain type of analytic initial data in $L^2$.Comment: Corrected errors in proofs in section

A Remark on Unconditional Uniqueness in the Chern-Simons-Higgs Model

The solution of the Chern-Simons-Higgs model in Lorenz gauge with data for the potential in $H^{s-1/2}$ and for the Higgs field in $H^s \times H^{s-1}$ is shown to be unique in the natural space $C([0,T];H^{s-1/2} \times H^s \times H^{s-1})$ for $s \ge 1$, where $s=1$ corresponds to finite energy. Huh and Oh recently proved local well-posedness for $s > 3/4$, but uniqueness was obtained only in a proper subspace $Y^s$ of Bourgain type. We prove that any solution in $C([0,T];H^{1/2} \times H^1 \times L^2)$ must in fact belong to the space $Y^{3/4+\epsilon}$, hence it is the unique solution obtained by Huh and Oh

Generalized Flow-Box property for singular foliations

We introduce a notion of generalized Flow-Box property valid for general singular distributions and sub-varieties (based on a dynamical interpretation). Just as in the usual Flow-Box Theorem, we characterize geometrical and algebraic conditions of (quasi) transversality in order for an analytic sub-variety $X$ (not necessarily regular) to be a section of a line foliation. We also discuss the case of more general foliations. This study is originally motivated by a question of Jean-Francois Mattei (concerning the strengthening of a Theorem of Mattei) about the existence of local slices for a (non-compact) Lie group action.Comment: Changes in Section

Trans Tessituras: Confounding, Unbearable, and Black Transgender Voices in Luso-Afro-Brazilian Popular Music

This dissertation shows how gay, trans and queer performers in Brazil, Portugal, and Angola, working in traditionally misogynistic, homo- and transphobic popular music genres, have successfully claimed and refigured those genres and repertoires through iterations of transgender voices and bodies. I show how Pabllo Vittar, Fado Bicha and Titica refigure normative gendered conventions of sex and song through trans formations of popular music genres. I locate them within a genealogy of queer Luso-Afro-Brazilian popular music practices and performances that deploy trans formations of voice, body, and repertoire. I trace a genealogy of transgender voice in Brazilian popular music to Ney Matogrosso’s 1975 debut release, through which I reveal a cacophony of queer, indigenous and Afro-Brazilian intersections; and in Portuguese popular music to António Variações 1982 debut, through whom I trace a fado genealogy of Afro-diasporic cultural practices, gender transgression and sexual deviance. Finally, I locate Titica’s music in practices of the black queer diaspora as a refiguring of Angolan postcolonial aesthetics. Together, these artists and their music offer a queer Luso-Afro-Brazilian diaspora in spectacular popular music formations that transit beside and beyond the Portuguese-speaking world, unbound by it, and refiguring hegemonic Luso-Afro-Brazilian discourses of gender, sexuality, race and nation