# Seminários

## HOJE

Quasi-nonassociativity from an exceptional spectrum-generating superalgebra.

**Expositor:**

*Francesco Toppan*- CBPF

**Teoria de Representações**

**Resumo: **Exceptional Lie (super)algebras are derived from octonions. I present the Calogero-deformed quantum oscillator derived from the spectrum generating superalgebra F(4). Its spectrum is a direct sum of F(4) lowest weight representations. This system is a unique example of “quasi-nonassociativity”. This means, in particular, that the Calogero coupling constants are determined in terms of the octonionic structure constants. The Hilbert space is a 16-ple of square integrable functions.

This talk is based on the paper arXiv:1711.02923[math-ph], published in J. Math. Phys. 59, 022101 (2018) in collaboration with N. Aizawa and Z. Kuznetsova.

Os efeitos da difusão capilar em sistemas não estritamente hiperbólicos de leis de conservação

**Expositor:**

*Luis Fernando Lozano Guerrero*- IMPA

**Colóquio dos Alunos**

**Resumo: **Resumo:

O problema de Riemann para o fluxo trifásico não linear em meios porosos tem soluções com estrutura muito rica, possivelmente por causa da perda de hiperbolicidade estrita. É prática padrão negligenciar os termos capilares e considerar as equações do ponto de vista de leis de conservação hiperbólicas. No entanto, muitos estudos consideram os efeitos da difusão na solução do problema de Riemann. Em alguns trabalhos, a difusão artificial foi levada em conta para comprovar a unicidade de certas soluções para o Problema de Riemann. Meu objetivo é apresentar o uso do método da curva de onda para encontrar soluções para problemas de Riemann com adição de efeitos capilares por meio de termos difusivos não lineares.

## PRÓXIMOS

Hydrodynamic quantum analogs

**Expositor:**

*John Bush*- Departamento de Matemática, MIT

**Matematica Aplicada e Computacional**

**Resumo: **Droplets walking on a vibrating fluid bath exhibit several features previously thought to be exclusive to the microscopic, quantum realm. These walking droplets propel themselves by virtue of a resonant interaction with their own wavefield, and so represent the first macroscopic realization of a pilot-wave system of the form proposed for microscopic quantum dynamics by Louis de Broglie in the 1920s. New experimental and theoretical results allow us to rationalize the emergence of quantum-like behavior in this hydrodynamic pilot-wave system in a number of settings, and explore its potential and limitations as a quantum analog.

Minimal immersions and relative nullity

**Expositor:**

*Theodoros Vlachos*- University of Ioannina, Greece

**Geometria Diferencial**

**Resumo: **We discuss minimal isometric immersions with relative nullity. We provide a classification of complete minimal isometric immersions into space forms with large index of relative nullity using tools from analysis.

The complexity of classical music networks

**Expositor:**

*Vitor Rolla*- IMPA

**Computação Gráfica**

**Resumo: **Previous work suggests that musical networks often present the scale-free and the small-world properties. From a musician's perspective, the most important aspect missing in those studies was harmony. In addition to that, the previous work made use of outdated statistical methods. Traditionally, least-squares linear regression is utilised to fit a power law to a given data set. However, according to Clauset et al. such a traditional method can produce inaccurate estimates for the power law exponent. In this paper, we present an analysis of musical networks which considers the existence of chords (an essential element of harmony). Here we show that only 52.5% of music in our database presents the scale-free property, while 62.5% of those pieces present the small-world property. Previous work argues that music is highly scale-free; consequently, it sounds appealing and coherent. In contrast, our results show that not all pieces of music present the scale-free and the small-world properties. In summary, this research is focused on the relationship between musical notes (Do, Re, Mi, Fa, Sol, La, Ti, and their sharps) and accompaniment in classical music compositions.

Local Hölder continuity of the isoperimetric profile in complete noncompact Riemannian manifolds with bounded geometry

**Expositor:**

*Abraham Munoz Flores*- UERJ

**Geometria Diferencial**

**Resumo: **For a complete noncompact connected Riemannian manifold with bounded geometry $M^n$, we prove that the isoperimetric profile function $I_{M^n}$ is a locally $(1-\frac{1}{n})$-Hölder continuous function so in particular it is continuous. Here for bounded geometry, we mean that M has Ricci curvature bounded below and volume of balls of radius $1$, uniformly bounded below with respect to its centers. We prove also the equivalence of the weak and strong formulation of the isoperimetric profile function in complete Riemannian manifolds which is based on a lemma having its own interest about the approximation of finite perimeter sets with finite volume by open bounded with smooth boundary ones of the same volume. This is a joint work with Stefano Nardulli.

The Noether-Lefschetz problem and the Hodge conjecture

**Expositor:**

*Ugo Bruzzo*- SISSA

**Álgebra**

**Resumo: **In this talk I will review some recent results about the Noether-Lefschetz problem for surfaces in normal 3-folds, in particular,about the density of the components of maximal codimension of the Noether-Lefschetz locus. Moreover, I will describe anapplication of some results about the Noether-Lefschetz problem to the Hodge conjecture for hypersurfaces in toric varieties.(Joint work with A. Grassi and partly with A. F. Lopez).

Cohomology of Lie algebroids on schemes

**Expositor:**

*Ugo Bruzzo*- Sissa

**Teoria de Representações**

**Resumo: **I will consider Lie algebroids on noetherian separated schemes and will show how their cohomology can be described as a derived functor. I will also describe applications to the nonabelian extensionproblem for such Lie algebroids. (Partly in collaborationwith E. Aldrovandi and V. Rubtsov).

Color Lie (super)algebras and Z2 × Z2 symmetries in the Levi-Leblond equation.

**Expositor:**

*Zhanna Kuznetsova*- UFABC

**Teoria de Representações**

**Resumo: **We investigate systems with color Lie (super) algebra symmetries.In the first part of the talk I give a brief introduction in color Liealgebras and superalgebras focusing on the Z2*Z2 particular case.In the second part I present an analysis of the symmetry operators of theLevy-Leblond equation which is a nonrelativistic wave equation of a spin 1/2 particle (nonrelativistic analog of the Dirac equation). It is shown that the equation has two kinds of symmetries. One is given by the super Schroedinger algebra and the other one by a Z2×Z2 graded Lie superalgebra. The realizationof the Z2*Z2 superalgebra is presented in terms of matrix differential operators.