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  • Torsion invariant on cellular complexes 

    Santos, Gustavo de Oliveira Cardoso dos (Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 20/08/2024)
    Classifying spaces up to homeomorphism, homotopy equivalence, or combinatorial equivalence is one of the main problems in Topology. To achieve this, we have several invariants in Algebraic Topology, such as Euler ...
  • Confinamento quântico: influência geométrica na análise espectral 

    Bello, Diana Carolina Suarez (Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 30/08/2024)
    Let $\Omega$ be a domain in $\mathbb {R}^3$. Consider $-\Delta_{\Omega_\beta}^D$ the Dirichlet Laplacian operator in $\Omega_\beta$. In this work, we performed a detailed analysis of the spectral properties of ...
  • Soluções normalizadas para equações de Schrödinger de massa supercrítica com potencial 

    Tomaz, Carolina Santana (Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 05/08/2024)
    In this work, we are interested in proving the existence of normalized solutions to the Schrödinger equation -∆u+V(x)u+λu=|u|^(p-2)u, in R^N, in the supercritical mass case and subcritical Sobolev case, 2+4/N < p < 2^* ...
  • Sequência espectral persistente de Leray e propriedades de separação para variedades generalizadas 

    Vellozo, Telmo Irineo Acosta (Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 22/08/2024)
    In this thesis we work on two different topics. On the one hand, we manage to construct a spectral sequence that calculates the persistent cohomology of a space from the persistent cohomology in each open and its interceptions ...
  • Minimalidade de coincidências do tipo Borsuk-Ulam em superfícies utilizando tranças 

    Silva, Caio Lima (Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 18/07/2024)
    Given topological spaces $M$ and $N$, with $M$ equipped with a free involution $\tau$, we define the set of Borsuk-Ulam coincidences as $$ \operatorname{BUCoin}(f; \tau) = \{ \{ x, \tau(x) \} \ | \ f(x) = f(\tau(x)) ...
  • Comportamento assintótico para equações de placa fracionárias 

    Picolli, Iago Aparecido da Silva (Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 16/07/2024)
    In this work, we consider two second-order fractional semilinear plate equations in time. In the first problem, we investigate an equation governed by a biharmonic operator, with clamped boundary conditions in a smooth ...
  • Pseudo-parallel immersions of Lorentzian manifolds in pseudo-Riemannian space forms 

    Estrada, Mynor Ademar Melara (Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 24/05/2024)
    In this Ph.D. thesis, we study pseudo-parallel submanifolds in pseudo-Riemannian space forms. We give a characterization of pseudo-parallel Lorentzian surfaces with non-flat normal bundle in pseudo-Riemannian space forms ...
  • Lebesgue solvability of equations associated to elliptic and canceling linear differential operators with measure data 

    Biliatto, Victor Sandrin (Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 10/04/2024)
    In this thesis, we present new results on the solvability of the equation A*(x,D) f = µ for f in L^p, with complex measure data µ, associated to an elliptic linear differential operator A(x,D) of order m with variable ...
  • Poliedros de Newton e invariantes de singularidades determinantais 

    Costa, Maicom Douglas Varella Costa (Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 31/01/2024)
    In this work, we study invariants of determinantal singularities, by analysing the Newton polyhedra which arise from the entries of a given matrix. The main contribution of this work is providing sufficient conditions, ...
  • Equações elípticas com o Laplaciano fracionário e não linearidades indefinidas 

    Gobbi, Ray Santos (Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 24/04/2024)
    In this work, we investigate the existence, non-existence and multiplicity of positive solutions of the problem below, \begin{equation*} \left\lbrace \begin{array}{rll} (-\Delta)^s u -\lambda u & = f(x)g(u) ,& ...
  • Operadores de Calderón-Zygmund, pseudo-diferenciais e espaços de Hardy 

    Vasconcelos Filho, Claudio Henrique Machado (Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 09/03/2018)
    The purpose of this work is to study the Hardy spaces Hp(Rn) on euclidean spaces and your localized version, known as hp(Rn). As an application of this theory, we are going to show that Calderón-Zygmund and pseudo-differential ...
  • Multiplicação de distribuições no estudo de soluções de ondas delta choque 

    Ferreira, Liliane da Cunha (Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 15/12/2023)
    In this work, we will find the delta shock wave solution for three Riemann problem where two are hyperbolic systems of conservation laws with linear damping and a three-component nonlinear chromatography model. We will ...
  • Soluções estacionárias positivas de equações de primeira ordem com termo de Kirchhoff e falta de coercitividade 

    Lourenço, Renan (Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 10/05/2023)
    In this work, we investigate the existence of positive stationary solutions of the Kirchhoff equations in a limited domain, an inhomogeneous spatial coefficient and a function of first order terms with growth up to the ...
  • Campos de vetores suaves por partes: preservação de medida, pressão topológica e dinâmica simbólica 

    Florentino, Marco Aurélio do Carmo (Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 10/08/2023)
    The study of piecewise smooth vector fields (PSVFs) has been consolidated in recent years not only because of the beauty of the theoretical results, but also because of the proximity of this area to applied sciences such ...
  • Merge trees decoradas e TDA 

    Falsarella, Guilherme de Carvalho (Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 10/08/2023)
    In this document, first we will introduce Persistance Homology and Category Theory basic concepts. Afterwards, we will develop the Merge Tree Theory which will be useful to keep track of connected components evolution of ...
  • Algumas aplicações de p-pontos 

    Zancul, Hugo Gili (Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 24/08/2023)
    In this work we analyze the concept of \(p\)-points in \(\omega\) and its relation with forcing, in particular Sacks forcing and side-by-side Sacks forcing. With this we verify that the existence of \(p\)-points with ...
  • On the classification of two dimensional flows 

    Thomaz, Rodrigo (Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 02/08/2023)
    Lawrence Markus, a well-known mathematician, published, in 1954, a strong result about classification of planar vector fields. Afterwards, Dean Arnold Neumann generalized such work for continuous flows, and the result ...
  • Teorema da esfera suave via fluxo de Ricci 

    Belli, Rafael da Silva (Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 04/08/2023)
    The goal of this dissertation is the theoretical development of the Ricci flow, a differential equation over a family of Riemannian metrics on an arbitrary differentiable manifold, and its use in the proof of the so-called ...
  • Campos de Yang-Mills fracamente estáveis na esfera de dimensão quatro 

    Caetano Junior, Claudinei (Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 03/05/2023)
    In this work we made a quick study on some basic results related to Groups and Lie Algebras, action of Groups and Fiber Bundles with the objective of defining connections in Principal Bundles and, later, in Associated ...
  • The period function for some planar piecewise vector fields 

    Santos, Mirianne Andressa Silva (Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 27/04/2023)
    In this work, we study the period function for fixed families of piecewise differential vector fields with a line of discontinuities. These systems, indistinctly called piecewise or nonsmooth, appear in several applications, ...

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