### Recent Submissions

• #### Hipoelipticidade global analítica e Gevrey de sublaplacianos sob condições Diofantinas ﻿

(Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 22/09/2022)
In this dissertation we consider the problem of global Gevrey regularity for a class of partial differential operators in the form of a sum of squares of vector fields and we show that these operators are globally Gevrey ...
• #### Camadas de heteroestruturas hexagonais planas modeladas por grafos quânticos ﻿

(Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 24/08/2022)
We started this work by reviewing an application of periodic quantum graph theory to model monolayer hexagonal materials with δ_a and δ_b parameters associated with the different types of atoms located in their vertices. ...
• #### Fecho integral de módulos, multiplicidades e poliedros de Newton ﻿

(Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 03/08/2022)
In this work, we study the integral closure of ideals, Newton polyhedra and Newton non-degenerate ideals. Moreover, we present generalizations of these concepts for modules then, we study the characterization of Newton ...
• #### Twisted Borel K-theory and isomorphisms between differential models of K-theory ﻿

(Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 04/07/2022)
In this thesis we discuss some topics about twisted K-theory calculations and equivalences between a couple of differential extension models. We start with a mathematical review of models for twisted K-theory, differential ...
• #### Estabilidade assintótica global para equações diferenciais no plano ﻿

(Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 25/05/1999)
Let x! = f(x) be a system of differential equations in the plane where / is C1. This work gives sufficient conditions which guarantee that the basin of attraction of an equilibrium point is the plane. This monograph reports ...
• #### Extensões H-cleft distinguidas por H-identidades polinomiais ﻿

(Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 27/05/2022)
Our main object of study is the well-known question asking whether the set of polynomials identities distinguishes PI-algebras up to isomorphism. Let k be an algebraically closed field of characteristic 0 and H a non-semisimple ...
• #### Compactly-supported and relative integration in differential cohomology ﻿

(Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 11/04/2022)
In this work, we have constructed more general versions of differential integration maps in differential cohomology theories. Among the obtained versions we can mention the integration with compact supports, the integration ...
• #### Soluções positivas para equações elípticas com operadores fracionários ﻿

(Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 18/03/2022)
In this work, we present results of existence, non-existence and multiplicity of positive solutions to elliptic problems involving the fractional p-Laplacian operator and the fractional Laplacian in the critical case, ...
• #### Attractors for processes on time-dependent spaces ﻿

(Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 12/04/2022)
The goal of this master’s degree dissertation is to study the asymptotic behavior of non-autonomous hyperbolic partial differential equations with time-dependent coefficients. In order to achieve that, we introduce the ...
• #### Não unicidade para uma classe de operadores do tipo parabólico ﻿

(Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 18/01/2022)
In this thesis we consider the non-uniqueness for a class of parabolic operators. We will prove that for certain real analytic perturbation of the Heat Operator there is a non unique solution for the Initial Value Problem.

(Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 24/03/2022)
In this work, we will initially present generalized bundles, a concept developed by Fadell with the objective of generalizing vector bundles, Stiefel-Whitney classes andWu’s formula from the context of smooth manifolds ...
• #### Polynomial Weingarten surfaces of tubular type ﻿

(Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 04/04/2022)
This work seeks to contribute to the classification of Weingarten surfaces. More precisely, it fully classifies three families of surfaces (named tubular, cyclic and canal surfaces) in a tridimensional space form (Euclidean, ...
• #### Geometric invariants of groups and property R-infty ﻿

(Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 05/01/2022)
In this thesis we study property R_\infty for some classes of finitely generated groups by the use of the BNS invariant \Sigma^1 and some other geometric tools. In the combinatorial chapters of the work (4, 5, 6, 10 and ...
• #### Leis de conservação: teoria geral ﻿

(Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 24/03/2022)
In this thesis we study some aspects of the theory of Partial Differential Equations (PDE's), the theory of the existence and the uniqueness of classical solutions to the Cauchy problem u_t+f'(u)u_x=0, u(0,x)=u_0(x) in the ...
• #### Ordinary and twisted K-theory ﻿

(Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 28/03/2022)
The main topic of this thesis consists in Ordinary and Twisted Topological K-Theory. We begin by describing generalized cohomology theories through the Eilenberg-Steenrod Axioms, in order to set Ordinary K-Theory in these ...
• #### Um princípio de tangência e aplicações ﻿

(Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 17/12/2021)
We present tools, such as a maximum principle for elliptic functions and properties of a-hyperbolic polynomials, to study a tangency principle between two hypersurfaces with r-mean curvatures of a Riemannian manifold, which ...
• #### Laplaciano de Dirichlet em faixas com cantos ﻿

(Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 24/02/2022)
Let $\Omega_\theta$ be an unbounded V-shaped set of the plane $\mathbb{R}^2$ , that is, a strip with a corner, and consider $- \Delta^{D}_{\Omega_\theta}$ the Dirichlet Laplacian in $\Omega_\theta$. In this work, we will ...
• #### Um estudo de valorizações transcendentes e algébricas via polinômios-chaves e pares minimais ﻿

(Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 24/02/2022)
The main goal of this work is to study transcendental valuations and algebraic valuations. To achieve this, we use some of the main objects in Valuation Theory, such as key polynomials, truncations and minimal pairs. These ...
• #### Categoria de Lusternik-Schnirelmann e aplicações ﻿

(Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 14/02/2022)
The Lusternik-Schnirelmann category associates a positive integer to each topological space. This number is an important invariant in algebraic topology, critical point theory and symplectic geometry. In this dissertation ...
• #### O número de Bruce-Roberts sobre uma ICIS ﻿

(Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Matemática - PPGM, Câmpus São Carlos, 19/01/2022)
In this work we study the relations between the Bruce-Roberts number, $\mu_{BR}(f,X)$, the relative Bruce-Roberts, $\mu_{BR}^{-}(f,X)$, of a function germ $f\in\mathcal{O}_{n}$ over an ICIS, $(X,0)\subset (\C^{n},0)$, and ...