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 ...

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 ...

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 ...

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 ...

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 ...

The aim of this Masters dissertation is to show a classication of parallel and semi-parallel hypersurfaces of Sn _ R, based on the work of Joeri Van der Veken and Luc Vrancken, in [12]. The classification that we will ...

The subject treated in this dissertation is functional identities (FI) of a especific ring. We present concepts, examples and some results involving the themes: standard solution of a FI, strong degree of a ring, strongly ...

In this work, we will use topological methods in combinatorics and geometry to present a proof of the topological Tverberg theorem and a result about many Tverberg partitions.

This work aims to give a description, under certain hypothesis, of the graded simple algebras and prove that they are determined by their graded identities. For this, we study the papers [3] and [19]. More precisely we ...

The objective of this dissertation is descrive formally the irreducible representations of finitedimensional semisimple Lie algebras g over a field F algebraically closed with characteristic zero, as also get some multiplicity ...