Mestrado em Matemática
URI Permanente para esta coleção
Nível: Mestrado Acadêmico
Ano de início: 2006
Conceito atual na CAPES: 3
Ato normativo: Homologado pelo CNE ( Port. MEC 609, de 14/03/2019, DOU 18/03/2019)
Periodicidade de seleção: Anual
Área(s) de concentração: Matemática
Url do curso: https://matematica.ufes.br/pt-br/pos-graduacao/PPGMAT/detalhes-do-curso?id=1401
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- ItemPerfil do cutoff do processo de exclusão no grafo completo(Universidade Federal do Espírito Santo, 2024-04-15) Oliveira, Éric Santana; Jara Valenzuela, Milton David; https://orcid.org/; http://lattes.cnpq.br/7496571533341165; Silva, Fábio Júlio da ; https://orcid.org/0000-0003-2405-7696; http://lattes.cnpq.br/8745134398831488; https://orcid.org/; http://lattes.cnpq.br/4639522148187770; Bessam, Diogo Manuel Fernandes ; https://orcid.org/; http://lattes.cnpq.br/2356936612360198; Hernandez Romero, Freddy Rolando ; https://orcid.org/0000-0001-5410-3062; http://lattes.cnpq.br/2961243559975382This dissertation delves into the study of Markov chains, evolutionary processes characterized by “memory loss”, widely applied in diverse fields such as biology, statistics, and finance. The convergence of these chains to a stationary distribution is analyzed using the “total variation distance”. The times of 𝜀-mixing are introduced, representing the time required for convergence. The concept of coupling between Markov chains is presented, demonstrating its utility in de termining bounds for mixing times. The phenomenon of cutoff, an abrupt decrease in total variation distance, is explored, providing a detailed understanding of convergence. The ulti mate goal is to calculate the cutoff profile for the simple exclusion processes on complete graphs. Chapters cover the construction of chains, technical concepts, couplings, and mixing times, cul minating in the analysis of the cutoff phenomenon and its specific application to the exclusion process in the complete graph
- ItemA Transformada de Fourier para o Laplaciano Generalizado(Universidade Federal do Espírito Santo, 2024-03-05) Ramos Junior, Jomar Ferreira; Valentim, Fábio Júlio da Silva; https://orcid.org/0000-0003-2405-7696; http://lattes.cnpq.br/8745134398831488; https://orcid.org/0009-0006-1032-5169; http://lattes.cnpq.br/1800635453022041; Aranda, José Miguel Mendoza; https://orcid.org/; http://lattes.cnpq.br/8615067875072268; Silva, Jean Carlos da; https://orcid.org/; http://lattes.cnpq.br/9490078990099931This academic dissertation aims primarily to contribute to the enhancement of understanding of the Fourier Theory applied to the generalized Laplacian. The proposed methodology involves the construction of an orthonormal basis of eigenfunctions for the operator, based on the appropriate choice of Green’s functions. The central problem consists of finding the solution u(x) that satisfies certain boundary conditions for the equation Lu = f, using a series representation of the eigenfunctions of the operator L. The dissertation addresses fundamental aspects such as the definition of the domain of the generalized Laplacian, the analysis of Green’s functions and their applications in solving partial differential equations, as well as transformations for the generalized Laplacian. The interest in consolidating the Fourier Theory for the generalized Laplacian aims to provide a deeper understanding of the properties of this operator and its relation to Fourier Theory, establishing a foundation for future research, including more complex cases such as the differential operator in reverse order. This work represents a significant contribution to the understanding of the theory of the generalized Laplacian and its connections with Fourier Theory.
- ItemHomologia de Morse e uma aplicação em geometria simplética(Universidade Federal do Espírito Santo, 2023-05-29) Flores, Thales Danton de Souza; Batoréo, Marta Jakubowicz; http://lattes.cnpq.br/1461528961848898; http://lattes.cnpq.br/0978245375441146; Nascimento, José Victor Goulart; https://orcid.org/0000-0001-6660-792X; http://lattes.cnpq.br/5273512936573286; Balseiro, Paula; http://lattes.cnpq.br/7655880123530492In this work some concepts and main results of Morse theory are presented, such as Morse’s lemma and Smale’s theorem. Furthermore, we will present a particular case of Arnold’s conjecture which is an application of Morse theory in symplectic geometry.
- ItemMétodos da teoria de calibre na gravitação newtoniana(Universidade Federal do Espírito Santo, 2023-03-30) Lima, Matheus dos Santos; Câmara, Leonardo Meireles; https://orcid.org/0000-0002-4637-8573; http://lattes.cnpq.br/9240898305551070; http://lattes.cnpq.br/6044154913017696; Martins, Gabriel Luchini; https://orcid.org/0000-0001-6627-3034; http://lattes.cnpq.br/3344738411070832; Earp, Henrique Nogueira de Sá; https://orcid.org/0000-0003-0475-4494; http://lattes.cnpq.br/4040588840128192Élie Cartan developed the concept of affine connection as a way to establish a local equivalence relation between sections of the tangent space to four-dimensional spacetime. This concept allowed for an intrinsic description of local geometric properties, independent of an external coordinate system. By adopting the method of moving frames, Cartan provided a precise geometric description of spacetime, enriching our understanding of the theory of general relativity. This dissertation aims to study Cartan’s works and highlight his contributions, through the affine connection, to the geometrization of the Newtonian physical system, as well as to identify possible connections with contemporary Gauge Theory, which offers a powerful framework for describing fundamental interactions of this nature. In this context, the main objective of this study is to propose equations that allow for finding an affine connection that is a Yang-Mills connection modeling the physical phenomena under study. By seeking this connection between Cartan’s theory and Gauge Theory, we aim to advance our understanding of fundamental interactions and possibly pave the way for future work.
- ItemUma Introdução a Grandes Desvios e Finanças Quantitativas(Universidade Federal do Espírito Santo, 2022-12-21) Moreira, Vinicio Rodrigues; Valentim, Fabio Julio da Silva; https://orcid.org/0000000324057696; http://lattes.cnpq.br/8745134398831488; https://orcid.org/; http://lattes.cnpq.br/; Coelho, Glauco Valle da Silva; https://orcid.org/; http://lattes.cnpq.br/; Bessam, Diogo Manuel Fernandes; https://orcid.org/; http://lattes.cnpq.br/abstract