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Colóquio de Alunos

A tour by the three great A’s of Mathematics: some trilogies between Arithmetic, Algebra and Analysis
Eduardo Alves da Silva

Instituto Nacional de Matemática Pura e Aplicada
Sexta-feira, 1 de novembro de 2019, 15:30
Auditorio 1

In Mathematics is very common some ideas and concepts from different areas are connected. These three areas have many relations which allow us transit between them and stablish several statements of different points of view like the notable Riemann-Roch Theorem and even the famous Riemann hypothesis, which some analogues have already been proved. I will comment about certain of these “3-connections” and historical facts, as well show and explore how a few concepts can be defined in different ways. In particular, relations between algebraic function fields, abstract Riemann surfaces and Riemann surfaces in the usual sense as complex manifolds will be explored.