On non-Archimedean valued fields: a survey of algebraic, topological and metric structures, analysis and applications
Viernes 20 de mayo de 2022 | 16.00 horas
Conferencista: Khodr Shamseddine de la Universidad de Manitoba, Canada.
Summary: In this talk, we will briefly review basic properties of ultrametric spaces, valued fields and ordered fields as well as the connection between these different mathematical objects. In particular, we will present a survey of their algebraic, topological and metric structures. As examples, we will introduce the p-adic fields and the so-called general Hahn fields and Levi-Civita fields, and we will present a summary of their key properties. Then, we will focus our attention on two special Levi-Civita fields: R and its complex counterpart C. Among all the non-Archimedean fields surveyed in the first part of the talk, R and C are unique from a pure Mathematical point of view as well as from a computational point of view. We will give a brief summary of our research work on R and C, with one computational application.