Exploring a text by Terence Tao

• Grant number: 22/01476-8
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: April 01, 2022
• End date: December 31, 2022
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Paulo Domingos Cordaro
• Grantee: Danielle Velloso Ferreira
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 18/14316-3 - Geometric theory of PDE and multidimensional complex analysis, AP.TEM

Abstract

Scientific Initiation Project - Exploring a text by Terence Tao In 2007, one of today's most brilliant mathematicians, Terence Tao, debuted a blog to address a variety of mathematical topics, ranging from his own research themes to undergraduate topics, passing through research articles. . The blog material has been published in several volumes by the "American Mathematical Society", one of them dealing exclusively with topics in Mathematical Analysis. The approach in these volumes is very original. Only a brilliant mind like Tao's would be able to expose basic topics intertwined with advanced topics in such an elegant way, leading the reader to feel challenged to go deeper into each issue addressed in the text. In my opinion, it is a very appropriate text for a Scientific Initiation program. I am proposing to guide the Scientific Initiation Program of Danielle Velloso Ferreira and of Luiz Felipe Silva Marques (both students at IME-USP). Both have shown excellent performance in their respective courses, and are very well prepared for the task. The idea would be to choose common topics at the beginning, and then specific topics for each of them, which characterize individual projects. I will have weekly meetings with both, where they will present on the board the topics studied and the results of their investigations. Bibliography. Terence Tao, An Epsilon of Room, I: Real Analysis. Graduate Studies in Mathematics, vol.117, AMS, 2010. Topics to be covered:1. Real analysis (measure and integration, functional analysis, topology, including the weak topology in topological vector spaces). Danielle and Luis.2. Special topics(a) Interpolation in Lpspaces. Danielle(b) Distributions, Fourier Transform and Sobolev spaces. Luiz(c) Hausdorff dimension. Luiz(d) Tarski's paradox. Danielle(e) Compactification and metrization. Luiz(f) The µ-regularization argument. Luiz. (AU)