Applications of ultrafilters to ergodic Ramsey theory

• Grant number: 18/08886-1
• Support Opportunities: Scholarships in Brazil - Master
• Start date: August 01, 2018
• End date: February 29, 2020
• Field of knowledge: Physical Sciences and Mathematics - Mathematics
• Agreement: Coordination of Improvement of Higher Education Personnel (CAPES)
• Principal Investigator: Leandro Fiorini Aurichi
• Grantee: José Carlos Fontanesi Kling
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

Our main goal is to study Ramsey Ergodic Theory, wich relates the areas of Dynamical Systems and Ramsey Theory. In this project our main tool will be the Stone-Cech compactification of a countable discrete semigroup, consisting of the set of ultrafilters over such semigroup. With this it is possible, for example, to generalize the concept of limit in a compact Hausdorff space, extending the operation of the semigroup (like the naturals) to its compactification. The selection of articles to be studied is intended to put the student in direct contact with recent researches, including two works published in 2018 and another in 2017. We also expect that the student will get an overview of the developments in the area and get to know the active members of the international community related to the subject. (AU)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

KLING, José Carlos Fontanesi. Ultrafilters applied to Ergodic Ramsey Theory. 2020. Master's Dissertation - Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) São Carlos.