Semigroup algebra in the Stone-Cech compactification of a discrete semigroup

• Grant number: 15/19857-4
• Support Opportunities: Scholarships in Brazil - Master
• Start date: January 01, 2016
• End date: December 31, 2017
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Artur Hideyuki Tomita
• Grantee: Matheus Koveroff Bellini
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

The student shall study in his master's program techniques and results concerning semigroup algebras and topology of Stone-Cech compactifications, with the intent of learning new and important techniques to his formation as a researcher, composing a thesis on the subject matter by the end of the program. A semigroup is a set endowed with an operation which is associative, and a Stone-Cech compactification of a topological space X is a compactification with the property that any continuous function from X to a compact codomain has a continuous extension to said compactificaition. When a discrete semigroup S is Stone-Cech compactified, its topological and algebraic properties become intertwined, thus enabling the discovery of more algebraic properties which would not be possible by purely algebraic means. The techniques and results of this subject matter are used to answer questions of combinatorial number theory, Ramsey theory and topological dynamics. (AU)

Academic Publications

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

BELLINI, Matheus Koveroff. Semigroup algebra in the Stone-Cech compactification of discrete semigroups. 2017. Master's Dissertation - Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI) São Paulo.