Ultrafilters and Topological Algebra

• Grant number: 17/15709-6
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: January 01, 2018
• End date: September 30, 2022
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• 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
• Associated scholarship(s): 19/02663-3 - Infinitary Combinatorics in General Topology and Topological Algebra, BE.EP.DR

Abstract

This Ph.D. research project gives sequence to the applicant's Masters project approved by FAPESP (2015/15166-7), with an end foreseen for 12/2017. We will study questions in topology, group theory and semigroup theory regarding the Stone-Cech compactification of the natural numbers (beta N), such as chains of left ideals, ordering of nonminimal idempotents, continuous homorphisms from beta N, existence of nondiscrete topological groups, and existence of uncountable free semigroups in beta N, of which the last two topics are also part of the advisor's research project approved by FAPESP (2016/26216-8). The applicant has already studied several scientific publications about these topics and the research will have as a starting point the study of some open problems proposed by world experts in these subjects. The expected result is to achieve advances in these areas that can be evaluated from their dissemination (publications of scientific articles, seminars and conferences).

Scientific publications

(4)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

BELLINI, MATHEUS KOVEROFF; BOERO, ANA CAROLINA; CASTRO-PEREIRA, IRENE; RODRIGUES, VINICIUS DE OLIVEIRA; TOMITA, ARTUR HIDEYUKI. Countably compact group topologies on non-torsion Abelian groups of size continuum with non-trivial convergent sequences. Topology and its Applications, v. 267, NOV 1 2019. (10/19272-2, 12/01490-9, 17/15709-6, 16/26216-8, 17/15502-2)

BELLINI, MATHEUS KOVEROFF; RODRIGUES, VINICIUS DE OLIVEIRA; TOMITA, ARTUR HIDEYUKI. On countably compact group topologies without non-trivial convergent sequences on Q((kappa)) for arbitrarily large kappa and a selective ultrafilter. Topology and its Applications, v. 294, MAY 1 2021. (16/26216-8, 17/15502-2, 17/15709-6)

BELLINI, MATHEUS KOVEROFF; BOERO, ANA CAROLINA; RODRIGUES, VINICIUS DE OLIVEIRA; TOMITA, ARTUR HIDEYUKI. Algebraic structure of countably compact non-torsion Abelian groups of size continuum from selective ultrafilters. Topology and its Applications, v. 297, p. 23-pg., 2021-04-29. (19/01388-9, 19/02663-3, 12/01490-9, 16/26216-8, 17/15709-6)

BELLINI, MATHEUS K.; HART, KLAAS PIETER; RODRIGUES, VINICIUS O.; TOMITA, ARTUR H.. Countably compact group topologies on arbitrarily large free Abelian groups. Topology and its Applications, v. 333, p. 23-pg., 2023-04-28. (17/15502-2, 21/00177-4, 16/26216-8, 17/15709-6)

Academic Publications

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

BELLINI, Matheus Koveroff. Countably compact group topologies on torsion-free Abelian groups. 2022. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI) São Paulo.