Ramsey expansions and their applications

• Grant number: 14/12405-8
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
• Start date: September 21, 2014
• End date: December 15, 2014
• Field of knowledge: Physical Sciences and Mathematics - Mathematics
• Principal Investigator: Artur Hideyuki Tomita
• Grantee: Dana Bartosova
• Supervisor: Alexander S. Kechris
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Institution abroad: California Institute of Technology, United States
• Associated to the scholarship: 13/14458-9 - Algebra in the Cech-Stone compactification and its applications to topological dynamics, ergodic theory and Ramsey theory., BP.PD

Abstract

During my research stay at the California Institute of Technology, I plan to focus on two lines of research that contain problems of major interest and that are closely related to my research project in Brazil. The two lines of research are dual to each other - the first one studies Fraisse classes and the second projective Fraisse classes. In both cases, we are looking for Ramsey expansions which have applications across mathematics and have enjoyed rapidly increasing interest over the past decade. We are particularly interested in applications in model theory, theoretical computer science, continuum theory, and topological dynamics. Conversely, we want to examine when topological dynamics can provide Ramsey expansions, which is a strong recent trend. (AU)

Scientific publications

(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)

BARTOSOVA, DANA; KWIATKOWSKA, ALEKSANDRA. THE UNIVERSAL MINIMAL FLOW OF THE HOMEOMORPHISM GROUP OF THE LELEK FAN. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, v. 371, n. 10, p. 6995-7027, MAY 15 2019. (14/12405-8, 13/14458-9)

BARTOSOVA, DANA; KWIATKOWSKA, ALEKSANDRA. Gowers' Ramsey theorem with multiple operations and dynamics of the homeomorphism group of the Lelek fan. JOURNAL OF COMBINATORIAL THEORY SERIES A, v. 150, p. 108-136, AUG 2017. (13/14458-9, 14/12405-8)