Algebra in the Cech-Stone compactification and its applications to topological dynamics, ergodic theory and Ramsey theory.

• Grant number: 13/14458-9
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: February 01, 2014
• End date: January 07, 2017
• Field of knowledge: Physical Sciences and Mathematics - Mathematics
• Principal Investigator: Artur Hideyuki Tomita
• Grantee: Dana Bartosova
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated scholarship(s): 15/09278-7 - Interactions between set theory, Banach space theory and topological dynamics, BE.EP.PD 14/12405-8 - Ramsey expansions and their applications, BE.EP.PD

Abstract

We study problems arising in topological dynamics and ergodic theory. We develop an alternate approach to treatment of dynamical notions and work on its applications. The theory combines tools from set theory, model theory,Ramsey theory, and topological groups and applies to the study of minimal flows.

Scientific publications

(6)

(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; LOPEZ-ABAD, JORDI; LUPINI, MARTINO; MBOMBO, BRICE. The Ramsey property for Banach spaces and Choquet simplices, and applications. COMPTES RENDUS MATHEMATIQUE, v. 355, n. 12, p. 1242-1246, DEC 2017. (12/20084-1, 13/24827-1, 13/14458-9)

BARTOSOVA, DANA; LOPEZ-ABAD, JORDI; LUPINI, MARTINO; MBOMBO, BRICE. THE RAMSEY PROPERTIES FOR GRASSMANNIANS OVER R, C. COMBINATORICA, NOV 2021. (12/20084-1, 13/24827-1, 13/14458-9)

BARTOSOVA, DANA; LOPEZ-ABAD, JORDI; LUPINI, MARTINO; MBOMBO, BRICE. The Ramsey property for operator spaces and noncommutative Choquet simplices. JOURNAL OF FUNCTIONAL ANALYSIS, v. 281, n. 9, NOV 1 2021. (13/24827-1, 12/20084-1, 13/14458-9, 16/25574-8)

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)

BARTOSOVA, DANA; LOPEZ-ABAD, JORDI; LUPINI, MARTINO; MBOMBO, BRICE. The Ramsey property for Banach spaces and Choquet simplices. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, v. 24, n. 4, p. 36-pg., 2022-01-01. (12/20084-1, 13/24827-1, 13/14458-9)