Twisted sums, positions and Ramsey theory in Banach Spaces

• Grant number: 13/11390-4
• Support Opportunities: Regular Research Grants
• Duration: October 01, 2013 - November 30, 2015
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Valentin Raphael Henri Ferenczi
• Grantee: Valentin Raphael Henri Ferenczi
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

From October 2013 to September 2015, several directions of research will be studied in the theory of Banach spaces. In the main line of research, called line A, the common denominator will be the theory of twisted sums, with concentration on the relation of this theory with interpolation and complex structures. The objective of line B is to gather the theory of complexity of equivalence relations in Polish spaces with the theory of positions of a Banach space inside another. In line C will be considered applications of Ramsey theory to embeddings of metric spaces into Banach spaces as well as to the study of the group of linear isometries of Gurariy's space.Are included in the project participations of the candidate in scientific events abroad, three visits of professors from the Universites of Extremadura and of Cantabria (Spain) and one visit from a po s-doc, Visiting Assistant professor at Texas A&M University (USA). (AU)

Scientific publications

(10)

(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)

CASTILLO, JESUS M. F.; FERENCZI, VALENTIN; GONZALEZ, MANUEL. SINGULAR TWISTED SUMS GENERATED BY COMPLEX INTERPOLATION. Transactions of the American Mathematical Society, v. 369, n. 7, p. 4671-4708, JUL 2017. (13/11390-4)

CASTILLO, JESUS M. F.; CORREA, WILLIAN H. G.; FERENCZI, VALENTIN; GONZALEZ, MANUEL. ON THE STABILITY OF THE DIFFERENTIAL PROCESS GENERATED BY COMPLEX INTERPOLATION. JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU, v. 21, n. 1, p. 303-334, JAN 2022. (13/11390-4, 18/03765-1, 15/17216-1, 16/25574-8)

CASTILLO, JESUS M. F.; CORREA, WILLIAN H. G.; FERENCZI, VALENTIN; GONZALEZ, MANUEL. Differential processes generated by two interpolators. REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, v. 114, n. 4, AUG 12 2020. (15/17216-1, 18/03765-1, 16/25574-8, 13/11390-4)

CASTILLO, JESUS M. F.; FERENCZI, VALENTIN. Group Actions on Twisted Sums of Banach Spaces. BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, v. 46, n. 4, p. 47-pg., 2023-07-01. (15/17216-1, 13/11390-4, 16/25574-8)

FERENCZI, VALENTIN; ROSENDAL, CHRISTIAN. NON-UNITARISABLE REPRESENTATIONS AND MAXIMAL SYMMETRY. JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU, v. 16, n. 2, p. 421-445, APR 2017. (13/11390-4)

FERENCZI, V; LOPEZ-ABAD, J.; MBOMBO, B.; TODORCEVIC, S.. Amalgamation and Ramsey properties of L-p spaces. ADVANCES IN MATHEMATICS, v. 369, p. 76-pg., 2020-08-05. (16/25574-8, 12/20084-1, 13/24827-1, 13/11390-4)

ANTUNES, LEANDRO; FERENCZI, VALENTIN; GRIVAUX, SOPHIE; ROSENDAL, CHRISTIAN. LIGHT GROUPS OF ISOMORPHISMS OF BANACH SPACES AND INVARIANT LUR RENORMINGS. PACIFIC JOURNAL OF MATHEMATICS, v. 301, n. 1, p. 31-54, JUL 2019. (16/25574-8, 13/11390-4)

ANISCA, RAZVAN; FERENCZI, VALENTIN; MORENO, YOLANDA. On the classification of positions and complex structures in Banach spaces. JOURNAL OF FUNCTIONAL ANALYSIS, v. 272, n. 9, p. 3845-3868, MAY 1 2017. (13/11390-4, 15/17216-1)

CASTILLO, JESUS M. F.; FERENCZI, VALENTIN; GONZALEZ, MANUEL. SINGULAR TWISTED SUMS GENERATED BY COMPLEX INTERPOLATION. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, v. 369, n. 7, p. 38-pg., 2017-07-01. (13/11390-4)

CASTILLO, JESUS M. F.; CUELLAR, WILSON; FERENCZI, VALENTIN; MORENO, YOLANDA. COMPLEX STRUCTURES ON TWISTED HILBERT SPACES. Israel Journal of Mathematics, v. 222, n. 2, p. 787-814, OCT 2017. (10/17512-6, 15/17216-1, 14/25900-7, 13/11390-4)