Stable vector bundles over projective plane and representations of posets in the category of unitary spaces

• Grant number: 10/15781-0
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: March 01, 2011
• End date: September 30, 2012
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Vyacheslav Futorny
• Grantee: Kostiantyn Iusenko
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 10/50347-9 - Algebras, representations e applications, AP.TEM

Abstract

This project is aimed to study the representation theory of partially ordered sets in unitary spaces with additional linear relation. Importance of such objects is due to their applications to moduli problems such as: description of toric vector bundles over projective plane, description of rigid unitary representations of the fundamental group over punctured disc among the others. (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)

FUTORNY, VYACHESLAV; SAMOILENKO, YURII; YUSENKO, KOSTYANTYN; ABRAMOV, V; FUCHS, J; PAAL, E; SHESTOPALOV, Y; SILVESTROV, S; STOLIN, A. Representations of posets: linear versus unitary. WAKE CONFERENCE 2021, v. 346, p. 17-pg., 2012-01-01. (10/15781-0, 10/50347-9)

BONDARENKO, VITALIJ M.; FUTORNY, VYACHESLAV; KLIMCHUK, TATIANA; SERGEICHUK, VLADIMIR V.; YUSENKO, KOSTYANTYN. Systems of subspaces of a unitary space. Linear Algebra and its Applications, v. 438, n. 5, p. 2561-2573, MAR 1 2013. (10/50347-9, 10/15781-0)

SAMOILENKO, YURII; YUSENKO, KOSTYANTYN. Kleiner's theorem for unitary representations of posets. Linear Algebra and its Applications, v. 437, n. 2, p. 581-588, JUL 15 2012. (10/15781-0)