Integrable evolution PDEs of geometric type and Bol's loops

• Grant number: 23/14060-7
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: February 09, 2024
• End date: June 06, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Alexandre Grichkov
• Grantee: Alexandre Grichkov
• Visiting researcher: Vladimir Sokolov
• Visiting researcher institution: Russian Academy of Sciences (RAS) , Russia
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• City of the host institution: São Paulo
• Associated research grant: 18/23690-6 - Structures, representations, and applications of algebraic systems, AP.TEM

Abstract

A geometric description of a class of integrable evolution PDE systems involves anane connection and a covariantly constant tensor of rank (1; 3). Integrability imposes strongconditions on both the ane connection and on the tensor. In particular, the tensor turns outto be a deformation of a triple Jordan system. The goal of the project is an investigation of theabove geometrical structures and a construction of new examples of corresponding integrablemodels. (AU)