Hyperkähler manifolds - Hodge-theoretic aspects

• Grant number: 24/23819-0
• Support Opportunities: Regular Research Grants
• Start date: August 01, 2025
• End date: July 31, 2028
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Andrey Soldatenkov
• Grantee: Andrey Soldatenkov
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

The research project is focused on the study of compact hyperkähler manifolds - the subject that lies at the intersection of differential and algebraic geometry and that has rich connections with various other fields of mathematics, such as symplectic geometry, geometric analysis and the theory of algebraic integrable systems. We propose to study The action of the Looijenga-Lunts-Verbitsky algebra, Hodge cycles, motives, limit mixed Hodge structures, Teichmüller spaces of hyperkähler manifolds, the mapping class group action, twistor families and the hyperkähler SYZ conjecture. (AU)