Borel-Weil-Bott theorem and applications

• Grant number: 25/03293-6
• Support Opportunities: Scholarships in Brazil - Master
• Start date: August 01, 2025
• End date: February 28, 2027
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Eder de Moraes Correa
• Grantee: Caio Martim Oriqui
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 21/04065-6 - BRIDGES: Brazil-France interplays in Gauge Theory, extremal structures and stability, AP.TEM

Abstract

This research project aims to introduce the scholarship holder to the study of geometric methods in representation theory of semisimple Lie algebras, using the Borel-Weil-Bott theorem as a central tool. It is expected that, at the end of the project, the student will have acquired a solid foundation in Hodge theory, sheaf cohomology, and representation theory. This knowledge will enable the student to develop original research in the future on topics related to Kostant's conjecture, Hochschild cohomology of projective homogeneous varieties, the Beilinson-Bernstein localization theorem, and the problem of the existence of exceptional collections of coherent sheaves on projective homogeneous varieties. (AU)