Mumford–Tate Groups in Hodge Theory - Aula 05

Explore advanced concepts in algebraic geometry through this fifth lecture of a minicourse on Mumford–Tate groups in Hodge theory, delivered by Professor Andrey Soldatenkov from UNICAMP as part of IMPA's Summer School 2026. Delve into the intricate mathematical framework that connects algebraic cycles, motives, and representation theory through the lens of Hodge structures. Examine how Mumford–Tate groups serve as fundamental tools for understanding the arithmetic and geometric properties of algebraic varieties, particularly in the context of period mappings and variation of Hodge structures. Learn about the classification of Hodge structures through their associated Mumford–Tate groups and discover applications to problems in arithmetic geometry and transcendental number theory. Build upon previous lectures in this comprehensive series to deepen your understanding of this sophisticated area where algebraic geometry meets representation theory and number theory.