Mumford–Tate Groups in Hodge Theory - Aula 03

Explore advanced concepts in algebraic geometry through this third 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 foundational knowledge of algebraic geometry, complex analysis, and representation theory to understand these sophisticated mathematical objects and their role in modern research. Access comprehensive coverage of theoretical developments alongside concrete examples that illustrate the power and elegance of this mathematical framework in contemporary algebraic geometry.