Mumford–Tate Groups in Hodge Theory - Aula 02

Explore the second lecture of a minicourse on Mumford–Tate groups in Hodge theory delivered by Professor Andrey Soldatenkov from UNICAMP as part of the 2026 Summer School at the Instituto de Matemática Pura e Aplicada. Delve into advanced concepts in algebraic geometry and complex analysis, focusing on the fundamental role of Mumford–Tate groups in understanding Hodge structures and their applications in modern mathematics. Learn about the intricate connections between algebraic cycles, motives, and the geometric properties of algebraic varieties through the lens of Hodge theory. Examine how Mumford–Tate groups provide crucial insights into the structure of Hodge decompositions and their behavior under various mathematical operations. Gain exposure to cutting-edge research techniques and theoretical frameworks that are essential for understanding contemporary developments in arithmetic geometry and algebraic topology. This lecture builds upon foundational concepts while introducing more sophisticated tools and methods used in the study of periods, L-functions, and the arithmetic properties of algebraic varieties.