Subgroup Tests and the Aldous-Lyons Conjecture

Explore the intricate connections between finite approximations, interactive proof systems, and the Aldous--Lyons conjecture in this Computer Science/Discrete Mathematics seminar. Delve into Michael Chapman's research on subgroup tests and their implications for probability theory and group theory. Discover how the resolution of Connes' embedding problem inspired a novel approach to refuting the Aldous--Lyons conjecture. Learn about the concept of Subgroup Tests as analogues to Non-local Games and understand their role in creating a new interactive proof system. Follow the high-level description of the proof strategy that links complexity theory to fundamental mathematical conjectures. Gain insights into the broader theme of limits in finite objects and their impact on various mathematical fields, all presented in an accessible manner requiring no specialized background.