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Explore the intricate connections between finite object limits, approximability, and major mathematical conjectures in this Computer Science/Discrete Mathematics seminar. Delve into Michael Chapman's presentation on Subgroup Tests and the Aldous--Lyons Conjecture, examining how the resolution of Connes' embedding problem inspired a novel approach to tackle other significant mathematical challenges. Learn about the development of a new interactive proof system and its implications for the Aldous--Lyons conjecture. Gain insights into the concept of Subgroup Tests as an analogue to Non-local Games and understand how complexity theory and undecidability in interactive proof systems contribute to refuting long-standing mathematical conjectures. No specialized mathematical background is required for this high-level overview of the proof strategy and main concepts, making it accessible to a broad audience interested in the intersection of computer science, discrete mathematics, and probability theory.
