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Explore a mathematics seminar that delves into the fascinating world of random Cayley graphs and their independent sets. Learn how these mathematical structures create connections between graph theory, additive combinatorics, and group theory by examining how generating sets are randomly chosen within finite groups. Discover recent breakthroughs in analyzing cliques and independent sets in random Cayley graphs, including how the study of Ramsey properties in dense random Cayley graphs led to solving a longstanding conjecture by Ruzsa in additive combinatorics. Investigate developments in the sparse regime, connecting to Ben Green's question about the largest subset of an abelian group that cannot be expressed as a sumset. Master advanced concepts involving the construction of efficient 'covers' for sumsets through combined analysis of physical and Fourier space, while gaining insights into robust results in additive combinatorics derived from a combinatorial perspective.
