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Explore the fourth part of a graduate-level lecture series on sublinear expander graphs, delivered by Matija Bucić from the University of Vienna at the IAS/PCMI Park City Mathematics Institute. Delve into the weaker notion of sublinear expansion introduced by Komlós and Szemerédi in the early 1990s, which has gained significant importance through remarkable applications in recent mathematical research. Build upon foundational knowledge of expander graph theory to understand the sublinear expansion concept, examine the pass to expander and expander decomposition lemma, and investigate key properties of these mathematical structures. Discover how sublinear expander graphs have been applied in contemporary research through concrete examples and applications. This lecture forms part of the PCMI 2025 Graduate Summer School focused on Probabilistic and Extremal Combinatorics, providing advanced training in discrete mathematics with connections to analysis, geometry, number theory, statistical physics, and theoretical computer science. Access accompanying lecture notes and problem sets to reinforce understanding of these sophisticated combinatorial concepts. Prerequisites include familiarity with basic graph theory, probability theory, and linear algebra.
