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In this 56-minute lecture, Venkat Chandrasekaran from the California Institute of Technology explores "Any-dimensional polynomial optimization" at IPAM's Statistical and Numerical Methods for Non-commutative Optimal Transport Workshop. Recorded on May 19, 2025, at UCLA, the talk addresses optimization problems that appear as sequences indexed by dimension, such as those in extremal combinatorics (indexed by graph size) or information theory (indexed by channel uses). Discover a systematic approach to deriving finite-sized semidefinite programming relaxations that bound the limiting optimal value of any-dimensional polynomial optimization problems. The methodology leverages de Finetti's theorem from probability and representation stability from algebraic topology, illustrated through various applications. This research represents joint work with Eitan Levin.
