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Universality conjecture for Hamiltonian dynamics
Dmitry Turaev (Imperial College London)
2025-12-10 (Wed) 16:00 — Gu Lecture Hall, SCMS
Abstract: A foundational fact of classical physics is that the time evolution of any isolated physical system is described by Hamiltonian differential equations (implying that the local dynamics of such system are represented by orbits of symplectomorphisms of a ball). We show that the choice of the Hamiltonian function is irrelevant here, because a typical Hamiltonian is universal: its local dynamics approximates, in high regularity, all symplectic dynamics possible for the given number of degrees of freedom. The universality conjecture suggests an explicit description of universal Hamiltonians.
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