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hep-th2026
Integrable Systems
Maciej Dunajski
These notes are based on lecture courses I gave to third year mathematics students at Cambridge. They could form a basis of an elementary one--term lecture course on integrable sys…
hep-th2025
Gravitational Instantons, old and new
Maciej Dunajski
This is a review of gravitational instantons -- solutions to Riemannian Einstein or Einstein-Maxwell equations in four dimensions which yield complete metrics on non-compact four-m…
hep-th2024
Integrability of quantum dots
Maciej Dunajski, Andrzej J. Maciejewski, Maria Przybylska
We determine the frequency ratios for which the Hamiltonian system with a potential \[ V=\frac{1}{r}+\frac{1}{2}\Big({ω_ρ}^2(x^2+y^2)+{ω_z}^2 z^2\Big) \] is compl…