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math-ph2026
Augmentation curve for torus knots
Alexander Hock, Sergey Shadrin
We prove a version of topological recursion for the correlation differentials of colored HOMFLY-PT polynomials of torus knots on the corresponding augmentation curves, following th…
math-ph2026
Universal Correlators on Exponentially Ramified Spectral Curves
Mohamad Alameddine, Alexander Hock
We investigate generalized topological recursion on compact spectral curves admitting exponential, and more generally essential, singularities as ramification points. Exploiting th…
math-ph2026
Geometry of Logarithmic Topological Recursion: Dilaton Equations, Free Energies and Variational Formulas
Alexander Hock, Olivier Marchal, Nicolas Orantin
One of the most important applications of topological recursion concerns spectral curves for which the functions defining the spectral curve are allowed to have logarithmic…