Constructs universal gauge-covariant Wilczynski currents for noncommutative differential operators on Riemann surfaces that recover classical invariants and become modular forms.
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This article is an elementary introduction to opers without new results. We hope it can be useful for students.
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Fluid dynamics is formulated as an intersection problem on a symplectic manifold associated with spacetime, yielding a geometric derivation of covariant hydrodynamics and extensions to multicomponent and anomalous fluids.
A comprehensive introduction to spectral networks that develops higher-rank Teichmüller theory in parallel with class S gauge theory and BPS spectra.
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Noncommutative Wilczynski Invariants, and Modular Differential Equations
Constructs universal gauge-covariant Wilczynski currents for noncommutative differential operators on Riemann surfaces that recover classical invariants and become modular forms.
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Fluid dynamics as intersection problem
Fluid dynamics is formulated as an intersection problem on a symplectic manifold associated with spacetime, yielding a geometric derivation of covariant hydrodynamics and extensions to multicomponent and anomalous fluids.
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Spectral Networks: Bridging higher-rank Teichm\"uller theory and BPS states
A comprehensive introduction to spectral networks that develops higher-rank Teichmüller theory in parallel with class S gauge theory and BPS spectra.