Applied Math Seminar

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Wave Topology and Topological Waves

Speaker: Hong Qin, Princeton

Location: Warren Weaver Hall 1302

Date: Friday, March 13, 2026, 2:30 p.m.

Synopsis:

We build fusion reactors as giant donuts rather than spheres, because the hairy-ball theorem forbids a smooth, nowhere-vanishing tangent magnetic field on a spherical surface. That same topological insight is now revealing hidden twists in waves in continuous media, with implications ranging from light’s missing orbital angular momentum to the birth of El Niño.

Topologically protected waves in continuous media, such as fluids and plasmas, have emerged as a rapidly expanding research frontier, extending the transformative successes of topological approaches in condensed matter physics. Recent theoretical work has established the fundamental significance of topological excitations in plasma systems. In particular, the bulk-edge correspondence and associated index theorems, central principles of topological physics, can be formulated for plasmas. Plasmas also display a distinctive signature: whereas periodic lattices in solids support nontrivial topology in momentum space, continuous plasmas exhibit nontrivial topology only in phase space, due to the topological triviality (contractibility) of momentum space.

Within this framework, topological plasma waves, including the topological gaseous plasmon polariton (GPP) and the topological Langmuir-cyclotron wave (TLCW), appear as spectral-flow modes that traverse band gaps. They propagate unidirectionally along interfaces tied to Weyl points and remain immune to backscattering even under strong perturbations or geometric irregularities. This robustness opens new mechanisms for particle acceleration and plasma heating.