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セミナー

seminar

Topological hydrodynamic modes on curved surfaces

I will review the usage of topological methods in the case of the Dirac fermion and their role in predicting trapped edge modes. I will then show that these methods can be applied to classical systems, in particular to hydrodynamic systems that describe a broad range of phenomena, from geophysical waves to waves in topologically non-trivial soft matter experiments. Some of these system include activity (i.e. self-propelled organisms within the fluid). In particular, I will derive an index theorem that relates the topology of Fourier space determined by the underlying Hamiltonian with the real space topology of the surface in which the waves are hosted. At the end, I will give details about how the same methods can be applied to high energy physics, in particular to astrophysics and the AdS/CFT correspondence.

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