Geometry, in the form of geometric phases such as the Berry phase, and topology are becoming part of the standard vocabulary of physics. Often, geometry and topology lead to simple and robust physical interpretations of complicated phenomena. In this talk I will discuss various geometric phases that occur in magnetization dynamics. First, I will discuss so-called Hannay angles [1], and give a simple interpretation of the magnon Berry phase as a Hannay angle. I will also discuss how this geometric angle is able to affect the magnon transport. Second, I will discuss a geometric phase that occurs in the non-linear driven-dissipative dynamics of spin-torque oscillators and that may be used to robustly tune their phase [2]. Finally, I will discuss our recent proposal for non-hermitian topological states in arrays of spin-torque oscillators, and how this may be used to selectively activate oscillators at the edge of the array [3].

[1] Andreas Rueckriegel and R.A. Duine, Annals of Physics 412, 168010 (2020).
[2] Andreas Rueckriegel and R.A. Duine, Phys. Rev. B 101, 144415 (2020).
[3] B. Flebus, R.A. Duine, and H.M. Hurst, arXiv:2003.01152.