In this talk I will present some surprising effects of the originally envisaged by Lifshitz usual Fermi surface topological transitions and introduce higher order ones. Two distinct examples will be presented: (i) the effects on ferromagnetic superconductors and in particular on URhGe [1] which stems from usual Lifshitz transitions and (ii) explanation of experimental puzzles of Sr₃Ru₂O₇ [2] which is an example of a higher order Fermi surface topological transition. Then I will touch upon ongoing work on the classification of these higher order transitions in two dimensions [3]. 

[1] Y. Sherkunov, A. V. Chubukov and J. J. B., Phys. Rev. Lett. 121, 097001 (2018).

[2] D. V. Efremov, A. Shtyk, A. W. Rost, C. Chamon, A. P. Mackenzie and J. J. B. Phys. Rev. Lett. 123, 207202 (2019).

[3] A. Chandrasekaran, A. Shtyk, J. J. B and C. Chamon, arXiv:1910.10183.