In this talk I will show that the Morse index of the critical Moebius band in the 4-dimensional Euclidean ball equals 5. This result makes use of the quartic Hopf differential technique and a comparison theorem between the index of a free boundary minimal surface in the Euclidean ball and its spectral index. The latter also enables us to reprove a well-known result that the index of the critical catenoid in the 3-ball equals 4.

Instructions to join: Zoom invitation is sent to the geometry and topology seminar list. If you are not on the list, please, contact Peter McGrath at pjmcgrat@ncsu.edu to get the link.