Abstract: I will first concentrate on doubling gluing constructions for minimal surfaces, including a recent construction for free boundary minimal surfaces in the unit ball (with D. Wiygul: arXiv:1711.00818).
I will then discuss the Linearized Doubling methodology and its applications so far (J. Differential Geom. 106:393-449, 2017; and with P. McGrath: arXiv:1707.08526),
and some further ongoing work expanding the scope of these methods to new cases.