I will talk about the existence of higher genus helicoids in $\mathbb{S}^2\times \mathbb{R}$ and $\mathbb{R}^3$ . This is a joint work with David Hoffman and Brian White.

Gluing is a well established procedure to construct examples of minimal surfaces. In the past year I have been interested in developping tools to glue infinitely many minimal surfaces together. In this talk I will describe several families of minimal surfaces of theoretical interest that were constructed along the way. Then I will explain some of the technicalities involved in this kind of project, including a connection with some discrete analysis problems on graphs.

El autor, en colaboración con Laurent Mazet, presenta la construcción de una superficie minimal embebida en el producto llano $\mathbb{R}^2\times\mathbb{S}^1$ que es casi-periódica pero no periódica.