Topology of minimal surfaces in $\mathbb{S}^2 \times \mathbb{R}$

In this talk we will begin by exploring when a Riemannian manifold admits compact minimal submanifolds. In the simplest affirmative cases we will study which topological types are admissible. We then focus on the Riemannian product $\mathbb{S}^2\times \mathbb{S}(r)$, for $r>0$, where we will show that every compact surface with even Euler characteristic can be minimally embedded. Finally, we will briefly present how to construct such embeddings using the “conjugate Plateau technique”.