# Geometry of minimal surfaces via integrable systems

## Granada (Spain)

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Professor

In this lecture, he will explain how we can construct and solve the period problem for minimal annuli in $\mathbb{S}^2\times\mathbb{R}$ and $\mathbb{S}^3$. Then we will explain how we can deform this annuli preserving the period and embeddness via Whitham deformation. We prove that the space moduli of embedded minimal annuli is path connected. Isolated property of annuli foliated by circles imply uniqueness of classical embedded examples. This theory apply to find a proof of Lawson conjecture and and present an unified theory with the classification of genus zero embedded minimal surfaces of $\mathbb{R}^3$ and $\mathbb{S}^2\times\mathbb{R}$.

**Laurent Hauswirth**will give a four-day course entitled*Geometry of minimal surfaces via integrable systems*.In this lecture, he will explain how we can construct and solve the period problem for minimal annuli in $\mathbb{S}^2\times\mathbb{R}$ and $\mathbb{S}^3$. Then we will explain how we can deform this annuli preserving the period and embeddness via Whitham deformation. We prove that the space moduli of embedded minimal annuli is path connected. Isolated property of annuli foliated by circles imply uniqueness of classical embedded examples. This theory apply to find a proof of Lawson conjecture and and present an unified theory with the classification of genus zero embedded minimal surfaces of $\mathbb{R}^3$ and $\mathbb{S}^2\times\mathbb{R}$.

Conferencia financiada por el programa de doctorado **Matemáticas** (MHE2011-00248)