This is a summer school in the area of Elliptic Partial Differential Equations (Elliptic PDE’s) with motivation from Geometrical Analysis. It is oriented to PhD and postdoc students that are interested in deepening into these topics. Women mathematicians are encouraged to participate.

The theory of second order elliptic equations has been flourishing during the last fifty years, and in the last decade has experienced some major advances. Deep mathematical concepts lead to the field of Elliptic PDE’s, such as competitive systems, scattering theory or the Yamabe problem. The frameworks of study may be also diverse, ranging from the Euclidean setting to hyperbolic spaces. Moreover, there are important applications to population dynamics, theoretical physics or differential geometry. In Europe there is an important mathematical community working in the area of Elliptic PDE’s, in particular brilliant women mathematicians with strong influence in the development of the field.

The aim of this summer school is to introduce two research lines of current interest in Elliptic PDE’s:

*Geometric Aspects of Phase Separation* and **The Fractional Yamabe Problem.**

There will be 2 courses of 5 hours each given by the 2 lecturers of the school. 5 invited speakers will give a 1 hour talk each. Most of the young participants will give a short talk. Poster session will also be organised.

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