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Within the last fifteen years, Dynamics and geometry in the Teichmüller space is and area that has known considerable progress and to which many first-class mathematicians have contributed. One such recent development is a theorem by Eskin and Mirzakhani that proves that complex geodesics and their closures in moduli space are surprisingly regular, rather than irregular or fractal, a fantastic new path that revolutionizes this area of research and was announced in 2012. The main topics we want to focus on in this workshop are at the border with geometry, algebraic geometry, topology, dynamical systems, ergodic theory and number theory. We are aiming at four fifty-minute talks per day and a total of 18 talks. This format is particularly adapted as it leaves a lot of space for discussion and informal work in smaller groups. This conference is aimed at experts in those areas but is also particularly designed for young researchers.