The goal of the DTU is to provide an excellent research and research training framework for a group of young scientists in subjects requiring the use of latest geometric and stochastic methods in order to generate progress in key research themes of current interest within mathematics and for applications, like those summarised below. It will strive to attract highly promising students and to offer them the best possible PhD training opportunity. They will be in contact with highly active junior and senior international researchers, and acquire a broad spectrum of mathematical knowledge and understanding. They will also be given the training and contacts necessary to develop a non-academic career.The DTU consortium consists of a group of internationally recognised researchers in geometry, probability, as well as geometric and/or stochastic methods. Its members are engaged in many interdisciplinary collaborations within the group and with international experts. The research programme will focus on a number of questions that are currently highly active at the international level, in the areas of geometry, probability and their applications.Geometric and stochastic methods are omnipresent in all parts of modern mathematics with a vast range of applications. Apart from the various disciplines in geometry (like Differential Geometry, Algebraic Geometry, Topology, etc.), geometric methods are of utmost importance, for instance, in mathematical physics, number theory (e.g. Fermat’s Last Theorem, Langlands Programme), cryptography (e.g. elliptic curve cryptography), analysis (e.g. harmonic analysis on symmetric spaces), probability theory, optimisation (e.g. convex optimisation), etc. The same can be said about stochastic methods, they are also predominant in mathematical physics (e.g. quantum field theory), number theory (e.g. random matrix theory), cryptography (e.g. cryptanalysis), analysis, optimisation, financial mathematics, etc.