Our research work lies at the intersection of foundational concepts in quantum theory and applications in cryptography. For instance, we study how fundamental quantum principles such as entanglement, nonlocality and no-cloning can be translated into protocols for a variety of cryptographic tasks, such as key distribution, randomness generation, or intrinsically quantum functionalities with no classical counterpart, such as certified deletion. We aim to develop these connections from both perspectives: deepening our understanding of foundational principles, while also exploring the prospects of inventing novel and interesting cryptographic protocols. To support this goal, we also aim to further develop rigorous mathematical results in the field of quantum information theory: for instance, characterising the properties of the many different forms of quantum entropy, which have proven greatly useful in providing rigorous security proofs with strong quantitative performance. Another significant aspect of our research is the use of convex optimisation in security proofs, ranging from the underlying convex analysis to the numerical software implementation. We welcome students from backgrounds in mathematics and physics, as well as students with experience in optimisation theory or implementation.