Apply to the KCL MPhil/PhD Mathematics Program
PGR Admission Tutor
Dr. Pierpaolo VivoContacts
PGR OfficeThe Disordered Systems group is constantly engaged in the supervision of PhD candidates in Mathematics and Applied Mathematics within our Department. All applications are processed through the King’s appplication system, accessible from the link below.
PhD projects
Exploring the non-equilibrium states of matter
Status: Open.
The studentships are funded for 3.5 years and include Tuition Fees, a Stipend at the UK Research Council rate (plus London weighting) and an allowance for research consumables and travel.
Description — Equilibrium statistical mechanics offers a precise framework for understanding macroscopic physical systems in their long-term state, characterized by maximal entropy for given values of globally conserved quantities. This simple precept allows to determine precisely the equilibrium states. However, the most captivating and profound phenomena in nature often manifest in systems that have not yet attained equilibrium, or that are driven out of it through some external forcing. In these instances, we lack any fundamental guiding principle that would permit an accurate description of matter at the macroscopic level. Consequently, we find ourselves exploring specific examples in a quest for a comprehensive theory.
The primary objective of this Ph.D. project is to delve into some of these examples using the tools of theoretical physics, mathematical physics and probability theory, with the emphasis on a precise and detailed understanding. Disordered interacting quantum systems offer a particularly rich phenomenology. In particular, the interplay between disorder and interactions may lead to the so called many-body localized phase where the approach to equilibrium is halted by emergent conserved quantities. The physical characteristics of this phase have been explored intensively since more than a decade and the field is probably reaching maturity from a phenomenological point of view. In contrast, the mathematical understanding remains very incomplete, reflecting into the fact that several fundamental aspects are still intensely debated. There is thus a clear need for the development of a better mathematical theory and the search for new techniques. A direct goal of this project will be to bring the theory on much firmer grounds. Moreover, from a broader perspective, the hope is that these contributions eventually lead to a more profound and cohesive understanding of non-equilibrium states of matter as a whole.
How to apply — The ideal candidate is a very motivated student with a solid background in either applied mathematics or theoretical physics. Most importantly, the successful candidate is expected to have some taste for deriving rigorous mathematical results. This position is open to both Home and Overseas students. Applicants should have a 2:1 or first-class undergraduate degree, or an MMath, MSci or Master’s degree with Merit and high grades in modules relating to the research area. A solid background in either applied mathematics or theoretical physics as well as some taste for deriving rigorous mathematical results are expected. To be considered for the position candidates must apply via the King’s Apply online application system. Please indicate François Huveneers as your desired supervisor, Disordered Systems as your desired research group and the project title in your application and all correspondence. A guide on other application details can be found here. Direct link to the application page
The mathematics of adaptive, stable and robust Artificial Intelligence
Status: Open.
The studentship covers tuition fees for Home/UK students and a stipend of £19,668 per annum. The funding is available for 3.5 years. Overseas applicants will be considered but they must demonstrate the capability to fund the difference between International full-time fees (currently £28,260 per annum for 2023/2024 academic year) and Home/UK fees.
Description — Recent years have seen explosive growth in the applications of Artificial Intelligence (AI). Notwithstanding significant successes of the new technology, empirical evidence points to numerous examples of errors in the decisions of state-of-the-art AI systems. Current theoretical works confirm that modern design practices and classical mathematical frameworks supporting these could suffer from various fundamental shortcomings including the typicality of adversarial attacks, susceptibility to backdoors and stealth attacks, instabilities, and hallucinations. At the same time, there is a plethora of under-explored and seemingly controversial phenomena, such as learning from scarce yet high-dimensional information, which has been broadly observed experimentally in large-scale AI systems but whose complete mathematical understanding is yet to be developed. Other factors hindering the performance of current AI systems include the need to adapt to concept drifts and unforeseen changes in operational conditions.
The project aims to explore and systematically assess major causes of AI errors and instabilities and develop appropriate mathematical foundations enabling the creation of stable and robust Artificial Intelligence capable of dealing with errors and concept drifts. The successful candidate will work alongside a team of early career researchers funded by the UKRI Turing AI Acceleration Fellowship (EP/V025295/2) and will benefit from the team’s established relationships with industrial partners, academic networks (Turing AI Fellows, Trustworthy Autonomous Systems Node in Verifiability EP/V026801/2), and other collaborators in academia, healthcare, defence & security.
How to apply — To state your interest, please contact directly Prof Ivan Tyukin.
Entanglement and universality in inhomogeneous and out-of-equilibrium many body quantum systems
Status: Open.
We would like to bring to your attention a funded home-student PhD fellowship available in the Disordered System group at King’s College London. This is to be co-supervised by Dr Paola Ruggiero and Prof Benjamin Doyon, and to start in October 2023. The PhD project covers a broad range of topics in statistical physics and quantum many-body systems, and will be adapted to the interests of the candidate. A general description of the project can be found below.
Description — The project lies at the intersection of several different fields: from statistical physics to quantum information, from high energy to condensed matter physics. The common denominators are the phenomenon of quantum entanglement and the out-of-equilibrium behaviour of many-body quantum systems, particularly in low dimensional quantum many body systems. While the emergence of universality is rather well established for systems which are homogeneous and are at equilibrium, the same is not true for inhomogeneous systems, both in and out of equilibrium. Those, on the other hand, are the rule rather than the exception in the context of quantum experiments. Different new tools are currently under study to investigate what remains of the aforementioned universality in such more complicated situations, and the projects aims to gain a better understanding of this topic, especially through the “lenses” of entanglement.
How to apply — If you have home-fees student status, in order to express your interest, please submit first your CV and two reference letters to Paola Ruggiero. As a next step, apply for an Applied Mathematics Research Degree in the Mathematics Department via the King’s application system. Direct link to the application page
Pierpaolo Vivo
Reader in Disordered Systems
