Subject areas:
Mathematics.
Funding type:
Tuition fee.
Stipend.
Research Training & Support Grant.
Fully-funded PhD studentship available to start in the 2025/26 academic year.
Award details
High-dimensional random landscapes are important tools to model e.g. the energy functions of disordered systems, or the cost functions used in machine-learning algorithms [1]. Considerable efforts have been put in quantifying their average deepest minimum, or the number of critical points (minima, maxima and saddles), which are expected to influence heavily the dynamical properties. The more difficult question of characterising fluctuations around these averages has received less attention in comparison. Extending current analytical methods [2,3] and developing new ones to investigate this question will be the central topic of this PhD project. Tools from Random Matrix Theory, Statistical Mechanics and Probability will be instrumental in the development of this program. The influence of these fluctuations on the static and dynamic properties of disordered systems will also be considered in detail.
[1] V. Ros and Y. V. Fyodorov, “The high-dimensional landscape paradigm: Spin-glasses, and beyond,” in Spin Glass Theory and Far Beyond: Replica Symmetry Breaking After 40 Years (World Scientific, 2023) pp. 95–114.
[2] V. Ros, G. Ben Arous, G. Biroli, and C. Cammarota, “Complex energy landscapes in spiked-tensor and simple glassy models: Ruggedness, arrangements of local minima, and phase transitions,” Physical Review X 9, 011003 (2019).
[3] B. Lacroix-A-Chez-Toine, Y. V. Fyodorov, and P. Le Doussal, “Replica-symmetry breaking transitions in the large deviations of the ground-state of a spherical spin-glass,” Journal of Statistical Physics 191, 11 (2024).
Award value
Funding is available for 3.5 years, covering stipend, Full Tuition Fees at Home or Overseas rate, and Bench Fees.
Eligibility criteria
Award open to UK and international 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.
Application process
To be considered for the position, candidates must apply via King’s Apply online application system. Details are available at the Department of Mathematics website.
Please apply for Applied Mathematics Research: Disordered Systems/Financial Mathematics/Probability MPhil/PhD, indicate Bertrand Lacroix A Chez Toine as the supervisor and quote the project title in your application and all correspondence.
Please ensure to add the following code “StartUpLacroix-A-Chez-Toine” in the Funding section of the application form. Please select option 5: ‘I am applying for a funding award or scholarship administered by King’s College London’ and type the code into the ‘Award Scheme Code or Name’ box. Please copy and paste the code exactly.
The selection process will involve a pre-selection on documents and, if selected, will be followed by an invitation to an interview. If successful at the interview, an offer will be provided in due course.
This post is for a June or October 2025 entry (please indicate your preference in your application).
Contact Details
Bertrand Lacroix A Chez Toine, bertrand.lacroix_a_chez_toine@kcl.ac.uk.
If you require support with the administrative side of the application process, please contact mathematics-pgr@kcl.ac.uk.