Doctoral programme in mathematics at Massachusetts Institute of Technology

Many random discrete models show particular (random or deterministic) characteristic behaviour when the size of the model grows. Often we can define a notion of convergence for the model when its size goes to infinity, and we say that the model has a scaling limit. The limiting object is typically a random continuum object with certain properties that characterize the large-size behaviour of the discrete model. I have studied discrete models inspired by applications in physics, geometry, computer science, and social sciences, and the continuum objects which are their conjectured or proven scaling limits. Conformally invariant scaling limits have been of particular interest to me.

The objective of the project is completing a doctoral degree in mathematics at Massachusetts Institute of Technology. The first 1-2 years of the programme will consist of courses and preparation for the qualifying exam, while the rest of the programme wil l consist of independent research activity leading to the doctoral dissertation. Indicative interest areas for the research period are analysis, partial differential equations and probability, but the exact topic of the dissertation will be decided after the start of the programme. The doctoral programme lasts for up to five years, of which this application for support concerns the period from June 2014 to August 2017.