Don't forget about our next Fridays@2 event, Talking Maths with Dr James Munro!
At some point you might find yourself talking about mathematics either at a conference, or in a seminar, or in a presentation as part of your course, or on an outreach event, or to a future employer. This Fridays@2 session has advice for various situations, with concrete actions and suggestions for you to take into consideration the next time you're talking maths.
It's great to see so many of our undergraduates making use of the Andrew Wiles Building to study and socialise! However, please be aware that the operational hours of the building are 8am-6pm, Monday - Friday (except on closure days such as over Christmas, around Easter and some bank holidays) with the main doors unlocked 8:15am - 5:30pm (when undergraduates can thus freely enter the building and use the mezzanine study spaces). Those without card access to the building such as undergraduates must leave the building by 6:15pm.
The Graduate Program in Mathematics and Applications of PSL University offers scholarships for students willing to enrol in the PSL Master of Mathematics Master (M1 or M2) for 2024-2025. The teaching language is English and the program is based on the research teams in mathematics at CEREMADE (Paris-Dauphine-PSL), at DMA (Ecole Normale Supérieure - PSL), at the Ecole des Mines Paris-PSL , at the Paris Observatory-PSL, at the EHESS, and Collège de France.
Planar random growth processes occur widely in the physical world. Examples include diffusion-limited aggregation (DLA) for mineral deposition and the Eden model for biological cell growth. One approach to mathematically modelling such processes is to represent the randomly growing clusters as compositions of conformal mappings. In 1998, Hastings and Levitov proposed one such family of models, which includes versions of the physical processes described above. An intriguing property of their model is a conjectured phase transition between models that converge to growing disks, and 'turbulent' non-disk like models. In this talk I will describe a natural generalisation of the Hastings-Levitov family in which the location of each successive particle is distributed according to the density of harmonic measure on the cluster boundary, raised to some power. In recent joint work with Norris and Silvestri, we show that when this power lies within a particular range, the macroscopic shape of the cluster converges to a disk, but that as the power approaches the edge of this range the fluctuations approach a critical point, which is a limit of stability. This phase transition in fluctuations can be interpreted as the beginnings of a macroscopic phase transition from disks to non-disks analogous to that present in the Hastings-Levitov family.
We consider the general framework of distributionally robust optimization under a martingale restriction. We provide explicit expressions for model risk sensitivities in this context by considering deviations in the Wasserstein distance and the corresponding adapted one. We also extend the dual formulation to this context.