Before this I was a postdoc in the Probability group at ETH Zürich, and I completed my PhD in the Cambridge Centre for Analysis under the supervision of Nathanaël Berestycki. I did my undergraduate and masters degrees at the University of Cambridge, Queens' College. I am also a former president of the Emmy Noether society for women in mathematics.
My CV is here.
My research involves, broadly, the study of random systems at criticality. I am particularly interested in critical phenomena, scaling limits and more generally, random geometry. This is the study of the random curves and surfaces which arise as scaling limits of critical statistical physics models.
I am especially keen to investigate problems concerning Gaussian multiplicative chaos, the Gaussian free field, and Schramm-Loewner evolutions. These objects are connected in many different ways: some explicit, while some rather subtle and intriguing. Exploring these relationships and developing them further is one of the main goals of my research.
Simulation of the discrete planar Gaussian free field
Publications and Preprints
- Critical Liouville measure as a limit of subcritical measures with Juhan Aru and Avelio Sepúlveda. Electronic Communications in Proability. Vol 24, paper no. 18, p1-16 (2019).
- Approximating Liouville measure using local sets of the Gaussian free field with Juhan Aru and Avelio Sepúlveda. Annales de l'institut Fourier (to appear) (2019).
- An invariance principle for branching diffusions in bounded domains. Probability Theory and Related Fields, Vol 173, No. 3, p999-1062 https://doi.org/10.1007/s00440-018-0847-8 (2019).
- Critical Gaussian chaos: convergence and uniqueness in the derivative normalisation. Electronic Journal of Probability. Vol 23, paper no.31, p1-26 (2018).
- Level lines of the Gaussian free field with general boundary data with Hao Wu. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques. Vol. 53, No. 4, p2229–2259 (2017).
- A characterisation of the Gaussian free field with Nathanaël Berestycki and Gourab Ray. To appear in Probability Theory and Related Fields (2019+).
- Conformal welding for critical Liouville quantum gravity with Nina Holden (2019).
Here is my PhD thesis.
This simulation, made by Henry Jackson, is a binary branching Brownian motion in the disc with killing at the boundary. This is (a particular version of) the main object of interest in the first paper listed above. In the simulation different coloured paths represent different particles.
Recent/Upcoming Talks & Conferences
August 2020 World congress in probability and statistics, Seoul.
May 2020 Recent progress in random walks, CIRM.
April 2020 UK easter probability meeting, University of Manchester.
January 2020 Inhomogeneous random systems, Institut Curie.
November 2019 Probability seminar, University of Bristol.
November 2019 Dimers, Ising Model, and their Interactions, Banff International Research Station.
September 2019 Recent advances in loop models and height functions, University of Fribourg.
June 2019 Workshop on branching processes and related topics, Beijing Normal University.
June 2019 Probability and quantum field theory, Porquerolles.
March 2019 Mathematical physics seminar, Université de Genève.
Spring 2020: Operations Research
In Autumn 2018, together with Juhan Aru, we organised a reading group on Yang-Mills theory.
Analysis I, Analysis II, Metric and Topological Spaces, Advanced Probability: University of Cambridge. (2013-2017)
Topics on the Gaussian free field, master's course: ETH Zürich. (Autumn 2018)
Schramm-Loewner Evolutions, master's course: ETH Zürich. (Autumn 2017)
Analysis I, undergraduate course: University of Cambridge. (Autumn 2015 & 2016)
Stochastic Calculus, master's course: University of Cambridge. (Spring 2017)
Address: Department for Mathematical Sciences, Durham University, Lower Mountjoy, Stockton Road, DURHAM DH1 3LE