Department of Mathematics

University of British Columbia

1984 Mathematics Road

Vancouver, BC, Canada V6T 1Z2

I am a PhD student in the probability group in the Department of Mathematics at the University of British Columbia in Vancouver. My supervisors are Asaf Nachmias and Omer Angel. Previously, I completed my BA and MMath at King's College, Cambridge. In the autumn of 2017 I will return to Cambridge to take up both a Herchel Smith Postdoctoral Research Fellowship in the Department of Pure Mathematics and Mathematical Statistics and a Junior Research Fellowship in Trinity College.

I was an intern in the Microsoft Research Theory Group in the summers of 2015 and 2016 under the mentorship of Ander Holroyd and Yuval Peres, and will be returning to Microsoft for a third internship in the summer of 2017. I am also a Microsoft Research PhD Fellow.

Probability: planar graphs, circle packing, random graphs, maps, and other structures, random walk, spanning forests, percolation, probability on groups, random permutations.

- The Strange Geometry of High-Dimensional Spanning Forests, Northwest Probability Seminar, MSR 2016. (slides)
- Circle Packing and Random Triangulations, MSR 2015.
- Indistinguishability of Trees in Uniform Spanning Forests, Banff 2015. (slides)
- Reversible Hyperbolic Triangulations: Circle Packing and Random Walk, Banff 2014. (slides)

- Omer talking about Parabolic and Hyperbolic Unimodular Maps, Cambridge 2015.
- Asaf talking about Uniform Spanning Forests of Planar Graphs, Cambridge 2015.

*The Component Graph of the Uniform Spanning Forest: Transitions in Dimensions 9, 10, 11, ...*

with Yuval Peres. Preprint.

[ arXiv | pdf | abstract | BibTeX ]-
*Hyperbolic and Parabolic Unimodular Random Maps*, with Omer Angel, Asaf Nachmias

and Gourab Ray. Preprint.

[ arXiv | pdf | abstract | BibTeX ] -
*Critical percolation on any quasi-transitive graph of exponential growth has no infinite clusters.***Comptes Rendus Mathematique**, Volume 354, Issue 9, Pages 944-947.

[ arXiv | pdf | abstract | BibTeX ] -
*Uniform Spanning Forests of Planar Graphs.*with Asaf Nachmias. Preprint.

[ arXiv | pdf | abstract | BibTeX ] -
*Interlacements and the Wired Uniform Spanning Forest.*Preprint.

[ arXiv | pdf | abstract | BibTeX ] -
*Boundaries of Planar Graphs: A Unified Approach.*with Yuval Peres. Preprint.

[ arXiv | pdf | abstract | BibTeX ] -
*Indistinguishability of Trees in Uniform Spanning Forests.*with Asaf Nachmias.**Probability Theory and Related Fields**, to appear.

[ arXiv | pdf | abstract | BibTeX ] -
*Collisions of Random Walks in Reversible Random Graphs.*with Yuval Peres.**Electronic Communications in Probability**, 20, no. 63, 1-6, 2015.

[ arXiv | pdf | abstract | BibTeX ] -
*Wired Cycle-Breaking Dynamics for Uniform Spanning Forests.***Annals of Probability**, to appear.

[ arXiv | pdf | abstract | BibTeX ] -
*Unimodular Hyperbolic Triangulations: Circle Packing and Random Walk.*with Omer Angel,

Asaf Nachmias and Gourab Ray.**Inventiones Mathematicae**, (2016) 206: 229. doi:10.1007/s00222-016-0653-9.

[ arXiv | pdf | abstract | BibTeX ]