I am a fifth year graduate student in mathematics at MIT. My adviser is Scott Sheffield. Previously, I was an undergraduate student at Northwestern University. During the summer of 2015, I was an intern in the Microsoft Research theory group in Redmond, WA. Next year, I will be a postdoc at the University of Cambridge, supported by both a Herchel Smith fellowship and a junior research fellowship at Trinity college.
I am interested in probability theory, particularly random curves and surfaces which arise in statistical mechanics. Topics I have worked on include Schramm-Loewner evolution, Liouville quantum gravity, random planar maps, first passage percolation, and Brownian surfaces.
Email: ewain at mit.edu
Here is a link to my CV: CV
Percolation on random planar maps
- Convergence of percolation on uniform quadrangulations with boundary to SLE6 on √ 8/3 -Liouville quantum gravity (with J. Miller). arxiv:1701.05175
- Characterizations of SLEκ for κ ∈ (4,8) on Liouville quantum gravity (with J. Miller). arxiv:1701.05174
- Convergence of the free Boltzmann quadrangulation with simple boundary to the Brownian disk (with J. Miller). Annales de l'Institut Henri Poincarè, to appear. arxiv:1701.05173
- Chordal SLE6 explorations of a quantum disk (with J. Miller). Electronic Journal of Probability, to appear. arxiv:1701.05172
Self-avoiding walk on random planar maps
- Convergence of the self-avoiding walk on random quadrangulations to SLE8/3 on √ 8/3 -Liouville quantum gravity (with J. Miller). arxiv:1608.00956
- Metric gluing of Brownian and √ 8/3 -Liouville quantum gravity surfaces (with J. Miller). arxiv:1608.00955
- Scaling limit of the uniform infinite half-plane quadrangulation in the Gromov-Hausdorff-Prokhorov-uniform topology (with J. Miller). Electronic Journal of Probability, 2017. arxiv:1608.00954 (link)
Fractal properties of SLE/LQG
Peanosphere convergence/mating-of-trees bijections
- Active spanning trees with bending energy on planar maps and SLE-decorated Liouville quantum gravity for κ > 8 (with
J. Miller, and
D. Wilson). Communications in Mathematical Physics, 2018. arxiv:1603.09722
- Joint scaling limit of a bipolar-oriented triangulation and its dual in the peanosphere sense (with N. Holden and X. Sun). arxiv:1603.01194
- Scaling limits for the critical Fortuin-Kasteleyn model on a random planar map III: finite volume case (with X. Sun). arxiv:1510.06346
- Scaling limits for the critical Fortuin-Kasteleyn model on a random planar map II: local estimates and empty reduced word exponent (with X. Sun). Electronic Journal of Probability, 2017. arxiv:1505.03375 (link)
- Scaling limits for the critical Fortuin-Kasteleyn model on a random planar map I: cone times (with C. Mao and X. Sun). Annales de l'Institut Henri Poincarè, to appear. arxiv:1502.00546
First passage percolation
- On Beckner’s Inequality for Gaussian Measures (with E. Hsu). Elemente der Mathematik, 2015. (link)
- Functional Inequalities for Gaussian and Log-Concave Probability Measures. Undergraduate Thesis. Northwestern University Undergraduate Research Journal, 2013. Adviser: Elton Hsu. (link)
- On a Quaternionic Analogue of the Cross Ratio (with M. Libine) Advances in Applied Clifford Algebras, 2012. arxiv:1112.0612
- The Poisson Integral Formula and Representations of SU(1,1). Rose-Hulman Undergraduate Math Journal, 2011. (link)
Works in progress or in preparation
- Convergence of the topology of critical FK planar maps to that of CLEκ on a Liouville quantum surface (with J. Miller).
- Conformal invariance of whole-plane CLEκ for 4 < κ < 8 (with J. Miller).
- Phases of Quantum Loewner evolution (with J. Miller, S. Sheffield, and X. Sun).