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.

*Office:* 2-341A

*Email:* ewain *at* mit.edu

Here is a link to my CV: CV

- Random walk on random planar maps: spectral dimension, resistance, and displacement (with J. Miller). arxiv:1711.00836
- A mating-of-trees approach for graph distances in random planar maps (with N. Holden and X. Sun). arxiv:1711.00723
- The Tutte embedding of the mated-CRT map converges to Liouville quantum gravity (with J. Miller and S. Sheffield). arxiv:1705.11161
- A distance exponent for Liouville quantum gravity (with N. Holden and X. Sun).
*Probability Theory and Related Fields*, to appear. arxiv:1606.01214

- Convergence of percolation on uniform quadrangulations with boundary to SLE
_{6}on √ 8/3 -Liouville quantum gravity (with J. Miller). arxiv:1701.05175 - Characterizations of SLE
_{κ}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 SLE
_{6}explorations of a quantum disk (with J. Miller).*Electronic Journal of Probability*, to appear. arxiv:1701.05172

- Convergence of the self-avoiding walk on random quadrangulations to SLE
_{8/3}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)

- Connectivity properties of the adjacency graph of SLE
_{κ}bubbles for κ ∈ (4,8) (with J. Pfeffer). arxiv:1803.04923 - Dimension transformation formula for conformal maps into the complement of an SLE curve (with N. Holden and J. Miller). arxiv:1603.05161
- An almost sure KPZ relation for SLE and Brownian motion (with N. Holden and J. Miller). arxiv:1512.01223
- Brownian motion correlation in the Peanosphere for κ > 8 (with N. Holden, J. Miller, and X. Sun).
*Annales de l'Institut Henri Poincarè*, to appear. arxiv:1510.04687 - Almost sure multifractal spectrum of SLE (with J. Miller and X. Sun).
*Duke Mathematical Journal*, to appear. arxiv:1412.8764

- Active spanning trees with bending energy on planar maps and SLE-decorated Liouville quantum gravity for κ > 8 (with
A. Kassel,
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

- Asymptotic behavior of the Eden model with positively homogeneous edge weights (with S. Bubeck). arxiv:1508.05140

- 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)

- Convergence of the topology of critical FK planar maps to that of CLE
_{κ}on a Liouville quantum surface (with J. Miller). - Conformal invariance of whole-plane CLE
_{κ}for 4 < κ < 8 (with J. Miller). - Phases of Quantum Loewner evolution (with J. Miller, S. Sheffield, and X. Sun).

- Jul. 2018. Random Geometry followup workshop at the Isaac Newton Institute.
- Jul. 2018. IMS Annual meeting on probability and statistics in Vilnius, Lithuania.
- Jun. 2018. IST Austria Summer School in Probability and Mathematical Physics.
- Mar. 2018. Stony Brook University analysis seminar.
- Feb. 2018. Brown University graduate student conference.
- Feb. 2018. University of Pennsylvania probability seminar.
- Dec. 2017. Tel Aviv university probability seminar.
- Oct. 2017. Oberwolfach seminar: Scaling limits of random planar maps and Liouville quantum gravity.
- Oct. 2017. Zurich graduate student probability seminar.
- Oct. 2017. Zurich probability seminar.
- Sep. 2017. Princeton University topics in probability seminar.
- May 2017. Stochastic Analysis: Geometry of Random Processes workshop at Oberwolfach.
- Apr. 2017. Brown discrete math seminar.
- Apr. 2017. AMS Sectional meeting at Indiana University.
- Mar. 2017. SLE, GFF, and LQG in NYC workshop at Columbia University.
- Feb. 2017. Cornell probability seminar.
- Jun. 2016. Recent developments in SLE conference at the Institut Mittag-Leffler.
- Feb. 2016. MIT probability seminar.
- Jan. 2016. University of Chicago probability seminar.
- Nov. 2015. Michigan State University probability seminar.
- Oct. 2015. Northwestern University analysis seminar.
- Aug. 2015.Microsoft Research, Redmond, WA. (video)
- Jan. 2015. Conformally invariant scaling limits conference at the Isaac Newton Institute. (video) (slides)