I am a postdoc in mathematics at University of Cambridge, supported by both a Herchel Smith fellowship and a junior research fellowship at Trinity college. Starting in July 2019, I will be supported by a Clay research fellowship.

I got my Ph.D from MIT in 2018, advised by 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.

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.

Here is a non-technical summary of my research aimed at an audience with some scientific background, not necessarily in math.

*Office:* D2.04

*Email:* eg558 *at* cam.ac.uk

Here is a link to my CV: CV

- KPZ formulas for the Liouville quantum gravity metric (with J. Pfeffer). arXiv:1905.11790
- Conformal covariance of the Liouville quantum gravity metric for γ ∈ (0,2) (with J. Miller). arXiv:1905.00384
- Existence and uniqueness of the Liouville quantum gravity metric for γ ∈ (0,2) (with J. Miller). arXiv:1905.00383
- Confluence of geodesics in Liouville quantum gravity for γ ∈ (0,2) (with J. Miller). arXiv:1905.00381
- Weak LQG metrics and Liouville first passage percolation (with J. Dubedat, H. Falconet, J. Pfeffer, and X. Sun). arXiv:1905.00380
- Local metrics of the Gaussian free field (with J. Miller). arXiv:1905.00379

- Liouville quantum gravity with central charge in (1,25): a probabilistic approach (with N. Holden, J. Pfeffer, and G. Remy). arXiv:1903.09111

- Bounds for distances and geodesic dimension in Liouville first passage percolation (with J. Pfeffer). arXiv:1903.09561
- External diffusion limited aggregation on a spanning-tree-weighted random planar map (with J. Pfeffer). arXiv:1901.06860
- The fractal dimension of Liouville quantum gravity: universality, monotonicity, and bounds (with J. Ding).
*Communications in Mathematical Physics*, to appear. arXiv:1807.01072 - A mating-of-trees approach for graph distances in random planar maps (with N. Holden and X. Sun). arXiv:1711.00723
- A distance exponent for Liouville quantum gravity (with N. Holden and X. Sun).
*Probability Theory and Related Fields*. arXiv:1606.01214 (journal)

- The Tutte embedding of the Poisson-Voronoi tessellation of the Brownian disk converges to √ 8/3 -Liouville quantum gravity (with J. Miller and S. Sheffield). arXiv:1809.02091
- Harmonic functions on mated-CRT maps (with J. Miller and S. Sheffield).
*Electronic Journal of Probability*, to appear. arXiv:1807.07511 - An invariance principle for ergodic scale-free random environments (with J. Miller and S. Sheffield). arXiv:1807.07515
- Anomalous diffusion of random walk on random planar maps (with T. Hutchcroft). arXiv:1807.01512
- Random walk on random planar maps: spectral dimension, resistance, and displacement (with J. Miller). arxiv:1711.00836
- The Tutte embedding of the mated-CRT map converges to Liouville quantum gravity (with J. Miller and S. Sheffield). arxiv:1705.11161

- Joint scaling limit of site percolation on random triangulations in the metric and peanosphere sense (with N. Holden and X. Sun). arXiv:1905.06757
- 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*. 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).
*Annals of Probability*, to appear. 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*. arxiv:1608.00954 (journal)

- Liouville quantum gravity surfaces with boundary as matings of trees (with M. Ang). arXiv:1903.09120
- Conformal invariance of CLE
_{κ}on the Riemann sphere for κ ∈ (4,8) (with J. Miller and W. Qian). arxiv:1811.00514 - 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*. arxiv:1510.04687 (journal) - Almost sure multifractal spectrum of SLE (with J. Miller and X. Sun).
*Duke Mathematical Journal*. arxiv:1412.8764 (journal)

- 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*. arxiv:1603.09722 (journal) - 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*. arxiv:1505.03375 (journal) - 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*. 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*. (journal) - Functional Inequalities for Gaussian and Log-Concave Probability Measures. Undergraduate Thesis.
*Northwestern University Undergraduate Research Journal*. Adviser: Elton Hsu. (journal) - On a Quaternionic Analogue of the Cross Ratio (with M. Libine)
*Advances in Applied Clifford Algebras*. arxiv:1112.0612 - The Poisson Integral Formula and Representations of SU(1,1).
*Rose-Hulman Undergraduate Math Journal*. (journal)

- Jul. 2019. Stochastic Processes and their applications conference at Northwestern University.
- Jun. 2019. Probability and quantum field theory: discrete models, CFT, SLE and constructive aspects, conference in Porquerolle, France.
- May 2019. University of Cambridge probability seminar.
- Mar. 2019. Vienna probability seminar.
- Feb. 2019. University of Warwick probability seminar.
- Dec. 2018. Amir Dembo birthday conference, Stanford University.
- Oct. 2018. Imerial College London stochastic analysis seminar.
- Oct. 2018. Columbia University probability seminar.
- Jul. 2018. Random Geometry followup workshop at the Isaac Newton Institute. (video)
- 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)