- [Preprint]
*Transport and Equilibrium in Non-Conservative Systems*, with L. Chayes. To appear in Advances in Differential Equations. -
*On the Rate of Convergence for Critical Crossing Probabilities*, with I. Binder and L. Chayes.

Ann. Inst. H. Poincare Probab. Statist. 51, no. 2, 672-715 (2015). *Hamiltonian ODE's on a Space of Deficient Measures*, with L. Chayes and W. Gangbo.

Communications in Mathematical Sciences, 11, no. 1, 1-31 (2013).- [UCLA Thesis]
*Critical Percolation, Universality, and SLE$_6$*[UCLA Thesis] *On Convergence to SLE$_6$ I: Conformal Invariance for Certain Models of the Bond-Triangular Type*and

*On Convergence to SLE$_6$ II: Discrete Approximations and Extraction of Cardy's Formula for General Domains*, with I. Binder and L. Chayes.

Journal of Statistical Physics 141, no. 2, 359-408 (2010).*Cardy's Formula for Certain Models of the Bond-Triangular Type*, with L. Chayes.

Reviews in Mathematical Physics 19, no. 5, 511-565 (2007).*Random Cluster Models on the Triangular Lattice*, with L. Chayes.

Journal of Statistical Physics 122, no. 4, 647-670 (2006).

*On Convergence to SLE$_6$*.*Convergence to SLE$_6$ for Percolation Models*.*A Universality Result for Critical 2D Percolation.*Click here for the abstract of L. Chayes' talk on the same subject.*Hamiltonian ODEs on a Space of Deficient Measures.**Inhomogeneous Continuity Equation With Application to Hamiltonian ODE (v1)*and script.*Viscosity Solution for Degenerate Diffusion With a Drift.*

- Critical Percolation.
- Some Notes on Field Theory Preliminaries.
- Einstein Summation Notation.
- Paralinearization of the Dirichlet Neumann Operator: I, II, III, IV.
- Notes on the first half of Otto's paper
*The Geometry of Dissipative Evolution Equations: The Porous Medium Equation (updated: March 2012).* *Degenerate diffusion with a drift potential: a viscosity solutions approach, joint work with I. C. Kim, truncated version.*

- Some material related to the UCLA numerical analysis qualifying exam.
- Some material related to the UCLA algebra qualifying exam.
- A write up of the random cluster expansion and another write up of the random cluster expansion and Edwards-Sokal measure.
- Notes for my talk on domino tilings for Math 290K (Fall 2005).
- Some (complex analysis) notes on Smirnov's paper.