Papers

• [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).

Slides

• 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.

Notes, etc.

• 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.