Research
I study nonlinear partial differential equations and probability. My research is partially supported by the National Science Foundation and the Sloan Foundation. The following is a list of my preprints and publications.

Armstrong and Smart, Quantitative stochastic homogenization of convex integral functionals, preprint.

Lee, Peres, and Smart, A Gaussian upper bound for martingale smallball probabilities, preprint.

Levine, Pegden, and Smart, The Apollonian structure of integer superharmonic matrices, preprint.

Armstrong and Smart,
Quantitative stochastic homogenization of elliptic equations in nondivergence form , preprint.

Armstrong and Smart, Stochastic homogenization of fully nonlinear elliptic uniformly elliptic equations revisited, preprint.

Levine, Pegden, and Smart, Apollonian Structure in the Abelian Sandpile, preprint.

Armstrong and Smart, Regularity and stochastic
homogenization of fully nonlinear equations without uniform ellipticity, Ann. Prob., to appear.

Hynd, Smart, and Yu, Nonuniqueness of infinity ground
states, Calc. Var. Partial Differential Equations, to appear.

Pegden and Smart, Convergence of the Abelian sandpile, Duke Math. J., to appear.

Armstrong, Sirakov, and Smart, Singular solutions of fully nonlinear elliptic equations and applications, Arch. Ration. Mech. Anal. 205 (2012), no. 2, 345394.

Armstrong and Silvestre, Partial regularity of solutions of fully nonlinear uniformly elliptic equations, Comm. Pure Appl. Math. 65 (2012), no. 8, 11691184.

Evans and Smart, Adjoint methods for the infinity Laplacian PDE, Arch. Ration. Mech. Anal. 201 (2011), no. 1, 87113.

Evans and Smart, Everywhere differentiability of infinity harmonic functions, Calc. Var. Partial Differential Equations 42 (2011), no. 12, 289299.

Sheffield and Smart, Vectorvalued optimal Lipschitz extensions, Comm. Pure. Appl. Math. 65 (2012), no. 1, 128154..

Armstrong, Crandall, Julin, and Smart, Convexity criteria and uniqueness of absolutely minimizing functions, Arch. Ration. Mech. Anal., 200 (2011), no. 2, 405443.

Armstrong and Sirakov, Fundamental solutions of homogeneous fully nonlinear elliptic equations, Comm. Pure. Appl. Math., 64 (2011), no. 6, 737777.

Armstrong and Somersille, An infinity Laplace equation with gradient term and mixed boundary conditions, Proc. Amer. Math. Soc., 139 (2011), no. 5, 17631776.

Armstrong and Smart, An easy proof of Jensen's theorem on the uniqueness of infinity harmonic functions, Calc. Var. Partial Differential Equations 37 (2010), 381384.

Armstrong and Smart, A finite difference approach to the infinity Laplace equation and tugofwar games, Trans. Amer. Math. Soc. 364 (2012), no. 2, 595636.

Smart, Interpreting Hasson's example, draft.
