AK 006
BS Mathematics Peking University 2007
PhD Mathematics Purdue University 2014

My research is broadly speaking in the area of Nonlinear Partial Differential Equations with applications to physics and materials science. Specifically, I am interested in applying comprehensive techniques from nonlinear partial differential equations, calculus of variations and geometric measure theory to understand complex singularity structures in certain physical systems, including superconductors, liquid crystals, thin film blisters, convection pattern formations and some systems described by hyperbolic conservation laws. The studies of these systems are highly interdisciplinary. The mathematical studies of such problems require the development of new mathematical tools, and these studies further foster the fundamental understanding in related fields of sciences.

Scholarly Work

On the Rank-1 convex hull of a set arising from a hyperbolic system of Lagrangian elasticity. (with A. Lorent) Calc. Var. Partial Differential Equations 59 (2020), no. 5, 156.

Rigidity of a non-elliptic differential inclusion related to the Aviles-Giga conjecture. (with X. Lamy and A. Lorent) Arch. Ration. Mech. Anal. 238 (2020), no. 1, 383–413.

Regularity of the Eikonal equation with two vanishing entropies. (with A. Lorent) Ann. Inst. H. Poincaré Anal. Non Linéaire 35 (2018), no. 2, 481–516.

Convergence of the Lawrence-Doniach energy for layered superconductors with magnetic fields near H_{c1} . SIAM J. Math. Anal. 49 (2017), no. 2, 1225–1266.