My research interests include nonlinear partial differential inclusions (PDEs), calculus of variations, and applied mathematics. Specifically, I am interested in applying techniques from nonlinear PDEs and calculus of variations to understand complex singularity structures in problems arising from materials science (e.g. liquid crystals, thin films, superconductors) and continuum mechanics. These problems are highly interdisciplinary, and their study often requires the development of new mathematical tools. Such mathematical investigations also contribute to a deeper fundamental understanding in related scientific fields.
My research interests include nonlinear partial differential inclusions (PDEs), calculus of variations, and applied mathematics. Specifically, I am interested in applying techniques from nonlinear PDEs and calculus of variations to understand complex singularity structures in problems arising from materials science (e.g. liquid crystals, thin films, superconductors) and continuum mechanics. These problems are highly interdisciplinary, and their study often requires the development of new mathematical tools. Such mathematical investigations also contribute to a deeper fundamental understanding in related scientific fields.
Applications to Materials Science and Continuum Mechanics
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.
More than 70 media outlets, including the Latin Trade , Pittsburgh Post Gazette, and the Oklahoman carried the news of WPI welcoming 19 full-time educators and researchers to its faculty for the 2020-21 academic year.
