Research
My research area is broadly Calculus of Variations and Partial Differential Equations. I am primarily interested in variational problems in a geometric setting, especially in problems where analysis meets geometry and topology.
Focal themes of my research include
Calculus of Variations
Direct methods in Calculus of variations from the viewpoint of differential forms.
Nonconvex minimization problem for functionals with large invariance groups.
Quasiconvexity and polyconvexity notions, weak lower semicontinuity and weak continuity results.
Geometric Variational problems
Variational problems for differential forms.
Harmonic and polyharmonic maps.
Yang-Mills connections and gauge theory.
Pullback equation for differential forms. Topological invariants below the continuity threshold.
Sobolev mappings between manifolds-- density, lifting, variational problems for manifold-valued Sobolev maps.
Regularity
Borderline and boundary regularity for nonlinear elliptic system of PDEs.
Nonlinear potential estimates.
Some other areas I am interested in........