Arunima Bhattacharya
استادیار · Geometric Analysis
University of North Carolina at Chapel Hillمعرفی
Arunima Bhattacharya is an Assistant Professor of Mathematics at the University of North Carolina at Chapel Hill and a Bill Guthridge Fellow. She holds a Ph.D. from the University of Oregon (2019), an M.Sc. from the Tata Institute of Fundamental Research (2014), and a B.Sc. from St. Xavier's College, Kolkata (2012). Her research focuses on geometric analysis, particularly fully nonlinear second- and fourth-order elliptic PDEs arising in differential geometry, with applications to Lagrangian mean curvature flow, Hamiltonian stationary equations, and minimal surface theory.
- Education:
- B.Sc., St. Xavier’s College, Kolkata (2012)
- M.Sc., Tata Institute of Fundamental Research (2014)
- Ph.D., University of Oregon (2019)
Her work applies tools from minimal surface theory, Lagrangian geometry, Kähler geometry, geometric measure theory, and elliptic equation theory to study area minimization problems in Lagrangian surfaces and geometric variational problems for the volume functional. She has developed regularity theory for fourth-order nonlinear elliptic equations and generalized Colding-Minicozzi entropy in Cartan-Hadamard manifolds, demonstrating novel rigidity phenomena.
Her research is supported by multiple NSF grants (DMS-2350290, DMS-2135998), a Simons Foundation grant (MPS-TSM-00002933), and the Bill Guthridge Fellowship. She has made significant contributions to the understanding of Hessian estimates, C^{2,α} regularity, and the Dirichlet problem for Lagrangian mean curvature equations.
- Scientific Awards & Grants:
- NSF Grant DMS-2350290 (PI)
- Simons Foundation Grant MPS-TSM-00002933 (PI)
- NSF RTG Grant DMS-2135998 (Senior Personnel)
- Bill Guthridge Fellowship (UNC)
Arunima Bhattacharya’s publications span regularity theory for Hamiltonian stationary equations, optimal regularity conditions for Lagrangian mean curvature type equations, CR-geometry, and geometric measure theory. Her work demonstrates the interplay between nonlinear PDEs and geometric structures, advancing the analysis of fourth-order equations in symplectic and CR-manifolds.
