Research

My research interests are:

Preprint(s):

On the nodal domain count under metric perturbations, Courant sharpness and boundary intersections (with Mayukh Mukherjee and Saikat Maji), available at arXiv: 2507.04928
Eigenfunction localization and nodal geometry on dumbbell domains (with Saikat Maji), available at arXiv: 2309.11441
Sharp lower bound on the "number of nodal decomposition" of graphs (with Hiranya K. Dey), available at arXiv: 2303.08417
Heat profile, level sets and hot spots of Laplace eigenfunctions (with Mayukh Mukherjee), available at arXiv: 2109.06531

Published/Accepted article(s):

Nodal sets of Laplace eigenfunctions under small perturbations (with Mayukh Mukherjee), Mathematische Annalen, available at arXiv: 2003.04833, Journal Link
On the effects of small perturbation on low energy Laplace eigenfunctions (with Mayukh Mukherjee), Journal of Spectral Theory, available at arXiv: 2108.13874, Journal Link
Concavity Properties of Solutions of Elliptic Equations under Conformal Deformations (with Gabriel Khan and Malik Tuerkoen), Mathematische Zeitschrift, available at arxiv.org/abs/2403.03200, Journal Link
A-priori Log-Concavity Estimates for Dirichlet Eigenfunctions (with Gabriel Khan and Malik Tuerkoen), Annals of Global Analysis and Geometry, available at arxiv.org/abs/2501.03504, Journal Link

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