Aryaman Chandra

This paper develops a precise correspondence between the static deformation of an interval and the spectral structure of the Dirichlet Laplacian. The torsion function generated by a uniform load decomposes into local quadratic profiles that coincide with the nodal intervals of each eigenfunction, while the reciprocal of each local profile identifies the unique extremum of the corresponding vibrational mode.

Aryaman Chandra

Independent research on Hausdorff dimensions and fractal geometry. Expository paper extending the work to Brownian motion and stochastic processes. Presented to 30+ peers at Euler Circle.