Google Scholar: Google scholar profile

• On Fast Johnson–Lindenstrauss Embeddings of Compact Submanifolds of $\mathbb{R}^N$ with Boundary
  • This paper gives guarantees for reducing the ambient dimension of a manifold object into a smaller dimension without distorting the shape more than some threshold.
• Lower bounds on the low-distortion embedding dimension of submanifolds of $\mathbb{R}^N$
  • This paper gives a lower bound for how much it is possible to reduce the ambient dimension of a manifold object without distorting it above a threshold.
• Wireless, passive strain sensor in a doughnut-shaped contact lens for continuous non-invasive self-monitoring of intraocular pressure
  • In collaboration with MHM Kouhani (a talented electrical engineer) and others, we investigated using a pressure sensor in a contact lense for measure the eye pressure.
• Characterizing unit spheres in Euclidean spaces via reach and volume
  • This paper shows that if a shape turns around and closes onto itself with a limit on curving and a limit on surface area, it must be a sphere. In higher dimensions a similar analog holds.