I'm a fourth-year computer science and mathematics student at Carnegie Mellon University. I am pursuing a BSc in computer science and an MSc in mathematics through CMU's Math Honors program.

Recently, I have been interested in problems arising in discrete geometry processing, geometric analysis, and optimal transportation.

My research advisors are Keenan Crane and Dejan Slepčev.


Research Projects

Optimal Cone Singularities for Conformal Parameterization
with Keenan Crane and Dejan Slepčev - since Summer 2017
I developed a new technique to determine the optimal configuration of cone singularities using insights from convex analysis and conformal geometry. Conformally flattening a curved surface can induce serious area distortion. One approach to mitigate this distortion is to introduce cone singularities: one first computes a conformal map to a domain that is flat everywhere except at an isolated number of cone points, next one cuts the surface through these points and flattens it into the plane without introducing any additional area distortion. Determining the optimal configuration of cone singularities for reducing area distortion has been an open problem in the computer graphics community for a number of years.

We are currently writing our results up for publication.
Differential Operators on Point Clouds
with Keenan Crane and Dejan Slepčev - Summer 2016
Inspired by mesh-free discretizations of the Laplace-Beltrami operator on point clouds, we wondered whether it would also be possible to discretize arbitrary first order differential operators in a principled way. We attempted a number of different approaches, but the approach that seems most promising is based on a spectral discretization of the quaternionic Dirac operator. We considered this Dirac operator, since it encodes all first order differential operators (such as the gradient and divergence).
Noisy Curvature Estimation
Spring 2016 [Final project for Discrete Differential Geometry]
Estimating the curvature of unstructured geometric data in arbitrarily large dimensions can be difficult, especially in the presence of noise. To tackle this problem I generalized some known integral invariants relating to curvature to work on submanifolds of R^n with arbitrary codimension. Furthermore, by using a nonparametric statistical bootstrap, I was able to increase the robustness and accuracy of the algorithm in the presence of noise. The algorithm was implemented, and the numerical error estimates were found to coincide with the theoretical predictions. [pdf]

Notes


Interactive Visualizations


Art


Other Projects

Conformal Wasserstein Distances
Lipman and Daubechies used the Wasserstein metric and the Uniformization theorem from complex analysis to compare and register surfaces that are homeomorphic to the disk. In this project, I implemented their technique and various mesh deformation algorithms. I was then able to do further testing regarding the limits, pros, and cons of this surface comparison technique. [pdf]

Worked with Adrian Hagerty. Final project for Advanced Topics in Analysis: Variational and PDE techniques in Data Analysis.
Automatic Clothing Segmentation
We tackled the problem of automatic clothing segmentation in natural photographs. We first estimate human pose using deep neural networks; then we oversegment the image and cluster the regions into clothing items using a conditional random field. We were able to achieve results that were slightly better, at a fraction of the cost, than the currently published state of the art.

Built with Sudev Bohra. Final project for Graduate Computer Vision.
Cube It!
CubeIt! is a Rubik’s Cube simulator and solver that implements heuristic methods to determine solutions to the Rubik's Cube very quickly. CubeIt! uses OpenGL for 3D rendering and allows the user to interact with the cube in a very natural manner. I embarked on this project to learn both basic computer graphics and artificial intelligence. The entire program was built from scratch in C++. [exe]

I lost the source code on a computer in my family's home :(
I'll look for it and post it the next time I go back to visit.