Research
Some research papers I have written:
Papers
- (1 + Ω(1))-Approximation to MAX-CUT Requires Linear Space
with M. Kapralov, S. Khanna, and M. Sudan
Manuscript.
- On the Sensitivity Conjecture for Read-k Formulas
with M. Bafna, S. Lokam, and S. Tavenas
MFCS 2016. (draft)
- Bridging the Capacity Gap Between Interactive and One-Way Communication
with B. Haeupler
ECCC TR16-090 and arXiv:1605.08792. (ECCC | arXiv)
- Communication with Partial Noiseless Feedback
with B. Haeupler and P. Kamath
RANDOM 2015.
- Towards Constructing Ramanujan Graphs Using Shift Lifts
with K. Chandrasekaran
arXiv:1502.07410. (arXiv)
- Approximating Data-Sensitive Distances
with M. Cohen, B. Fasy, G. Miller, A. Nayyeri, and D. Sheehy
WADS 2015. Also arXiv:1502.08048. (arXiv)
- An Entropy Sumset Inequality and Polynomially Fast Convergence to Shannon Capacity Over All Alphabets
with V. Guruswami
CCC 2015. Also ECCC TR14-165 and arXiv:1411.6993. (ECCC | arXiv)
- See video presentation from the Simons Institute's workshop on Coding: From Practice to Theory.
- Note: This work shows that polar codes over prime alphabet are the first-known construction of efficiently encodable and decodable codes to exhibit a polynomial speed of convergence for all symmetric channels.
- Limitations on Testable Affine-Invariant Codes in the High-Rate Regime
with V. Guruswami, M. Sudan, and C. Wang
SODA 2015. Also ECCC TR14-067. (ECCC)
- A Fast Algorithm for Well-Spaced Points and Approximate Delaunay Graphs
with G. Miller and D. Sheehy
SoCG 2013. Also arXiv:1304.0524. (arXiv)
- Restricted Isometry of Fourier Matrices and List Decodability of Random Linear Codes
with M. Cheraghchi and V. Guruswami
SODA 2013. Journal version: SIAM Journal of Computing 42(5), pp. 1888-1914, 2013. Also ECCC TR12-082 and arXiv:1207.1140. (ECCC | arXiv)
- Note: This work relates list-decoding of random linear codes to analyzing the Restricted Isometry Property (RIP) of subsampled DFT matrices from compressed sensing.
- We show that the number of row samples needed for NxN matrices and sparsity k is O(k log^2 k log N), which improves on bounds by Candès-Tao and Rudelson-Vershynin!
- Subsequent work: A further improvement of our compressed sensing bound has been obtained by Haviv and Regev.
- Subsequent work: Our list-decoding result has been improved by Mary Wootters using a different approach.
- Meshing log n Dimensions in Polynomial Time
with G. Miller and D. Sheehy
Extended abstract in CG:YRF 2012
- On an Exact Formula for the Coefficients of Han's Generating Function
Accepted to Annals of Combinatorics. (pdf)
- On the Erdős-Straus Conjecture: Properties of Solutions to its Underlying Diophantine Equation
with M. Monks
Manuscript. (pdf)
Other Articles
- My Favorite Problem: An Unconventional Inequality, Harvard College Math Review 2008. (pdf)