I am a 4th year graduate student in the Computer Science department at Princeton University being advised by Zeev Dvir. I am broadly interested in Combinatorics and Computational Complexity.

**Linear Hashing with l-$\infty $ guarantees and two-sided Kakeya bounds**
*with* Zeev Dvir

manuscript

[arXiv][ECCC]

**The Kakeya Set Conjecture for Z/NZ for general N **

manuscript

[arXiv]

**Proof of the Kakeya set conjecture over rings of integers modulo square-free N **
*with* Zeev Dvir

Combinatorial Theory, 2021:1

[arXiv][Journal link][Quanta article on this paper]

**Simple proofs for Furstenberg sets over finite fields **
*with* Zeev Dvir and Ben Lund

Discrete Analysis Journal 2021:22

[arXiv][Journal link]

**Furstenberg sets in finite fields: Explaining and improving the Ellenberg-Erman proof **
*with* Zeev Dvir and Ben Lund

manuscript

[arXiv]

**Linear Maps are good l-$\infty $ Hash functions**

Microsoft Research Redmond Algorithms Group, June 2022

**The Kakeya Set conjecture over Z mod N for general N**

University of British Columbia Discrete Math Seminar, March 2022

**The Kakeya Set conjecture over Z mod N for general N**

University of Toronto CS Theory seminar, Jan 2022

[slides]

**The Kakeya Set conjecture over Z mod N for general N**

IAS Computer Science and Discrete Math (CSDM) seminar, Nov 2021

[video][slides]

In an earlier life I did some Machine Learning research.

**Modeling Sparse Deviations for Compressed Sensing using Generative Models **

Manik Dhar, Aditya Grover, Stefano Ermon

International Conference on Machine Learning (ICML), 2018.

[arXiv]

**Flow-GAN: Combining Maximum Likelihood and Adversarial Learning in Generative Models**

Aditya Grover, Manik Dhar, Stefano Ermon

AAAI Conference on Artificial Intelligence (AAAI), 2018.

[arXiv]

**Robust kernel principal nested spheres **

Suyash Awate, Manik Dhar, Nilesh Kulkarni

International Conference on Pattern Recognition (ICPR), 2016

[IEEE]