I am an Instructor (postdoc) of Applied Mathematics at Massachusetts Institute of Technology. I am broadly interested in Combinatorics and Computational Complexity. You can read about some of my work on the Kakeya conjecture in this nice Quanta article.

**Rigidity matroids and linear algebraic matroids with applications to matrix completion and tensor codes **
*with* Joshua Brakensiek, Jiyang Gao, Sivakanth Gopi, and Matt Larson

manuscript

[arXiv]

**(n,k) -Besicovitch sets do not exist in Z_p^n and Ẑ^n for k≥2 **

manuscript

[arXiv]

**AG codes achieve list decoding capacity over contant-sized fields **
*with* Joshua Brakensiek, Sivakanth Gopi, and Zihan Zhang

manuscript

[arXiv]

**Generalized GM-MDS: Polynomial Codes are Higher Order MDS **
*with* Joshua Brakensiek and Sivakanth Gopi

manuscript

[arXiv]

**A construction of Maximally Recoverable LRCs for small number of local groups **
*with* Sivakanth Gopi

ISIT 2023

[arXiv]

**Improved Field Size Bounds for Higher Order MDS Codes **
*with* Joshua Brakensiek and Sivakanth Gopi

ISIT 2023

[arXiv]

**Maximal and (m,ε)-Kakeya bounds over Z/NZ for general N **

manuscript

[arXiv]

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

Foundations of Computer Science (FOCS) 2022

[arXiv][ECCC]

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

to appear in Advances in Combinatorics

[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

to appear in Discrete and Computational Geometry (DCG)

[arXiv]

**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]

**Furstenberg problem for higher dimensional flats over F_q, R, Z_p**

Online Analysis Research Seminar, Apr 2024

**Beyond the polynomial method: Kakeya over general N and higher dimensional generalizations**

Richard Stanley Combinatorics Seminar MIT, Sep 2023

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

University of Michigan theoretical computer science seminar, Feb 2023

**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]