Manik Dhar
Postdoc @ MIT
Email: dmanik at mit dot edu
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.
(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- 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]
Beyond the polynomial method: Kakeya over general N and higher dimensional generalizations
Richard Stanley Combinatorics Seminar MIT, Sep 2023
Linear Maps are good l- Hash functions
University of Michigan theoretical computer science seminar, Feb 2023
Linear Maps are good l- 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]