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.
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- 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- 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]