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07/20/2023
Ellipsoid fitting up to constant via empirical covariance estimation
The ellipsoid fitting conjecture of Saunderson, Chandrasekaran, Parrilo ...
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09/06/2022
Concentration of polynomial random matrices via Efron-Stein inequalities
Analyzing concentration of large random matrices is a common task in a w...
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12/02/2021
Explicit Abelian Lifts and Quantum LDPC Codes
For an abelian group H acting on the set [ℓ], an (H,ℓ)-lift of a graph G...
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11/17/2021
Sum-of-Squares Lower Bounds for Sparse Independent Set
The Sum-of-Squares (SoS) hierarchy of semidefinite programs is a powerfu...
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11/11/2020
Unique Decoding of Explicit ε-balanced Codes Near the Gilbert-Varshamov Bound
The Gilbert-Varshamov bound (non-constructively) establishes the existen...
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11/11/2020
List Decoding of Direct Sum Codes
We consider families of codes obtained by "lifting" a base code 𝒞 throug...
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09/11/2020
Explicit SoS lower bounds from high-dimensional expanders
We construct an explicit family of 3XOR instances which is hard for O(√(...
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07/18/2019
Approximating Constraint Satisfaction Problems on High-Dimensional Expanders
We consider the problem of approximately solving constraint satisfaction...
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04/10/2018
Approximating Operator Norms via Generalized Krivine Rounding
We consider the (ℓ_p,ℓ_r)-Grothendieck problem, which seeks to maximize ...
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02/21/2018