20 citations · 164 across the 63 of their papers we have counts for
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Limitations of the slice rank method in additive combinatorics
Sankeerth Rao Karingula, Shachar Lovett
The slice rank method gives exponential bounds for sets with no three-term arithmetic progression in finite vector spaces of odd characteristic and for three-sunflower-free familie…
An elementary proof of the Komlós conjecture
Sankeerth Rao Karingula, Shachar Lovett
We give an elementary proof of the Komlós conjecture by simplifying the recent proof of Guo, Fang, and Lu. We show that any vectors with $\|v_i\|_2\…
Quasipolynomial bounds for the corners theorem
Michael Jaber, Yang P. Liu, Shachar Lovett +2
Let be a finite abelian group and be a subset of which is corner--free, meaning that there are no and such that …
Corners in Quasirandom Groups via Sparse Mixing
Michael Jaber, Shachar Lovett, Anthony Ostuni
We improve the best known upper bounds on the density of corner-free sets over quasirandom groups from inverse poly-logarithmic to quasi-polynomial. We make similarly substantial i…
Strong Bounds for Skew-Corner-Free Sets
Michael Jaber, Shachar Lovett, Anthony Ostuni
Motivated by applications to matrix multiplication algorithms, Pratt asked (ITCS'24) how large a subset of could be without containing a skew-corner: three points…
Approximate union closed conjecture
Zachary Chase, Shachar Lovett
A set system is called union closed if for any two sets in the set system their union is also in the set system. Gilmer recently proved that in any union closed set system some ele…