Sharp threshold result showing Θ(n²) random points in F_p^n pierce all algebraic sets defined by ≤s polynomials of degree ≤k, with application to random Szemerédi theorem.
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Establishes codimension and irreducibility properties of multilinear varieties over infinite fields and uses them to prove stability of partition rank and related tensor ranks for perfect infinite fields.
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Randomly piercing algebraic sets
Sharp threshold result showing Θ(n²) random points in F_p^n pierce all algebraic sets defined by ≤s polynomials of degree ≤k, with application to random Szemerédi theorem.
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Geometry of multilinear varieties over infinite fields and its applications
Establishes codimension and irreducibility properties of multilinear varieties over infinite fields and uses them to prove stability of partition rank and related tensor ranks for perfect infinite fields.