For every constant d, we design a subexponential time deterministic
algo...
We show that for every homogeneous polynomial of degree d, if it has
det...
We design nearly-linear time numerical algorithms for the problem of
mul...
Multivariate multipoint evaluation is the problem of evaluating a
multiv...
Multipoint evaluation is the computational task of evaluating a polynomi...
In this work, we present an abstract framework for some algebraic
error-...
Assuming that the Permanent polynomial requires algebraic circuits of
ex...
Robust sunflowers are a generalization of combinatorial sunflowers that ...
The multiplicity Schwartz-Zippel lemma bounds the total multiplicity of
...
The determinantal complexity of a polynomial P ∈𝔽[x_1, …,
x_n] over a fi...
For every constant c > 0, we show that there is a family {P_N, c} of
pol...
We show that there is a defining equation of degree at most
𝗉𝗈𝗅𝗒(n) for ...
Schur Polynomials are families of symmetric polynomials that have been
c...
We show that any Algebraic Branching Program (ABP) computing the polynom...
We show that any Algebraic Branching Program (ABP) computing the polynom...
A hitting-set generator (HSG) is a polynomial map G:F^k →F^n such that f...
A hitting-set generator (HSG) is a polynomial map Gen:F^k →F^n such that...
We study the problem of constructing explicit families of matrices which...
In this note, we give a short, simple and almost completely self contain...
We show that any n-variate polynomial computable by a syntactically
mult...
The classical lemma of Ore-DeMillo-Lipton-Schwartz-Zippel
[Ore22,DL78,Zi...
The classical lemma of Ore-DeMillo-Lipton-Schwartz-Zippel states that an...
In recent years, there has been a flurry of activity towards proving low...
In this paper, we prove new relations between the bias of multilinear fo...
We show that over the field of complex numbers, every homogeneous
polyno...
In a sequence of seminal results in the 80's, Kaltofen showed that the
c...
We prove a lower bound of Ω(n^2/^2 n) on the size of any
syntactically m...