We develop algorithms for writing a polynomial as sums of powers of low degree
polynomials in the non-degenerate case. This problem generalizes symmetric tensor …

We give an n^O(\logn)-time (n is the input size) blackbox polynomial identity testing
algorithm for unknown-order read-once oblivious arithmetic branching programs (ROABPs) …

A read-once oblivious arithmetic branching program (ROABP) is an arithmetic branching
program (ABP) where each variable occurs in at most one layer. We give the first polynomial …

We show that any nonzero polynomial in the ideal generated by the r× r minors of an n× n
matrix X can be used to efficiently approximate the determinant. Specifically, for any nonzero …

In this paper we study polynomials in VP_ {e}(polynomial-sized formulas) and in ΣΠΣ
(polynomial-size depth-3 circuits) whose orbits, under the action of the affine group GL^{aff} …

Kayal has recently introduced the method of shifted partial derivatives as a way to give the
first exponential lower bound for computing an explicit polynomial as a sum of powers of …

The orbit of an n-variate polynomial over a field is the set. The orbit of a polynomial f is a
geometrically interesting subset of the set of affine projections of f. Affine projections of …

We give improved hitting sets for two special cases of Read-once Oblivious Arithmetic
Branching Programs (ROABP). First is the case of an ROABP with known order of the …

Read-k oblivious algebraic branching programs are a natural generalization of the well-
studied model of read-once oblivious algebraic branching program (ABP). In this work, we …

In recent years, there has been a flurry of activity towards proving lower bounds for
homogeneous depth-4 arithmetic circuits, which has brought us very close to statements that …