Symbolic matrices in non-commuting variables, andthe related structural and algorithmic
questions, have a remarkablenumber of diverse origins and motivations. They …

We propose a new second-order method for geodesically convex optimization on the natural
hyperbolic metric over positive definite matrices. We apply it to solve the operator scaling …

In this paper, we present a deterministic polynomial time algorithm for testing whether a
symbolic matrix in non-commuting variables over QQ is invertible or not. The analogous …

We give deterministic black-box polynomial identity testing algorithms for multilinear read-
once oblivious algebraic branching programs (ROABPs), in n O (log2 n) time. Further, our …

Mulmuley [Mul12a] recently gave an explicit version of Noether's Normalization Lemma for
ring of invariants of matrices under simultaneous conjugation, under the conjecture that …

We present a single common tool to strictly subsume all known cases of polynomial time
blackbox polynomial identity testing (PIT), that have been hitherto solved using diverse tools …

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) …

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 show that, over \mathbbQ, if an n-variate polynomial of degree d=n^O(1) is computable
by an arithmetic circuit of size s (respectively, by an arithmetic branching program of size s) …

In this paper we study the problems of polynomial identity testing (PIT) and reconstruction of
read-once formulas. The following are some deterministic algorithms that we obtain. An nO …