Malte Beecken, Johannes Mittmann, Nitin Saxena

Algebraic independence is an advanced notion in commutative algebra that generalizes independence of linear polynomials to higher degree. Polynomials $\{f_1,\ldots, f_m\} \subset \mathbb{F}[x_1,\ldots, x_n]$ are called algebraically independent if there is no non-zero polynomial $F$ such that $F(f_1, \ldots, f_m) = 0$. The transcendence degree, $\mbox{trdeg}\{f_1,\ldots, f_m\}$, is the maximal ... more >>>

Johannes Mittmann, Nitin Saxena, Peter Scheiblechner

A set of multivariate polynomials, over a field of zero or large characteristic, can be tested for algebraic independence by the well-known Jacobian criterion. For fields of other characteristic $p>0$, there is no analogous characterization known. In this paper we give the first such criterion. Essentially, it boils down to ... more >>>

Mrinal Kumar, Shubhangi Saraf

In recent years there has been a flurry of activity proving lower bounds for

homogeneous depth-4 arithmetic circuits [GKKS13, FLMS14, KLSS14, KS14c], which has brought us very close to statements that are known to imply VP $\neq$ VNP. It is a big question to go beyond homogeneity, and in ...
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