Emanuele Ventura

On the real rank of monomials

In this paper we study the real rank of monomials and we give an upper bound for it. We show that the real and the complex ranks of a monomial coincide if and only if the least exponent is equal to one.

Finite phylogenetic complexity and combinatorics of tables

We prove that the phylogenetic complexity -- an invariant introduced by Sturmfels and Sullivant -- of any finite abelian group is finite.

The Poset of Proper Divisibility

We study the partially ordered set

Real rank boundaries and loci of forms

P(a_1,\ldots, a_n)

Real rank geometry of ternary forms

of all multidegrees

A note on the Waring ranks of reducible cubic forms

(b_1,\dots,b_n)

Real and complex Waring rank of reducible cubic forms

of monomials

Complex and real ranks of reducible cubics

x_1^{b_1}\cdots x_n^{b_n}

Partially symmetric variants of Comon's problem via simultaneous rank.

which properly divide

Phylogenetic complexity of the Kimura 3-parameter model

x_1^{a_1}\cdots x_n^{a_n}