Boulos El Hilany

collaborators

4 papers

math.AG2024

Improved fewnomial upper bounds from Wronskians and dessins d'enfant

Boulos El Hilany, SÃ©bastien Tavenas

We use Grothendieck's dessins d'enfant to show that if $P$ and $Q$ are two real polynomials, any real function of the form $x^{I^} \pm (1 - x)^{2} P - Q$ , has at most $A^° P + A^° Q + 2$ roots in…

math.AG2024

Counting positive intersection points of a trinomial and a $T$ -nomial curves via Groethendieck's dessin d'enfant

Boulos El Hilany

We consider real polynomial systems $f = g = 0$ in two variables where $f$ has $t \geq 3$ monomial terms and $g$ has $3$ monomials terms. We prove that the number of positive isolated s…

math.AG2024

Stratification of Projection Maps From Toric Varieties

Boulos El Hilany, Martin Helmer, Elias Tsigaridas

We prove a combinatorial version of Thom's Isotopy Lemma for projection maps applied to any complex or real toric variety. Our results are constructive and give rise to a method fo…

math.OC2024

Bounds on the infimum of polynomials over a generic semi-algebraic set using asymptotic critical values

Boulos El Hilany, Elias Tsigaridas

We present precise bit and degree estimates for the optimal value of the polynomial optimization problem $f^{*} := inf_{x \in X} f (x)$ , where $X$ is a semi-al…

Improved fewnomial upper bounds from Wronskians and dessins d'enfant

Counting positive intersection points of a trinomial and a T-nomial curves via Groethendieck's dessin d'enfant

Stratification of Projection Maps From Toric Varieties

Bounds on the infimum of polynomials over a generic semi-algebraic set using asymptotic critical values

Counting positive intersection points of a trinomial and a $T$ -nomial curves via Groethendieck's dessin d'enfant