Boulos El Hilany

collaborators

4 papers

math.AG2024

Improved fewnomial upper bounds from Wronskians and dessins d'enfant

Boulos El Hilany, Sébastien 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 $x^{α} (1 - x)^{β} P - Q$ , has at most $° P + ° Q + 2$ roots in the…

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…

math.AG2024

The polyhedral type of a polynomial map on the plane

Boulos El Hilany, Kemal Rose

Two continuous maps $f, g : C^{2} \to C^{2}$ are said to be topologically equivalent if there exist homeomorphisms $φ, ψ : C^{2} \to C^{2}$ satisfying $ψ\circ…