Boulos El Hilany

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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…