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Boulos El Hilany

About me

I am a post-doc mentored by Gaetan Borot in the Max-Planck-Institut für Mathematik, Bonn.

My previous post-doc position was with Johannes Rau in the Geometry work group at the Eberhard Karls Universität Tübingen.
My Ph.D. thesis was supervised by Frédéric Bihan, and defended on 21 September 2016 at Université Savoie Mont Blanc.

Here you can find my CV.

Research interests

  • Tropical Geometry

  • Fewnomial Theory

  • Real Algebraic Geometry

  • Real Hurwitz Numbers

Talks

  • Signed counts of real simple rational functions (joint work with J. Rau).
    Algorithmic algebra group weekly seminar,
    Technische Universität Berlin.

  • Constructing polynomial systems with many positive solutions using tropical geometry.
    Nonarchimedean and Tropical Geometry conference,
    Universität Regensburg, Germany.

  • The equations for the moduli space of n points on the line.
    Image Processing and Computer Vision conference,
    Eberhard Karls Universität Tübingen, Germany.

  • Real Hurwitz numbers and simple rational functions (a joint work with Johannes Rau).
    Algebra group seminar,
    Eberhard Karls Universität Tübingen, Germany.

  • Topology of real K3 surfaces.
    Reading Group on Real Algebraic Geometry,
    Max Planck Institute MIS, Leipzig, Germany.

  • Nombres de Hurwitz réels et fonctions rationnelles simples (travaux commun avec Johannes Rau).
    Geometry group seminar,
    LAMA, Université Savoie Mont Blanc, France.

  • Constructing polynomial systems with many positive solutions using tropical geometry.
    Algebra group seminar,
    Eberhard Karls Universität Tübingen, Germany.

  • Constructing polynomial systems with many positive solutions using tropical geometry.
    Geometry group seminar,
    Universität des Saarlandes, Saarbrücken, Germany.

Papers

  • B. El Hilany, J. Rau.
    Signed counts of real simple rational functions. (32 pages)
    Submitted, arXiv:1712.05639.

  • B. El Hilany.
    Constructing polynomial systems with many positive solutions using tropical geometry. (17 pages)
    Accepted in Revista Matematica Complutense, arXiv:1703.02272

  • B. El Hilany.
    Characterization of circuits supporting polynomial systems with the maximal number of positive solutions. (13 pages)
    Discrete & Computational Geometry, arXiv:1603.01813

  • B. El Hilany.
    Counting positive intersection points of a trinomial and a t-nomial curves via Groethendieck's dessin d'enfant. (32 pages)
    Submitted, arXiv:1512.05688

  • F. Bihan, B. El Hilany.
    A sharp bound on the number of real intersection points of a sparse plane curve with a line. (14 pages)
    Journal of Symbolic Computations, arXiv:1506.03309

Teaching

2015 - 2016

  • Fourier Series

  • Basic Calculus

2014 - 2015

  • Inferential Statistics

  • Statistics and Probabilities

Contact

E-mail

elhilany
(at)mpim-bonn.mpg.de

Work address

Max-Planck-Institut für Mathematik,
Vivatsgasse 7, 53111 Bonn, Germany.