.inria.fr
1 rue Honoré d'Estienne d'Orves
Campus de l'École polytechnique
91120 Palaiseau
France
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Recent and forthcoming activities
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21 oct 2020new preprint
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25 jun 2020seminar
Calcul symbolique-numérique d’intégrales de volumes, séminaire AriC, LIP, ENS Lyon (online).
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24 feb 2020seminar
Périodes : calcul numérique et applications, kick off seminar of ANR project “De rerum natura”, Palaiseau.
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19 aug 2019conference
Finding one root of a polynomial system (How to improve the complexity?), Complexity of numerical computation, Felipe's Fest, Berlin.
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7 may 2019seminar
Périodes numériques et géométrie algébrique effective, séminaire de géométrie complexe, Institut de mathématiques de Marseille.
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6 may 2019seminar
Périodes numériques et géométrie algébrique effective, Seminar “Computations and Proofs” at Specfun, Palaiseau.
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2 may 2019new preprint
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29 jan 2019conference
Numerical periods in effective algebraic geometry (with a focus on quartic surfaces), Workshop „Calabi-Yau Motives“, Mainz.
Latest work
Average analysis of structured polynomial system solving
2020
w/ P. Bürgisser and F. Cucker
In “Rigid continuation paths II”, we develop an algorithm to compute an approximate zero of a polynomial system given as a black-box evaluation function. It follows the main lines of the algorithm from Part I but with a probabilistic estimation of the step length for the numerical continuation.
Going a step further, we show that, on average, the algorithm behaves well on a universal family of polynomial system with low evaluation cost. More precisely, we introduce the model of Gaussian random algebraic branching program and show that our algorithm performs $\operatorname{poly}(n, \delta)$ operations on average to solve a random ABP in $n$ variables, of degree $\delta$ and of size $\operatorname{poly}(n, \delta)$.
