Guillaume Rond

Maître de Conférences

bat. TPR2 bur. 121

Institut de Mathématiques de Marseille
Campus de Luminy, Case 907
13288 Marseille Cedex 9
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Curriculum Vitae

Research Area:

Commutative algebra, theory of singularities, algebraic geometry, local analytic geometry.


I have defended my Habilitation thesis (November 19, 2013). The text of the thesis is available here.

I defended my PhD thesis, Fonction de Artin et théorème d'Izumi, in June 2005 at the University of Toulouse. My supervisor was Mark Spivakovsky. The text of the thesis is available here.

Research papers:

Multiparameter perturbation theory of matrices and linear operators (with Adam Parusiński), 13 pp. (PDF)

Support of Laurent series algebraic over the field of formal power series (with Fuensanta Aroca), Proc. Lond. Math. Soc., to appear, 31 pp. (PDF)

Remarks on Artin approximation with constraints (with Dorin Popescu), Osaka J. Math., to appear, 9 pp. (PDF)

Local topological algebraicity with algebraic coefficients of analytic sets or functions, Algebra Number Theory, to appear, 16 pp. (PDF)

Linear nested Artin approximation Theorem for algebraic power series (with Francisco-Jesús Castro-Jiménez and Dorin Popescu), Manuscripta Math., to appear, 17 pp. (PDF)

Artin Approximation, J. Singul., 17 (2018), 108-192. (PDF)

Local zero estimates and effective division in rings of algebraic power series, J. Reine Angew. Math., 737 (2018), 111-160. (PDF)

Higher order approximation of analytic sets by topologically equivalent algebraic sets (with Marcin Bilski, Krzysztof Kurdyka and Adam Parusiński), Math. Z., 288 (2018), no. 3-4, 1361-1375. (PDF)

An irreducibility criterion for power series (with Bernd Schober), Proceedings of the A.M.S., 145 (2017), no 11, 4731-4739. (PDF)

Local topological algebraicity of analytic function germs (with Marcin Bilski and Adam Parusiński), J. Algebraic Geom., vol. 26, (2017), 177-197. (PDF)

About the algebraic closure of the field of power series in several variables in characteristic zero, J. Singul., 16, (2017), 1-51. (PDF)

The analogue of Izumi's Theorem for Abhyankar valuations (with Mark Spivakovsky), J. Lond. Math. Soc.,  vol. 90 (3), (2014),  725-740. (PDF)

Łojasiewicz inequality over the ring of power series in two variables, Math. Res. Lett., vol. 20 (2), (2013), 1-13. (PDF)

The Abhyankar-Jung Theorem, (with Adam Parusiński), Journal of Algebra, vol. 365, (2012), 29-41. (PDF)

Approximation of holomorphic solutions of a system of real analytic equations, (with Michel Hickel), Canad. Math. Bull, vol. 55 (4), (2012), 752–761. (PDF)

Bornes effectives des fonctions d'approximation des solutions formelles d'équations binomiales, Journal of Algebra, vol. 323, no. 9, (2010), 2547-2555. (PDF)

Sur la lissification de type Płoski-Popescu, C. R. Math. Acad. Sci. Paris, vol. 348, no. 13-14, (2010), 727-729. (PDF)

Asymptotic behaviour of standard basis, Proceedings of the A.M.S., vol. 138 (2010), 1979-1982. (PDF)

Homomorphisms of local algebras in positive characteristic, Journal of Algebra, vol. 322, no. 12, (2009), 4382-4407. (PDF)

Séries de Poincaré motiviques des singularités d'hypersurfaces irréductibles quasi-ordinaires, Differential equations and Singularities. 60th year of J. M. Aroca, Astérisque, vol. 323, (2009), 371-396. (PDF)

Propriétés de régularité des morphismes d'algèbres analytiques, Rev. Semin. Iberoam. Mat., vol. 3 fasc. V-VI (2008), 125-145. (PDF)

Approximation de Artin cylindrique et morphismes d'algèbres analytiques, Proceedings of the Lêfest - Singularities I: Algebraic and Analytic Aspects, Contemp. Math., vol. 474, (2008), 299-307. (PDF)

Exemples de fonctions de Artin de germes d'espaces analytiques, Adv. Stud. Pure Math., vol. 46, (2007), 197-210. (PDF)

Approximation diophantienne dans les corps de séries en plusieurs variables, Ann. Institut Fourier, vol. 56, no. 2, (2006), 299-308.  (PDF)

Lemme d'Artin-Rees, théorème d'Izumi et fonction de Artin, Journal of Algebra, vol. 299, no. 1, (2006), 245-275.  (PDF)

Sur la linéarité de la fonction de Artin, Ann. Sci. École Norm. Sup. (4), vol. 38, no. 6, (2005), 979-988.  (PDF)

À propos de la fonction de Artin en dimension N≥2, C. R. Math. Acad. Sci. Paris, vol. 340, no. 8, (2005), 577-580.  (PDF)
















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