Education
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2010-2012 |
Postdocoral Fellow at Stanford University |
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2009-2010 |
ATER (Instructor) at Paris 7 University . |
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2006-2009 |
Ph.D in Applied Mathematics on wave propagation and time reversal in random waveguides under the supervision of Josselin Garnier, at the Laboratoire de Probabilités et Modèles Aléatoires (LPMA), Université Paris 7. |
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2005-2006 |
Master's degree in probability and applications, Université Paris 6. |
I got the Agregation of Mathematics. Moreover, I got a B.S and the first year of the Master program in Mathematics at the University of Cergy-Pontoise.
A cv in pdf format is available here.
Publications and research interests
My research topics concern the analysis of wave propagation and wave focusing in random media. Wave propagation in random media is a very active research field and arises in numerous applications. This analysis is very important for applications because it gives very valuable indications about the resolution limits of imaging processes in complex media, such as in medical imaging (ultrasound ecography), underwater acoustics (sonar), or in geophysics (seismic imaging).
Publications and preprints
Ph.D Thesis : Wave propagation and time reversal in random waveguides. (pdf)
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C. Gomez : Time-reversal superresolution in random waveguides, SIAM Multiscale Model. Simul., vol. 7, No. 3, pp. 1348-1386 (2009). (pdf)
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C. Gomez : Wave propagation in shallow-water acoustic random waveguides, Commun. Math. Sci., vol. 9, No. 1, pp. 81-125 (2011). (pdf)Long version (70 pages) : arxiv:0911.5646v1 [math PR](pdf)
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C. Gomez : Radiative transport limit for the random Schrödinger equation with long-range correlations, To appear in J. Math. Pures Appl.. Available on arxiv: 1110.3301 [math AP] (pdf)
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C. Gomez : Wave propagation in shallow-water acoustic waveguides with rough boundaries, Submitted to SIAM Multiscale Model. Simul.. (upon revision) Available on arxiv: 0911.5646 [math AP] (pdf)
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C. Gomez : Wave decoherence for the random Schrödinger equation with long-range correlations, Submitted to Commun. Math. Phys.. (upon revision) Available on arxiv: 1112.1663 [math AP] (pdf)
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C. Gomez : Loss of resolution for the time reversal of wave in underwater acoustic random channel, Submitted to Math. Mod. Meth. App. Sci.. Available on arxiv: 1201.5157 [math AP] (pdf)
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C. Gomez : Statistical instability in time reversal of wave in changing underwater acoustic random channels, To be submitted.
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C. Gomez and K. Solna : Front propagation in a single-mode random waveguide with long-range correlations, In progress.
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C. Gomez and G. Wainrib: Time reversal of wave in random media with long-range correlations, In progress.
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C. Gomez and O. Pinaud: Fractional Ito-Schrödinger approximation for wave propagation in long range random media, In progress.
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C. Gomez and O. Pinaud: Splitting scheme for the random Schrödinger with long-range correlations, In progress.
Talks
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02/12 |
Probability seminar, Marseille, France. |
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02/12 |
Probability seminar, Nice, France. |
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01/12 |
Probability seminar, Georgia tech Atlanta, USA. |
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01/12 |
Probability seminar, Toulouse, France. |
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11/11 |
Applied math seminar, UC Irvine, USA. |
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11/11 |
Applied math seminar, Stanford University, USA. |
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05/10 |
Colloquium jeunes probabilistes et statisticiens, Mont Dore, France. |
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04/10 |
Probability Seminar, Nancy, France. |
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01/10 |
Seminar on mathematical methods for imaging at IHP, France. |
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06/09 |
Meeting between the Ph.D students of the LPMA and Laboratoire Jacques-Louis Lions (LJLL). |
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05/09 |
Workshop non-conventinal imaging and focusing techniques : from acoustic to optics, Cargèse, France. |
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12/08 |
Ph.D students workshop at LPMA. |
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06/08 |
Probability summer school, Saint-Flour, France. |
Teaching
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2009-2010 |
Tutorials, linear algebra and calculus, B.S second year. Tutorials, probability, B.S first year. |
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2007-2009 |
Tutorials, linear algebra and calculus, B.S second year. |
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2006-2007 |
Tutorials, probability, B.S second year |