Education
2012-... |
Assistant Professor at Aix-Marseille University |
2010-2012 |
Postdocoral Fellow at Stanford University |
2009-2010 |
ATER (Instructor) at Paris 7 University . |
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. |
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). More recently, I have joined the group Mathematics and
cancer of the I2M. My research with this group concerns stochastic
models for microtubule dynamic instability under the influence of
anti-microtubule agents. The main goal of this work is to reproduce
and predict experimental results. Microtubules are a component of
the cytoskeleton playing a important role in many cellular processes
such as mitosis, intracellular transport... This is the reason why
these are very interesting target for cancer therapies.
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) (journal).
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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)(journal).
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C. Gomez : Radiative transport limit for the random Schrödinger equation with long-range correlations, J. Math. Pures Appl., vol. 98, No. 3, pp. 295-327 (2012) (pdf)(journal).
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C. Gomez : Wave decoherence for the random Schrödinger equation with long-range correlations, Commun. Math. Phys., Vol. 320, Issue 1, pp 37-71 (2013). (pdf)(journal).
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C. Gomez : Loss of resolution for the time reversal of wave in underwater acoustic random channels, Math. Mod. Meth. App. Sci., vol. 23, No. 11, pp. 2065-2110 (2013) (pdf)(journal).
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C. Gomez and O. Pinaud : Asymptotics of a time-splitting scheme for the random Schrödinger equation with long-range correlations, Math. Model. Numer. Anal., 48, pp.411-- 431 (2014) (pdf)(journal).
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C. Gomez : Wave Propagation in Underwater Acoustic Waveguides with Rough Boundaries. Commun. Math. Sci., 13 pp 2005-2052 (2015) (pdf)(journal).
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C. Gomez, O. Pinaud, and L. Ryzhik : Hypoelliptic estimates in radiative transfer, Commun. Part. Diff. Eq, 41, pp. 150-184 (2015) (pdf)(journal).
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C. Gomez, O. Pinaud, and L. Ryzhik : Radiative transfer with long-range interactions: regularity and asymptotics. SIAM Multiscale Model. Simul., 15, pp. 1048–1072 (2017). (pdf)(journal).
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C. Gomez and O. Pinaud : Fractional White-Noise Limit and Paraxial Approximation for Waves in Random Media , Arch. Rat. Mech. Anal., 226, pp. 1061-1138 (2017) (pdf) (journal).
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C. Gomez and N. Hartung : Stochastic and deterministic models for the metastatic emission process: formalisms and crosslinks. Cancer Systems Biology : Methods and Protocols Springer 2018 (pdf).(book).
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C. Gomez and K. Solna : Wave propagation in random waveguide with long-range correlations. To appear in Commun. Math. Sci. (pdf).
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C. Gomez and O. Pinaud : Monte Carlo methods for radiative transfer with singular kernels. To appear in SIAM J. Sci. Comput. (pdf)
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C. Gomez and M. Hauray : Rigorous derivation of Lindblad equations from quantum jumps processes in 1D, Preprint (pdf).
Talks
09/17 |
Workshop Wave Propagation and Imaging in Random Media, ICERM Brown University, USA |
07/17 |
Conference Equadiff 2017, Bratislava, Slovakia |
05/17 |
Workshop Computational Inverse Problems for Partial Differential Equations, Oberwolfach, Germany |
06/17 |
SMAI Ronce les bains, France. |
06/15 |
SMAI Les Karellis, France. |
05/14 |
Workshop between the groups of applied analysis from Nice-Toulon-Marseille, Porquerolles, France |
04/14 |
CANUM, Carry-le-Rouet, France |
12/13 |
Conference SIAM PDEs, Orlando, USA |
07/13 |
Conference Applied Inverse Problem, Daejeon, South Korea |
05/13 |
Workshop Probability and PDEs, Pisa, Italy |
03/13 |
Workshop Interplay of Theory and Numerics for Deterministic and Stochastic Homogenization, Oberwolfach, Germany |
08/12 |
13th week of the condensed matter, Montpellier, France. |
02/12 |
Probability seminar, Marseille, France. |
02/12 |
Probability seminar, Nice, France. |
01/12 |
Probability seminar, Georgia tech Atlanta, USA. |
01/12 |
Probability seminar, Toulouse, France. |
11/11 |
Applied math seminar, UC Irvine, USA. |
11/11 |
Applied math seminar, Stanford University, USA. |
05/10 |
Colloquium jeunes probabilistes et statisticiens, Mont Dore, France. |
04/10 |
Probability Seminar, Nancy, France. |
01/10 |
Seminar on mathematical methods for imaging at IHP, France. |
06/09 |
Meeting between the Ph.D students of the LPMA and Laboratoire Jacques-Louis Lions (LJLL). |
05/09 |
Workshop non-conventinal imaging and focusing techniques : from acoustic to optics, Cargèse, France. |
12/08 |
Ph.D students workshop at LPMA. |
06/08 |
Probability summer school, Saint-Flour, France. |