Laetitia Colombani · PhD in maths
I have been a postdoc since September 1st, 2023, in collaboration with Sylvie Méléard, in the team PEIPS in Centre de Mathématiques Appliquées (CMAP) of Ecole Polytechnique. My funding comes from the ERC SINGER obtained by Sylvie Méléard.
I was previously a postdoc from September 2022 to August 2023 in David Ginsbourger's team and Riccardo Gatto's team at the Institute of Mathematical Statistics and Actuarial Science. I also collaborated with the Department of BioMedical Research of Bern.
I obtained my PhD in the IMT laboratory in Toulouse, in the team Probability, under the supervision of Patrick Cattiaux and Manon Costa. My defense was in July 2022.
My resume is available in English .
(Last update: 2024/02/05).
Research
Research topics
I’m interested in several stochastic processes, in particular in ones which can be applied in biology.
In my current postdoc position, I study the dynamics of lineages, when the environment varies over time.
During my first postdoc position, I studied processes driven by SDEs, which model efficacy changes in drug therapy (loss of efficacy with time, and random emergence of better cure). I also developed a model of cell growth and studied its optimal design (i.e. the "best choice" for measuring moments to optimise the estimation of the parameters). It was a collaborative project with the Department of BioMedical Research of Bern (DBMR).
During my thesis, I worked on Hawkes process, which are jump processes. They model various phenomenas, such as occurrence of earthquakes – which is their traditional application, but isn’t used anymore - , spread of neuronal information, publications on social networks, etc. I studied their asymptotic behaviors when they are non-linear and inhibited.
To that end, I worked on more general processes, named cumulative processes, in order to obtain large deviations inequalities.
I've also studied processes following FitzHugh-Nagumo equations. They are continuous path processes. These equations model neuronal activity, in a simple way. In particular, I study propagation of chaos properties in a mean-field framework.
I also had the opportunity to make my internship of Master 1 in one of the pharmaceutical laboratory Servier, and to study compartment pharmacokinetic models.
Publications
- Asymptotic deviation bounds for cumulative processes. Patrick Cattiaux, Laetitia Colombani and Manon Costa. Stochastic Processes and their Applications (2023) 10.1016/j.spa.2023.05.010 - (Version publiée en PDF ici)
2109.07800
-
Propagation of chaos in mean field networks of FitzHugh-Nagumo neurons. Laetitia Colombani and Pierre Le Bris. Mathematical Neuroscience and Applications (2023) 10.46298/mna.9748 - (Version publiée en PDF ici)
2206.13291
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Limit theorems for Hawkes processes including inhibition. Patrick Cattiaux, Laetitia Colombani and Manon Costa. Stochastic Processes and their Applications (2022) 10.1016/j.spa.2022.04.002 - (Version publiée en PDF ici)
2109.07126
-
Computation of the Distribution of the Absorption Time of the Drifted Diffusion with Stochastic Resetting and Mixed Boundary Conditions. Riccardo Turin, Juan Magalang, Javier Aguilar, Laetitia Colombani, Daniel Sanchez-Taltavull and Riccardo Gatto. 2023. Submitted.
2311.03939
Communications
Some talks were not on-site, but were online in visioconference. When it was the case, it is indicated. The default is on-site talks.
- Seminary of Probability, January 2024, IRMAR at Rennes ;
- Poster in "Journées Math Bio Santé" (Math Bio Health Days), November 2023, University Gustave Eiffel, organised by the research group MathSAV and the thematic group Mabiome ;
- Seminario de Probabilidades de Chile, November 2023, Chile (videoconference) ;
- Seminary of Probability's group, November 2023, CMAP at Polytechnique ;
- Seminary of Probability and Statistics, October 2023, LmB at Besançon ;
- Potsdam Research Seminar in Probability Theory, April 2023, Potsdam (Allemagne);
- Seminary of Probability and Statistics, November 2022, Laboratory J. A. Dieudonné at Nice;
- Workshop of the projet ANR EFI, November 2022, Lyon;
- Seminary of Probability and Statistics, November 2022, IECL at Nancy;
- MAS Days, August 2022, Rouen, organised by the MAS group (Stochastic modelisation and Statistic) of the SMAI (Société de Mathématiques Appliquées et Industrielles) - session Limit Theorems;
- Potsdam Research Seminar in Probability Theory, June 2022, Potsdam (Germany), organised by the Probability Theory Chaire (videoconference);
- Aussois Summer School, June 2022, Aussois, organised by the MMB (Mathematical Modelisation and Biodiversity) chaire;
- Workshop New trends on Hawkes Processes, June 2022, Toulouse, organised by Anthony Réveillac, Mahmoud Khabou and I ;
- Workshop Metastability, mean-field particle systems and non linear processes, May 2022, St-Etienne, organised by ANR projects METANOLIN and QuAMProcs ;
- Workshop, Mai 2022, Bern (Switzerland), organised by statistical teams of Bern and Toulouse ;
- Mathematics, Biology and Health Group, January 2022, Mathematical Institute of Toulouse ;
- PhD day of team Probabilities, January 2022, Mathematical Institute of Toulouse ;
- Forum des jeunes mathématicien.ne.s (Young mathematicians fair), December 2021, Besançon, organised by the association Femmes et Mathématiques (Women and Mathematics association) ;
- Stochastic processes and statistical machine learning, III, November 2021, Potsdam (Germany), organised by the Collège Doctoral Franco-Allemand (French-German Doctoral College) - Slides available on the website of the event ;
- Colloque Jeunes Probabilistes et Statisticiens (Young Probabilists and Statisticians colloquium) , October 2021, Ile d'Oléron (France), organised by the group MAS of the SMAI - Slides available in an archive on their website ;
- Seminary of SAMM: Statistics, Analysis and Multidisciplinary Modelisation, October 2021, University Paris 1 Panthéon-Sorbonne ;
- Journées de travail sur les processus de Hawkes (Workshop on Hawkes processes), July 2021, IHP (Paris), organised by Arnaud Le Ny from LAMA ;
- Journées de Probabilité (Probability Days), June 2021, Lorient, organised by University of Rennes - Slides available on their website ;
- PhD day of team Probabilities, February 2021, Mathematical Institute of Toulouse ;
- Seminary of PhD students , January 2021, Laboratory of Mathematics Jean Leray in Nantes (videoconference) ;
- Seminary of young mathematicians , June 2020, Mathematical Institute of Orsay (videoconference) ;
- PhD and Post-doc day of team ESP, November 2019, Mathematical Institute of Toulouse ;
You can see the introduction on Hawkes processes and an insight of my work in the slides of my talk at the Seminary of PhD Students in Nantes.
I outlined cumulative process (also named renewal-reward process, or renewal compound process) in the short talk of Young Probabilists and Statiscians colloquium in October 2021. You'll find the slides here .
Scientifical and administrative responsibilities
- June 2022 : Co-organisator of the workshop New trends on Hawkes Processes ;
- November 2021 : Organisator of the annual information day for PhD students in IMT ;
- October 2020 : Co-organisator of the annual information day for PhD students in IMT ;
- October 2019 - July 2022 : Representative of PhD Students in the Doctorale School EDMITT ;
- Stochastic Processes and their Applications
- January 2024 : Participation to the Budding maths day of popularization on mathematics research for L3 mathematics students, organised by the Fondation Mathématique Jacques Hadamard ;
- April and May 2023 : Online speed-meetings for teenage girls (middle and high school), organized by the association Femmes et Mathématiques (Women and Mathematics) ;
- 12 May 2022 : Talk about May 12 and Matilda effect, in the PhD student seminar of IMT;
- March 2022 : Scientifical "Speed dating" in the Quai des savoirs to introduce mathematical research ;
- 2019-2022 : Mentoring of teenagers (around 15 years old) during their job shadowing for some days ;
- 2023 - now : Member of the chaire Mathématiques et Modélisation en Biologie (Véolia, Ecole Polytechnique, Muséum d'Histoire Naturelle) ;
- November 2021 - Summer 2022 : Participation to the Mathematics, Biology and Health Group (Toulouse) ;
- Spring 2021 : Participation to a study group on Hawkes processes (Toulouse) ;
Teaching
- In charge with Mao Fabrice Djete of the course Mathematical Modeling for 1st year of Bachelor (L1) (around 20h)
Taught in English. Probability. ODE. Applications in biology, biochemistry, economy.
- Lecture and tutorials of Introduction to Statistics for a class of L3 Biology (18h)
- Practical work on Tools for Discrete Maths for two classes of L1 (2 x 6h)
- Lectures and tutorials of Introduction to Statistics for a class of L3 Biology (18h + 2h TP)
Basic facts in Probability. Estimation, confidence intervals. Statistical tests.
Python 3. Euclidean algorithm, exponentiation by squaring, congruences.
Basic facts in Probability. Estimation, confidence intervals. Statistical tests.
- Tutorials of Mathematics for two classes of L1 Biology (2 x 32h)
Probability, sequences, usual functions, derivation, integration, ODE
- Tutorials of Mathematics for a class of L1 Biology (32h)
- Practical work on Stochastic Modelisation for M1 MAPI3 (Applied Mathematics for Engineering, Industry and Innovation) (around 32h)
Probability, sequences, usual functions, derivation, integration, ODE
Python 3. Monte-Carlo Method, Gaussian Model, Branching process, Poisson process, etc.
Resume
Current situation
Study of the dynamics of lineage when the environment varies over time.
Funds from the ERC grant SINGER obtained by Sylvie Méléard.
Previous positions
Postdoc position on modeling the efficacy of drug treatments. On the one hand, study of stochastic properties of a process driven by a SDE, with random breaks corresponding to random changes in treatment. On the other hand, developing with colleagues from the Department of Biomedical Research of Bern a model of cell growth and studying its statistical properties and its optimal design.
Funds from the UniBE ID Grant (Interdisciplinary grant from the University of Bern) provided to the project of Riccardo Gatto.
Current situation
Postdoc position on process driven by SDE, which models random changes in drug therapy.
Training
Under the supervision of Patrick Cattiaux and of Manon Costa.
Title : On asymptotic behavior of stochastic processes in neuroscience
Defense : July 4th, 2022
Jury :
- President : Gersende Fort (CNRS - Toulouse - IMT )
- Reviewer : Eva Löcherbach (University Paris 1)
- Reviewer : François Bolley (ENS of Rennes)
- Examiner : Christophe Poquet (University Lyon 1)
- PhD supervisor : Patrick Cattiaux (University Toulouse 3 - Paul Sabatier)
- PhD supervisor : Manon Costa (University Toulouse 3 - Paul Sabatier)
- M2 Mathematics of randomness, University Paris-Sud. 2018-2019
Internship : Study of Hawkes processes (IMT, Toulouse ; supervised by Manon Costa and Patrick Cattiaux)
- M2FESUP, Preparation of the "agrégation" (French competitive exam for high school and university teacher), ENS of Cachan. Probability option. Admitted at the 45th rank. 2017-2018
- M1 Mathematics, Track Jacques Hadamard, ENS of Cachan and University Paris-Sud. 2016-2017
Internship : Study by simulations of bayesian estimatio in non-linear mixed models in PK/PD (IRIS, Suresnes ; supervised by Adrien Tessier)
- L3 Mathematics, ENS of Cachan and University Paris Diderot. 2015-2016
Internship : A semi-supervised learning approach to annotate medical data (CMLA, Cachan; supervised by Nicolas Vayatis and Charles Truong)
Admission with competitive exam at the ENS of Cachan: Exam 2017
Admission with application file at the ENS of Cachan in 2015
Lycée Champollion, Grenoble. MP* branch, Informatic option.
Miscellaneous information
- I have First Aid Certification (in France, PSC1) since 2021.
- I have my driving licence.
- I've a very famous namesake (she's also French and has a French wikipedia page), don't confuse us!
Contact
Centre de Mathématiques Appliquées, Ecole Polytechnique, Paris
CMAP
Ecole Polytechnique
Route de Saclay
91128 Palaiseau Cedex
Bureau 00 20 34 (1er étage, aile 0)
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