Laetitia Colombani PhD Student in Maths

I'm postdoc since September 1st, 2022, in David Ginsbourger's team and in Riccardo Gatto's team, in the Institute of Mathematical Statistics and Actuarial Science.
I obtained my PhD in the IMT laboratory in Toulouse, in the Probability team, under the supervision of Patrick Cattiaux and Manon Costa. My defense was in July 2022.

My resume is available in English .
 

   Logo IMSV    Logo University of Bern

(Last update: 2022/09/06).


 Research

 Research topics

I’m interested in several stochastic processes, in particular in ones which can be applied in biology.

In my postdoc position, I'm studying process driven by SDE, which models efficacy changes in drug therapy (loss of efficacy with the time, and random emergence of better cure).

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

Articles
  1. Limit theorems for Hawkes processes including inhibition. Patrick Cattiaux, Laetitia Colombani et Manon Costa. Stochastic Processes and their Applications (2022)   10.1016/j.spa.2022.04.002    2109.07126
Preprints
  1. Chaos propagation in mean field networks of FitzHugh-Nagumo neurons. Laetitia Colombani et Pierre Le Bris. 2022. Submitted.    2206.13291
  2. Large deviation principle for cumulative processes and application. Patrick Cattiaux, Laetitia Colombani et Manon Costa. 2021. Submitted.    2109.07800

 Communications

Talks and Posters

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.

  • 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);
  • Aussoix Summer School, June 2022, Aussoix, 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 .

 Internal events

Study group
  • November 2021 - Summer 2022 : Participation to the Mathematics, Biology and Health Group (Toulouse) ;
  • Spring 2021 : Participation to a study group on Hawkes processes (Toulouse) ;

 Other activities

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 ;
  • Since october 2019 : Representative of PhD Students in the Doctorale School EDMITT ;
Vulgarization
  • 12 May 2022 : Talk about May 12 and Matilda effect, in the PhD student seminar of IMT;
  • January 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 ;

 Teaching

2021 · 2022 : University Paul Sabatier, in Toulouse
  • Lecture and tutorials of Introduction to Statistics for a class of L3 Biology (18h)
  • Basic facts in Probability. Estimation, confidence intervals. Statistical tests.

  • Practical work on Tools for Discrete Maths for two classes of L1 (2 x 6h)
  • Python 3. Euclidean algorithm, exponentiation by squaring, congruences.

  • 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.

2020 · 2021 : University Paul Sabatier, in Toulouse
  • Tutorials of Mathematics for two classes of L1 Biology (2 x 32h)
  • Probability, sequences, usual functions, derivation, integration, ODE

2019 · 2020 : University Paul Sabatier, in Toulouse
  • Tutorials of Mathematics for a class of L1 Biology (32h)
  • Probability, sequences, usual functions, derivation, integration, ODE

  • Practical work on Stochastic Modelisation for M1 MAPI3 (Applied Mathematics for Engineering, Industry and Innovation) (around 32h)
  • Python 3. Monte-Carlo Method, Gaussian Model, Branching process, Poisson process, etc.


 Resume

 Current situation

Postdoc, IMSV, Riccardo Gatto's and David Ginsbourger's teams
Since September 2022

Postdoc position on process driven by SDE, which models random changes in drug therapy.

 Training

PhD, IMT, Probability Team
October 2019 - August 2022

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)
  • Examinator : Christophe Poquet (University Lyon 1)
  • PhD supervisor : Patrick Cattiaux (University Toulouse 3 - Paul Sabatier)
  • PhD supervisor : Manon Costa (University Toulouse 3 - Paul Sabatier)

You can access to my manuscript and to my slides (in French).

ENS of Cachan (or Paris-Saclay)
2015 · 2019

  • 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

  • Admission with competitive exam at the ENS of Cachan: Exam 2017

  • 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 application file at the ENS of Cachan in 2015

CPGE: Preparatory class for "Grandes écoles"
2013 · 2015

Lycée Champollion, Grenoble. MP* branch, Informatic option.


 Miscellaneous information


 Contact

Institute of Mathematical Statistics and Actuarial Science, Bern

Institut für Mathematische Statistik und Versicherungslehre
Alpeneggstrasse 22
3012 Bern (Suisse)

Bureau -104 (étage -1)

laetitia.colombani@stat.unibe.ch

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