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Les journées d’été des mathématiciens tunisiens à l'étranger
Jul 20, 2016 to Jul 21, 2016

Location : IHET- Sidi Dhrif

Les journées d’été de mathématiques s’inscrivent dans la tradition des rencontres mathématiques d’été dont le coup d’envoi a été à Dar El Hout 1998.

Ces journées sont aujourd’hui egalement un hommage perdurant dans le temps pour notre cher et regretté Abbas Bahri.

Ces deux journées ont pour objectif de rassembler les mathématiciens tunisiens à l’étranger pendant le retour des grandes vacances d’été. Ceci est une belle occasion pour raffermir les liens entre eux et avec leurs collègues tunisiens, ainsi que pour permettre aux jeunes étudiants tunisiens d’avoir un accès direct à la recherche mathématique qui se fait en dehors de leurs laboratoires. En particulier, ce rassemblement a pour objectif premier de renforcer la collaboration entre les collègues du nord et du sud, d’encourager le coencadrement des étudiants et de diversifier les thématiques de recherche.

Les journées 2016 sont dediées à la mémoire de nos regrettés Abbas Bahri (1955-2016) et Hedi Ben Saad (1950-2016).

Programme: sept exposés par des mathématiciens Tunisiens à l’étranger.

Un cours avancé sera dispensé par Faouzi Triki ( Université Joseph Fourier, Grenoble) sur 2 jours. Ce cours sera destiné à des étudiants en thèse et aux collègues.

Organizing Commitee:
Slim Tayachi, Mohamed Majdoub

Scientific Commitee:
Slim Tayachi, Mohamed Majdoub, Ali Baklouti, Sadok Kallel

Sponsors:
MIMS-SMT

  1. Mohamed Ben Alaya (Universite Paris 13)
  2. Tej-Eddine Ghoul (NYU, Abu Dhabi)
  3. Houssem Haddar (INRIA, Palaiseau)
  4. Taoufik Hmdi (Univesite de Rennes)
  5. Elyes Jouini (Universite Paris Dauphine)
  6. Ali Maalaoui (American University RAK)
  7. Mohamed Masmoudi (Institut de Mathématiques de Toulouse et ADAGOS)
  8. Sofiane Souaifi (IRMA, Strasbourg)

 

Mohamed Ben Alaya

Multilevel Monte Carlo Method and Importance Sampling

The efficiency of Monte Carlo simulations is significantly improved when implemented with variance reduction methods. Among these methods we focus on the popular importance sampling technique based on producing a parametric transformation through a shift parameter $\theta$. The optimal choice of $\theta$ is approximated using Robbins-Monro procedures, provided that a non explosion condition
is satisfied. Otherwise, one can use either a constrained Robbins-Monro algorithm (see~[Arouna 2004] and [Lelong 2008]) or a more astute procedure based on an unconstrained approach (see~[Lemaire and Pagès 2010]). We develop a new algorithm based on a combination of either the Statistical Romberg Method (see~[Kebaier 2005]) or the Multilevel Monte Carlo Method (see~[Giles 2008]) with the importance sampling technique. These methods is known for reducing efficiently the complexity compared to the classical Monte Carlo one. We prove a central limit theorems for the new algorithms and we illustrate by numerical simulation the efficiency of our methods through applications in
option pricing.
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Houssem Haddar
Some imaging algorithms for structured/unstructured backgrounds

We present some recent advances in the analysis of so called sampling methods for solving inverse scattering problems. Our focus will be on the extension of this type of methods to the imaging problem in complex unknown backgrounds. We exploit in particular the link between the indicator function and solutions to so-called interior transmission problems to design an imaging algorithm based on differential measurements. Some applications to non destructive testing of concrete type materials or periodic media will be discussed.
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Tej-Eddine Ghoul

Stability of infinite time blow up for the Patlak Keller Segel system.
 
It is well known that for the Patlak-Keller-Segel equation there exists a threshold. Indeed, since the mass M is a conserved quantity if the mass of the initial data of the solution M < 8π then the solution exists globally. But if M > 8π then the solution blows up in finite time. And if M = 8π the problem is energy critical and mass critical. The solution exists globally but it can blow up in infinite time. In this talk we will present a complete description of the dynamic of the blow up in infinite time and prove the stability when M = 8π. The proof brings a new idea which can be used in many other critical problems. The idea is to pass to the limit from the subcritical case to the critical case.


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Taoufik Hmidi
Equilibres relatives  dans des écoulements incompressibles.

Dans cet exposé je vais présenter quelques aspects sur  la dynamique des tourbillons pour  les équations d'Euler incompressibles dans le plan et le disque.   Il s'agit d'explorer les poches de tourbillon  se déplaçant sans déformation et tout particulièrement celles animées d'un mouvement de rotation uniforme. Nous analysons l'existence de ces structures pour des   topologies différentes( simplement connexe,  doublement connexe).  Des simulations et conjectures numériques  seront aussi présentées. Le contenu  est d'après des travaux récents avec Z. Hassainia, F. de la Hoz, J. Mateu  et J. Verdera.

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Ali Maalaoui
Topological approach to the problem of Dirac-Geodesics.

In this talk we will discuss a topological method to prove the existence of non-trivial solution to a certain geometric PDE, namely the Dirac-Geodesics equation. This problem comes from the super-symmetric non-linear Sigma model in physics. The problem is firstly
stated for the case of surfaces then we reformulate it for loops. We will give the basic methodology and constructions of a homology  generated by the critical points of a given functional then we will show how this homology can be computed and extract from it some existence results.
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Mohamed Masmoudi
Mathématiques discrètes et topologies optimales

La demande du monde économique est de plus en plus forte dans le domaine des mathématiques appliquées et tout particulièrement les mathématiques discrètes. Nous présenterons quatre exemples proposés par des acteurs des nouvelles technologies et qui ont donné lieu, pour la plupart, à des brevets industriels. Nous mettrons en évidence la diversité des outils mathématiques utilisés. En effet, nous avons fait appel à différents domaines tels que l’arithmétique,  l’algèbre ou l’analyse. Si les outils d’arithmétique et d’algèbre ont permis de résoudre des problèmes ponctuels, les outils d’analyse semblent  avoir un impact beaucoup plus général.
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Sofiane Souaifi
Une introduction à la formule des traces
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Elyès Jouini
Gender, Math, Underconfidence and Stereotypes : a Decision Making Model

There is a gender gap in mathematics in self-confidence levels and in choices:
- Girls are less represented than boys in math intensive fields. In the US, only 22% of the bachelor's degrees given in the math and physical sciences go to women, and only 13% of Ph.Ds go to women. It goes on after graduation. In academia for instance, in the top US universities, only 9% to 16% of tenure track positions in maths intensive fields are occupied by women and among full professors, women are 7.1%.
- The first assertions remains valid controlling for ability. Among equally gifted students, males are many times more likely to select college majors that are considered to be high in math content and, for instance, white women enter EMS (engineering, mathematics, computer science and physical science) fields at no more than half the rate of men with the same mathematics test scores.
- Girls are less confident than boys in their abilities in mathematics
- The first assertion remains valid controlling for confidence. 
The fact that the under-representation of girls is valid even when controlling for ability eliminates explanations purely based on identity, girls being less able in mathematics and more able in other fields.
Starting from the recognition that there is a pervasive stereotype that girls are less able than boys in mathematics, a model of (optimal) beliefs formation and choices permits to establish that the presence of such a stereotype exposes boys and girls to different self-esteem risk, hence generates different self-esteem protection strategies. The underconfidence of girls as well as their less ambitious, less risk tolerant or competitive choices are their best response to their self-esteem threat; by adopting modest confidence levels and by choosing less ambitious options, they reduce the future psychological risk of disappointment and of self-esteem loss in case of failure.
This approach permits to explain all the above mentioned stylized facts about girls underconfidence and choices in math.
Besides, differences in self esteem risk also generate differences in the nature of the relation between ability and self selection in difficult tasks. The relation is more positive for boys. This means that more able boys self-select more in more difficult options, and leads to a better ability conditional on participation, i.e. a better performance of boys in these options. 
To sum up, the model shows that the presence of the stereotype leads girls to adopt lower levels of confidence and to self-select less in math difficult options, especially for the most competent, which leads to the underperformance of girls in mathematics, especially at the right tail of the distribution. These features all contribute to the survival of the stereotype about girls in mathematics. The same approach can be applied to gender issues in general, leading to lower confidence of girls in general, to lower risk tolerance and lower competitiveness. This approach can help explain the overrepresentation of boys in most selective tracks, as well as the wage gap. More generally, this approach can be applied to any negatively stereotyped group, leading to underconfidence, the avoidance of the stereotyped field, less ambitious choices, possible underperformance, and the survival of the stereotype.

Date / Heure

 

 de 9h00 9h50 10h40 11h10 12h10 13h40 14h30 15h30 16h00
à 9h40 10h30 11h10 12h00 13h40 14h20 15h20 16h00 16h50
Mercredi

20/07/2016

 Houssem Haddar ElyèsJouini PauseCafé Tej-Eddine Ghoul Déjeuner  

Mohamed Masmoudi

 

 Cours Avancé

Faouzi Triki

 

 Pause Café Cours Avancé

Faouzi Triki

 
Jeudi

21/07/2016

 Taoufik Hmidi Mohamed Ben Alaya Sofiane Souaifi Ali Maalaoui Cours Avancé

Faouzi Triki

 

 Cours Avancé

Faouzi Triki
List of participants to this conference
Jul 20, 2016 to Jul 21, 2016

No participants
Contact
secretary@mims-institut.org

Les journées d’été des mathématiciens tunisiens à l'étranger