## Les événements de septembre 2017

• ### Jeudi 28 septembre 2017 15:00-17:30 - Mathieu Colin (Univ. de Bordeaux) ; Alberto Farina (Univ. d’Amiens)

Séminaires Equations aux Dérivées Partielles

Résumé : Mathieu Colin : "Ondes solitaires et systèmes de Schrödinger"
Alberto Farina : "Un résultat de type Bernstein pour l’équation des surfaces minimales"

Lieu : 316B

• ### Lundi 11 septembre 2017 11:00-12:00 - Landy Rabehasaina - LMB

Séminaire PS : ASYMPTOTICS FOR MULTIDIMENSIONAL AND FRACTIONAL POISSON IBNR PROCESSES

Résumé : Several papers have investigated closed form formulas for distribution (Laplace Transform or cdf) or moments of Incurred But Non Reported claim processes, See Willmott & Drekic (2002/2009), Landriault et al (2014/2016). We are interested in this talk in such a process generalized by including a discounting factor, and considering $k>1$ branches, i.e. correlated IBNR processes. As closed form expressions are not in general available (see Woo (2016)), we will give in this talk asymptotics for joint moments as well as the limiting distribution of the $k$ dimensional processes properly rescaled, in the case where interclaims are light tailed. Finally, in the particular $k=1$ case where claims arrive according to a Poisson fractional process, we will provide asymptotics for the moments and variance of the (non discounted) IBNR process. This is joint work with E.C.K.Cheung, J.K.Woo and R.Xu (Hong Kong Univ.)

Lieu : Salle 316 - LMB

• ### Mardi 26 septembre 2017 13:45-14:45 - Colin Petitjean - UFC

The linear structure of some dual Lipschitz free spaces

Résumé : Consider a metric space $M$ with a distinguished point $0_M$. Let $Lip_0(M)$ be the Banach space of Lipschitz functions from $M$ to $\mathbb R$ satisfying $f(0_M) = 0$ (the canonical norm being the best Lipschitz constant). The Lipschitz-free space $\mathcal F(M)$ over $M$ is defined as the closed linear span in $Lip_0(M)^*$ of $\delta(M)$ where $\delta (x)$ denotes the Dirac measure defined by $\langle \delta (x) , f \rangle = f(x)$. The Lipschitz free space $\mathcal F(M)$ is a Banach space such that every Lipschitz function on $M$ admits a canonical linear extension defined on $\mathcal F(M)$. It follows easily from this fundamental linearisation property that the dual of $\mathcal F (M)$ is in fact $Lip_0(M)$. A considerable effort to study the linear structure and geometry of these spaces has been undergone by many researchers in the last two or three decades.
In this talk, we first focus on some classes of metric spaces $M$ for which $\mathcal F(M)$ is isometrically isomorphic to a dual Banach space. After a quick overview of the already known results in this line, we define and study the notion of "natural predual". A natural predual is a Banach space $X$ such that $X^* = \mathcal F(M)$ isometrically and $\delta(M)$ is $\sigma(\mathcal F(M),X)$-closed. As we shall see, $\delta(M)$ is always $\sigma(\mathcal F(M),Lip_0(M))$-closed but it may happened that it is not $\sigma(\mathcal F(M),X)$-closed for some predual $X$. We characterise the existence of a natural predual in some particular classes of metric spaces. Notably, we concentrate on the class of uniformly discrete and bounded (shortened u.d.b.) metric spaces, for which it is well known that $\mathcal F(M)$ is isomorphic to $\ell_1$. In particular, we exhibit an example of a u.d.b. metric space $M$ for which $\mathcal F(M)$ is a dual isometrically but which does not have any natural predual. We also provide a u.d.b. metric space $M$ such that $\mathcal F(M)$ is not a dual isometrically. We finish with the study of the extremal structure of Lipschitz free spaces admitting a natural predual.
This is part of a joint work with L. García-Lirola, A. Procházka and A. Rueda Zoca.

Lieu : 316Bbis

• ### Jeudi 28 septembre 2017 16:30-18:00 -

Commission Informatique (CI)

Lieu : Salle 316Bbis

• ### Vendredi 29 septembre 2017 10:00-12:00 -

Soutenance de thèse de Tianxiang GOU

Lieu : Salle 316B (LMB, UFR ST)

• ### Mardi 26 septembre 2017 14:15-16:00 -

Soutenance d’habilitation d’Antoine PERASSO

Lieu : Salles de Actes (UFR ST, Besançon)