Ce séminaire est organisé par les doctorants, stagiaires et post-doctorants du CAMS.
Vendredi 29 septembre 2017 à 11h, A4-47, EHESS, 54 boulevard Raspail, 75006 – Paris
Post-doctoral reasearcher, CAMS, ReaDi
Propagation in multi-dimensional Fisher-KPP equations
Fisher-KPP equations are a type of reaction-diffusion equations that model population dynamics. Their behavior is characterized by the invasion of an unstable state by a stable one, which leads to the phenomenon of spreading. In one dimension, it is known that localized data give rise to solutions that lag behind the slowest traveling front by a logarithmic term. In this talk, I will first discuss these past results, then focus as some recent ones about the asymptotic rates of spreading along each direction for the Cauchy problem in periodic media in R^n.
Vendredi 27 octobre 2017 à 11h, A4-47, EHESS, 54 boulevard Raspail, 75006 – Paris
Gabrielle Saller Nornberg
PhD student, Puc-Rio, Brazil
Multiplicity and Regularity results for fully nonlinear elliptic equations with quadratic growth in the gradient
The study of quasi-linear elliptic equations with quadratic dependence in the gradient started in the 80s, with the works of Boccardo, Murat and Puel and has been an object of research until now. The multiplicity of solutions phenomenon in the coercive case, for a particular example with the laplacian, was first observed by Sirakov, in 2010. Further improvements were done in the last years, specially by Jeanjean et al. in order to give a more clear picture of the set of solutions, still for the laplacian and using divergence tools. In this talk, we will discuss some recent results obtained for the fully nonlinear case in the context of Lp-viscosity solutions connected to purely nondivergence techniques, together with a generalization of the regularity results of Swiech-Winter, to our equations, that naturally appears in the midway.
Vendredi 27 novembre 2017 à 11h, A4-47, EHESS, 54 boulevard Raspail, 75006 – Paris
PhD Student, CAMS/CFM
A new mechanism for power-law distributions
Empirical power-law distributions are often found to be an excellent fit for very unevenly distributed quantities, such as the wealth of individuals, the size of firms or cities and the frequency use of words in a language. These distributions are strikingly different from gaussian, or normal, distributions, in that they may not have a mean or variance and that they do not possess a characteristic scale. Understanding the emergence of these distributions from a mechanistic standpoint is key to understanding the origins of inequality and the scale-free structure of the economy, and its implications in policy and regulation.
The mechanism leading to a given power-law greatly constrains the value of its exponent, and many quantities sharing the same exponent may in fact fall within the same universality class. In this talk, we will demonstrate this by showing a simple and intuitive mechanism that leads to a bounded continuum of exponents and that can be exactly solved using tools and premises from statistical physics.