In most real life applications Mathematics not only face the challenge of modeling (typically by means of ODE and/or PDE), analysis and computer simulations but also the need control and design. And the successful development of the needed computational tools for control and design cannot be achieved by simply superposing the state of the art…
What links gas molecules, charged particles, bacteria and fish? Partial differential equations help us understanding their collective behaviour. Kinetic modelling allows for a multi-scale strategy in a number of important applications in science and technology. Mean field limits and kinetic descriptions have become one of the most powerful tools in applied mathematics to bridge microscopic and…
In this talk, we are concerned with the expected values of certain functionals of the path of a stochastic process during a given time period. High-order asymptotic characterizations of such values when the time period shrinks to 0 have a wide range of applications. In statistics, they are crucial in obtaining the infill asymptotic properties…
Recently, there has been an increasing interest from the community in real-life complex system modeling. The most popular example is provided by systems where the number of agents is so large, that only a statistical description (reminiscent to the statistical mechanics description of systems in thermodynamics) turns out to be viable. The usual way to…
Several topics will be presented in this talk. In the first part, we consider some portfolio optimization problems with stochastic dividends, stochastic volatility or delays. The Hamilton-Jacobi-Bellman (HJB) equations are derived, which are second order nonlinear PDEs. We then establish the existence results of the HJB equations and prove the verification theorems. In the second…
The regulation of cell division, cell sizes and cell arrangements is central to tissue morphogenesis. To study these processes, we develop a mechanistic hybrid continuum-discrete mathematical model of cell dynamics that has advantages over previous approaches. This model borrows ideas from statistical physics, materials science and applied mathematics and follows the framework of dynamic density…
Reception to follow in SAS Hall Atrium. Recent advances in large scale sequencing of microbial DNA without culturing or isolation gives us easy and direct access to “wild” microbial metagenomes that are otherwise virtually impossible to study. However, because these data sets are large and relatively unstructured, analyzing them requires advancing data science techniques…