Program

Dr. Jonas Lätt, Head of Research – University of Geneva
Numerical modeling, fluid mechanics, biomedical simulations, modeling of rivers and canals
We develop numerical models and write programs for computer simulations of physical systems that involve fluid flow. Our methods are particularly efficient in complex situations that arise from the interaction between different physical phenomena. We simulate for example blood flow in human arteries, taking into account how biological processes of blood constituents affect the fluid mechanics of the blood plasma and vice versa. Although our methods have a large range of applications, our presentation focuses on two specific domains: computer simulation in biomedical applications, and the simulation of rivers and canals.

Prof.Sylvain Sardy, Associate Professor – University of Geneva
Statistics, high dimensional data modeling, machine learning
The goal of Statistics is to extract information from data. We illustrate with two applications: one of lung cancer detection from peptides measurements and one of emissivity estimation of galaxy clusters from telescope data. We will see that modern statistical and mathematical tools adapt to the great increase in data collections (big data) and allow great improvement over older statistical methods.

Prof. Bart Vandereycken, Assistant Professor – University of Geneva
Numerical analysis, mathematical optimization
In mathematical optimization we try to find a maximum (or minimum) of a real-valued function by iterative methods. Typical examples are process control and regression (fitting a curve through data points). For many problems, existing methods are very effective and we can solve even incredibly large problems, e.g., machine learning for big data. There exist, unfortunately, also nasty problems that won’t ever be solved in a lifetime… of the universe! My main message, however, is that by cleverly reformulating the problem or using additional information, we can again obtain nice optimization problems. I will illustrate this with two examples: recommender systems (personalised film suggestions by Netflix or Swisscom TV), and financial portfolio allocation.

Prof. Martin J. Gander, Full Professor – University of Geneva
Numerical analysis, iterative methods
The arrival of computers has fundamentally changed the difficulty of mathematical problems. Instead of trying to find an exact solution, one tries to find inexpensive approximations, which are then refined by iteration until a given error tolerance in the desired solution is reached. Using this approach, it becomes possible to simulate car crash tests, atomic bombs, create MRI images, obtain weather predictions and understand volcanos.

Dr. Gilles Vilmart, Research Associate – University of Geneva
Numerical analysis, differential equations
Differential equations (equations involving a function and its derivatives) are among the main tool for modeling physical, chemical or mechanical phenomena. In natural and industrial applications, their complexity typically does not allow for an exact analytical solution and one instead has to resort to computing numerical approximations.In some situations, standard general numerical tools even fail to produce a correct solution at a reasonable computational cost and well adapted numerical schemes are needed.This is illustrated for a few applications such as computing the evolution of the solar system, satellite and rigid body motions and dynamics at the molecular scale.