Computers are getting more and more powerful, and computer scientists are developing better and better algorithms. Despite this constant progress, it is still extremely difficult to simulate things we see in everyday life, like splashing liquids, fracturing solids, tiny bubbles and foams, and detailed water ripples. Our approach to solving these problems combines numerical algorithms for solving differential equations with geometric algorithms for computing shapes. I will present some of our research on the simulation of natural phenomena, including new methods for animating liquids, smoke, foams, fracture patterns, and knitted fabrics. These techniques have potential applications in computational physics, engineering, the motion picture and clothing industries, virtual reality, and video games.
We present an overview of research done in the group, which concerns mainly the mathematical analysis of the many-body problem in quantum mechanics. We will try to explain the aims and challenges, and conclude with a concrete example of recent results on the polaron problem.