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I started doing research in the field of dynamical systems,
tackeling especially ergodic and spectral theoretical questions. The
thesis introduction
explains this a bit. old interests
page shows what I had been working on until 2000. Later, I tackled dynamical system questions in probability theory and elementary number theory. The last chapter of my probability notes contains some material in that direction. Check out also the slides on the seminar page. Mathematical problems also appear in computer science. I like to explore things with computer algebra systems. I started to program in Cayley (now Magma) ( an episode), macsyma and reduce as an undergraduate and use Mathematica before its first version appeared (ETHZ had good connections and faculty members who were involved in the development of early versions of Mathematica). Since then, I use Mathematica almost daily to explore things or simply for illustration purposes. Here is a computer algebra project from Summer 2007 written in Mathematica 6. During the years, also a passion for mathematical problems in computer science has emerged, especially for various inverse problems, whether it is in analysis, geometry or cryptology. Currently, inverse problems in computer vision are at the top my list. Here is some work done in the Summer of 2007 with Jose Ramirez. I have for long been fascinated by almost periodicity: almost periodic packings, almost periodic fluids, almost periodic Schroedinger operators, almost periodic random walks, almost periodic cellular automata etc. In the summer of 2008, John Lesieutre and I studied almost periodic Dirichlet series, an exciting topic in analysis with many open questions. Here is the project page. Since I always loved teaching, I got also more and more interested in pedagogical questions, especially in web pedagogy and the use of technology in teaching. You can find more about this on the pedagogy page. |
