| I started doing research in the field of dynamical systems, tackling ergodic and spectral questions. The thesis introduction explains this a bit. old interests as well as the publication pages and seminar page indicates what I have been working on. Then, dynamical system questions in probability theory and elementary number theory started to interest me. The last chapter of probability notes contains some material in that direction: [PDF]. Mathematical problems also appear in computer science and I like to run experiments on the computer which is now called experimental mathematics. I started to program in Cayley (now Magma) ( an episode), Macsyma and Reduce as a student, I use now mostly Mathematica to explore things (an example) or for illustrations in courses. The programming activities led to a passion for mathematical problems in computer science, especially for inverse or discrete structures, whether it is in analysis, geometry or cryptology. Interests in panorama photography led to structure from motion themes explored with Jose Ramirez which led to a master thesis of Jose at the extension school. Also related to technology is Elizabeth Slavkovsky thesis on 3D printing in education. Always having been fascinated by almost periodicity (almost periodic packings, almost periodic fluids, almost periodic Schroedinger operators, almost periodic random walks, almost periodic cellular automata), John Lesieute and I studied in the summer of 2008 almost periodic Dirichlet series. A particular question on Birkhoff sums was investigated in the spring of 2010 with Folkert Tangerman, structures which are now pretty well clarified by looking at the Birkhoff sum of the cotangent function. While playing with polyhedra a paper in graph theory appeared. The topic continued to interest me because fundamental ideas of mathematics can be explained here in a discrete setup with relatively little effort like a Lusternik-Schnirelmann theorem (work done with Frank Josellis) or something about operators. 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. See the pedagogy page. Also more for teaching purposes is a collection of movies with math content. On the historical side, here [PDF] is a course developed in the spring of 2010 for the Harvard extension school which runs now the 4th time. |
