I started in the field of dynamical systems tackling ergodic and spectral questions. The thesis, a page on old interests as well as publication and preprints and seminar page indicates a bit. Probability theory and elementary number theory have always interested me. The last chapter of probability notes contains some material in that direction: [PDF]. Mathematical problems also appear in computer science and I always like to run experiments on the computer doing 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 for research or for illustrations in courses or just to play around. 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), or almost periodic Dirichlet series (with John Lesieutre). A particular question on Birkhoff sums was investigated with Folkert Tangerman, structures which are now pretty well understood by looking at the Birkhoff sum of the cotangent function. While playing with polyhedra, a paper in graph theory appeared. The topic continues 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. I love movies, especially if they contain math. Here 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 the 5th time. |