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My earlier research is in the field of dynamical systems,
tackling ergodic and spectral theoretical 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. Later, I tackled dynamical system questions in probability theory and elementary number theory. The last chapter of probability notes contains some material in that direction. See Scan [PDF]. Mathematical problems also appear in computer science and I like to explore things with computer algebra systems (this is now called experimental math). I started to program in Cayley (now Magma) ( an episode) and Macsyma and Reduce. Since then, I use Mathematica almost daily to explore things (an example) or for illustrations in courses. During the years, I developed also a passion for mathematical problems in computer science especially for inverse or numerical approximations with discrete structures, whether it is in analysis, geometry or cryptology. A structure from motion theme was tackled in the Summer of 2007 with Jose Ramirez which continued with a master thesis of Jose at the extension school. Elizabeth Slavkovsky currently writes a 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. Here is something in graph theory discovered by playing with geomag. This paper has now appeared. The topic continues to interest me because fundamental ideas of mathematics can be explained here in a discrete setup. 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. On the more general side, Here [PDF] is a course developed in the spring of 2010 for the Harvard extension school which continuous to run. Finally, here is a collection of movies with some mathematical content. |
