as well as
or the last chapter in my probability book
illustrate earlier work in ergodic and spectral theory.
Having always been programming math and do what one calls today experimental mathematics,
I have a passion for mathematical problems in computer science, with discrete structures, geometry or probability.
Always having been fascinated by almost periodicity (packings,
fluids,operators, walks cellular automata), or
A particular question on Birkhoff sums
or the Birkhoff sum of the cotangent function
A couple of years ago, playing with polyhedra led to a paper
in graph theory
to interest me.
Through teaching I also got more and more interested in
, especially in web pedagogy and
the use of technology in teaching. I love movies, especially
if they contain math
And history: here [PDF]
course developed and ran first in the spring of 2010 and now for
the 7th time
- A Cauchy-Binet formula gives the coefficients of the characteristic polynomial of a product
of two arbitrary mxn matrices matrices article
(preprint), slides [PDF]).
- A graph theoretical take on the Lefshetz fixed point theorem:
the fixed point index sum of a graph automorphism agrees with the cohomologically defined Lefshetz number.
- Illustrating mathematics and proofs using 3D printers, with Elizabeth Slavkovsky.
- Some analytic continuation results for almost periodic Dirichlet series with John Lesieutre.
- Some spectral theory in ergodic theory. Example:
weakly ergodic shift invariant measures are generic for a Zd shift.
- An ergodic theoretical approach of sphere packings. In that class, periodic packings maximize the packing density.
- For an aperiodic ergodic sequence of SL(2,R)-valued random variables,
the class with positive Lyapunov exponent are dense.