The

thesis,

old interests as well as

publication and

preprints and

seminar page
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

Dirichlet series.
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
which

continues to interest me.
Through teaching I also got 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.
And history:

here [PDF] is a
course developed and ran first in the spring of 2010 and now for

the 7th time.

Work samples:

- 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.
article.
- Illustrating mathematics and proofs using 3D printers, with Elizabeth Slavkovsky.
In book,
Updated preprint,
talk.
- Some analytic continuation results for almost periodic Dirichlet series with John Lesieutre.
Journal
Project Page
- Some spectral theory in ergodic theory. Example:
weakly ergodic shift invariant measures are generic for a Z
^{d} shift.
PDF.
- An ergodic theoretical approach of sphere packings. In that class, periodic packings maximize the packing density.
HTML,
PDF,
Some code.
- For an aperiodic ergodic sequence of SL(2,R)-valued random variables,
the class with positive Lyapunov exponent are dense.
PDF.