Keywords
Mathematics in Industry

Dynamical systems

Applied Mathematics
Research interests. I am interested in complex
analytical dynamical systems and applications of mathematics within
industry.
When a systems evolves with time in a way that can be described
mathematically, then one calls it a dynamical system. The motion of
the planets in the solar system, and the balance of an savings
account from term to term when interest is applied, are two
examples of dynamical systems. In the first example, time varies
continuously, whereas in the second time jumps from term to term.
In the latter case, we say time is discrete. I am interested in
dynamical systems where time is discrete, the state is given by one
or more complex numbers, and the rule dictating the evolution of
the system is a complex analytic function.
It turns out, that complex analytical dynamical systems can behave
in two different ways. In an orderly fashion where you can make
long term predictions, and in a chaotic fashion where long terms
predicitons are impossible. This dichotomy between order and chaos
gives rise to complicated geometric figures known as fractals. The
study of dynamical systems and fractals is an exciting field where
algebra and geometry, as well as analysis and combinatorics
meet.
There are many applications of mathematics, you can even consider
the natural sciences as applied mathematics, and not surprisingly
mathematics also play an important role within industry. It
fascinates me, how classical mathematics is useful in a tecnical
context. Whether it is geometry, statistics, dynamical systems or
something else entirely is not important to me; that it can be
instrumental in finding solutions is what matters.
European Study Groups with Industry, ESGI, is a good
example where mathematics can contribute to industry, and industry
can supply good problems to mathematics. In a study group, industry
representatives pose problems to industry and then work together
with a group of mathematicians intensively for a week on solving
these problems. Afterwards reports are written describing the
progress made. In my experience both industry representatives and
mathematicians learn a lot from these sessions.