Theoretical physics in maths research

Uploaded by UniversityOfBristol on 23.03.2012

I study models of complex systems -
let's say a cell, a very complex
collection of molecules, and I try to make
mathematical models which illustrate processes which are happening.
So, for example, how do cells move?
I use methods from theoretical physics
to try to develop these mathematical models.
This is clearly a very complicated system,
so a large part of the model that I do
is trying to identify the essential elements of this system.
And this is where my background
as a theoretical physicist comes into its own.
NINA: Although it may sound as though what Tannie and I do
are very different things, in fact we use the same approach,
we both have a background in mathematical and theoretical physics.
We both use that background to model the thing that we want to understand.
Tannie models things that are very practical,
I use my background to model
questions in number theory.
Questions to do with prime numbers
and the Riemann zeta for instance, which have been around for 150 years
and which are, as yet, unanswered.
So what we aim to do is use a technique that actually
originates in physics called the random matrix theory.
It turns out that, amazingly, surprisingly,
there's a connection between these number-theoretical functions,
which are all connected with prime numbers and very pure mathematics.
TANNIEMOLA: Another thing which is of particular interest to me
is how one could efficiently design some machine
which is very small, as small as, let's say, one of our cells
that could move autonomously efficiently.
For this, the essential part of making such a system
is identifying what are the key ingredients that would make it work.
What we've done is to model a biological system
then also model a synthetic system, but then use ideas from both
to help us in our understanding
of how one can quantitatively describe these systems.
You often have groups of people working from different backgrounds,
so you might have, as well as people doing experiments,
maybe chemists, physicists, biologists.
You might also have engineers or mathematicians
who might be making models of these systems.
And actually, you often find that
the kind of models that I and my collaborators make
are the models which try to capture the essence of the system
and then this other person can then fill in the details
of exactly how this, if you want - machine works.
And we tend not to
model all the way to the last detail of the system,
we make models which capture the qualitative behaviour
and then usually we stop
because usually that's the bit we like!
NINA: Mathematicians do mathematics
because we're curious, there's a question out there
that no-one knows the answer to
and we want to know what the answer is and so,
over the years, mathematicians have invented mathematical methods
and then sometime in the future, it could be 10 years, 100 years,
someone else will see a use for that.
So all the technology we have around us today
is all based on mathematics
somewhere along the line,
but we do the mathematics because we love it.