I was asked to talk about something that I normally would not talk about.

This is the explicit calculation that leads to this massive formula at the very top.

So typically I talk about the mathematical structures which are behind, but in the end

at the last step you have to do some trickery to get some real results and I'll talk about

this step which I normally skip.

So maybe one wants to look at the formula at the very top.

The only thing that I find interesting about this formula is that there's no pi squared.

This is something that we expect because we see this in lower orders.

It's just a missing Galois conjugate of pi squared in the kind of general theme that

the Galois conjugates are sort of sometimes missing or sparse in a certain sense.

That's the only thing that I would say otherwise the numbers look sort of normal.

There's a numerical result.

These are single thetas and it was double thetas and it comes from the self-energy and

this is a sequence of graphs.

And I should say that I have a very, very mixed audience today.

The local audience is purely mathematical so I don't assume any physical background

in quantum field theory whatsoever and it will be very elementary.

So everybody who's annoyed by the low level of the talk just, you could just leave or

do something else.

That's the advantage of having these virtual talks.

So you don't have to know what these graphs mean.

I just give you an impression what they look like and then I, you know, this is, it starts

with small graphs and then you pick up more and more dots in the middle and the dots are

the G's and you get a maximum number of G's.

This is the coefficient of G to the 8th so it means you have 8 dots in the middle.

And G is the coupling.

Yeah, and I tried to draw one of these 1,157 graphs with 8 dots in the middle.

I tried to draw something slightly impressive.

I'm not sure if I got a good graph.

So that's the way they look, the other 1,156 graphs look like.

So we want to do this calculation and the calculation, whatever that means, we'll see

later what these graphs mean.

This rests on the theory or the method of graphical functions which has sort of three

pillars and one is the graphical functions in functions in even dimensions.

We need a minimum of four dimensions and here we only need four dimensions because this

is a purely four dimensional thing.

I won't tell you what the gamma function means.

This gamma function is the anomalous dimension of the field.

I don't want to go into it in physics there.

It's just, if you're a mathematician, it's just something that you would like to know

in physics.

So one thing is the graphical functions theory in even dimensions.

This is with Michy Borinsky.

The second thing is the generalized single-line variant hyperbox.

These are special functions on the complex plane which are single-line and have punctures.

This is the function space that you need to do the calculations.

This is the general mathematically nice theory in a fixed number of dimensions.

And then you have a third thing which I normally don't talk about and it's not central in my

project because my DfG grant is in mathematics and this is slightly physical.

You need an extension away from four dimensions or six dimensions or whatever dimensions you