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Okay, it's great being here. Last lecture of the day for you.

I will just get started today on my subject and there,

I hope there will probably not be outrageously new things, at least for some of you today.

So it will be half of what I'm talking about today will have an introductory, somewhat introductory character.

Of course, slow me down, speed me up by making comments otherwise, that's most welcome.

So I'll be talking about a particular way of looking at quantum gravity,

non-perturbative quantum gravity to be more specific and to be even more specific.

I work with a specific method that's called causal dynamical triangulations

and that's what these lectures will be about once they become a little more specific.

So the full title of my lecture is non-perturbative quantum gravity,

quantum gravity from causal dynamical triangulations.

And often I use the abbreviation CDT for this.

Now as a subject, it fits well with the general theme of this school, which is quantum geometry,

because it can be seen as an attempt to understand the quantum geometry of space-time on very short scales.

CDT is one specific approach of trying to do this.

It also with some success tries to quantify what quantum geometry might be

and how to actually put this into numbers with some success.

Now before getting to the specifics of this approach, I'll try to give some motivation

and also embed it into a somewhat more general context of what people have been looking at.

Some of this may be familiar to some of you, but I don't think to all of you.

So anyway, what is our primary aim in this whole business of gravity and quantum gravity?

Well, we really want to understand what space-time is on all scales, including the very small.

And of course, the very small that will take us to the theme of quantum gravity.

So here's my starting point we want to understand and describe and emphasize quantitatively.

Quantitatively, the structure and also the dynamics of space-time on all scales.

And it's something we haven't completely succeeded in doing.

So this is an active area of research.

So what I like to begin this kind of general introduction with in the context of gravity

is to draw a picture of physical scales.

So along a one-dimensional axis, oops, so a lot of space I have here,

where I'm using a logarithmic scale in meters.

So a powers of 10, I start out here at very small distances, 10 to the minus 35,

and I go all the way to rather large distances of 10 to the 24.

Now what characterizes physically the scale of 10 to the 24, that's about the size of the visible universe.

So time, light has had time to propagate just about from that distance to us.

So that sets a large scale.

So where are we?

Well, somewhere around here, 10 to the zero.

That's us, happily.

And of course, a lot of stuff out here.

Solar system is about here.

Then you have larger scale structure of the universe.

You have galaxies, classes of galaxies, and all the way up to this largest scale.

On the other hand, if you go now down in powers of 10, we have here is about 10 to the minus 9.

So that's nanometers, nanoscale.

So around about here, you get atomic and nuclear phenomena starting right about here.

And our current best accelerator, particle accelerator, the LHC,

resolves distances of around about 10 to the minus 19 meters.

So that's where the LHC, kind of what we can probe directly with experiment,