Thank you very much for this introduction.

And actually, I mean, the topic of the workshop is trends in.

At the moment, I try to catch up with the status quo because of these additional jobs.

So I don't know whether my talk will have some trends involved.

Nevertheless, it's a topic where at least I'm interested in a couple of more people here also sitting in the first row.

I think you all know this joke with the driver of the former professors who doesn't know that.

I mean, in former days, professors had their own drivers and the professor was always invited

and basically gave all the same talk and everything runs smoothly.

And all the questions have been the same at once in a while.

The driver with the professor said, why not switch in the next talk?

And then the driver gave the talk and the professor was sitting in the first row and everything runs smoothly.

And for whatever reason, there was one question that has never been there before.

And then the driver sat there and said, well, the question is so easy that even my driver in the first row

can answer it. And the first, the drivers here are Martin Gugard and Günter Leugering,

because the later we are on my slides, the more we get into PDE stuff, as you will see.

And I have basically no glue, still no glue about PDEs.

And so whenever questions show up, here are the professors sitting in the first row, the drivers.

So actually, I'm from discrete or integer optimization.

And I guess there are not many few frauke's here and myself.

So we are guess more on this left side, discrete integer programming.

So I will come to this point in a moment.

But as you will see in the applications that we have in mind,

there will be various aspects of applied mathematics will be involved.

And this is which we summarize here.

And I guess every one of you feels home in one of these pillars.

So if either it comes to mathematical modeling simulation, yeah,

and or you are involved in nonlinear business and optimization and control or the integer part

where my home field is is combinatorial integer optimization.

And if you look at the four key in each of these pillars, sometimes they are similar.

But very often, they are also different.

So you look for existence results, efficient algorithms on one side or in nonlinear optimization.

You only focus only in quotation marks because I think you can't do more for local optimal

whereas an integer programming, every solution is a local optimum.

So you look for a global optimal solution and, of course, also methods that guarantee global optimality.

And the challenge somehow is to bring these fields together.

And actually, I think more than two decades ago,

Gunda and also Martin, you have also been in the business at that time.

We started thinking of how can we bring these things together?

And we all know if you are in one pillow, you have a hammer, everything looks like a nail.

And the question is, how can you bring these things together?

And here is such an application that we have in mind and that follows us for the last 10, 15 years.

And also Enrique is involved.

We have a corporate research center running on that, which is now headed by Frauke,

where all we try to bring these things together.

And the application is that of physical networks or in particular, gas networks.

And so you have a classical network structure.

You have a graph with sources and things.

You have nodes. You have arcs.

And then you bring something from the sources to the things.

And even in discrete optimization, this is one of our first theorems.