 Okay, so we can start. Welcome you all. I'm Claudio, Claudio Arezzo, one of the organizers, and I'm supposed to tell you a little bit where you are, and why we are here, besides the obvious thing, of course, that we are here to learn geometric measure theory and optimal transport, okay? Now, I'd be brief so we can have the first coffee break in 10 minutes, okay? So, where are you? Well, this institute was born 49 years ago. Basically, it's a one-man dream, okay? Abdul Salam was one of the founding fathers of unifying theories in theoretical physics, a Nobel Prize in the 80s, and he was especially important for he was the first Nobel Prize in physics coming from a developing country, and he had this dream about building an institute where people from scientists from developing countries and scientists from developed countries could meet and discuss science freely. Remember, we are in the 60s, so this was a highly non-trivial thing, even though even now, it's not as easy as one can think, okay? And he made the point that everything should be run by scientists for scientists, okay? So, the director, the vice director, the any decision-making process is made by scientists here, okay? There is no bureaucratic involvement by other people. So, what is our mission? As I said, the mission is really to help the growth of advanced physics and mathematics, especially in developing countries, through meetings like this, where people from everywhere can meet and discuss together. Okay, quick fact, who is paying? It's always better to be grateful to the people who pay, so this is an institute, it's a UNESCO Institute, but it's UNESCO and the IAEA, which is an acronym for an International Atomic Agency in Vienna and plus supported by the Italian minister of research for more than a half of the budget, okay? Just to, well, what we do here, I mean, it's a quite small institute in the sense of people who are permanently in place. I'll show you a bit later how much. And this is more or less the kind of impact, I like this picture because it gives you a feeling of the amount of impact the institute manages to have all around the world, okay? So we are speaking about, in 45 years, about 120,000 people have come here. 120,000 scientists have come here to discuss their work, to hear about other people's work and so on. And of course there is an increasing attention to the gender distribution of scientists, and of course there is a focus on increasing women in science everywhere. So now this is, what, the issue is divided in, actually I thought we were five. It seems like we are four groups, okay? Condense matter, high energy and cosmology and astroparticle physics, mathematics and the earth system physics, okay? But, okay, how many we are? We are 30 scientists here, working here the whole time, okay? But then there are a number of positions which are kind of related to scientists in place that I would like to describe you, especially because I hope some of you might be interested in the long term to be involved in other activities here of different type, okay? Well, and of course one of the most expensive and most important thing that we support is our library, okay? Our library is probably, is actually one of the best, more complete libraries in Europe, okay? Which is particularly important for our scientists coming here because, you know, there are budget cuts everywhere and it's more and more difficult to find a library, a complete library for mathematics and theoretical physics, okay? Now, why I'm telling you all this, first because I'm supposed to, but what kind of programs do we run? Well, programs like this, okay? Schools, conferences of this type, so I don't have to introduce you to this type of things. And there are more or less 60 per year of this type, okay? So, but we don't do just things here in Trieste. We are, we can, and in fact we are willing to organize activities in developing countries, okay? And this is more or less, these are the main centers where we usually organize things, okay? Scientific events. But especially for those of you really coming from developing countries in this room, let me tell you, let me spend two minutes on what kind of programs you can be interested in. If you have a bachelor degree in mathematics, let me talk about mathematics because that's what we are, you might be considering the idea of coming here to study. I'm telling you because probably all of you are overqualified for what I'm going to tell you, but you might have students in your own place. You might have, you might know people who might be interested in this. So, we have what is called a diploma program. Diploma program is basically a one year post-graduate course, full immersion in mathematics. Our students are really supposed to work very hard. The spirit is basically to prepare students from developing, we actually, in mathematics, for example, we take about a dozen per year, okay? To take these graduate students and to bring them to the level to be able to apply with some reasonable chance of success to the major graduate schools in the US, in Europe and so on, okay? And this is a pretty successful program. Okay, of course, students are selected in developing countries and then they are fully support, travel, and living expenses plus a little salary here. So, it's a very successful program. I mean, our students, at least in the last three or four years, the time I've been here, I can tell you they have been quite successful after our diploma course in many important schools in Europe, for example. We sent two or three students in the last couple of years to the Occult Polytechnic in Paris. We sent a couple of students to the Max Planck in Bonn. I believe also in Leipzig and people seem to be pretty happy to accept these students. So, that's a very successful thing. Plus, we have a PhD course joined with CISA, which is, of course, our nearby, unfortunately not the nearby anymore, but, I mean, almost nearby scientific cousin here. Up hill, we have a PhD, a joint PhD in mathematics and physics, okay? At the moment, this is restricted to students who have attended our diploma course. But, I mean, these are things that can change. Well, all the other things are not really relevant for mathematicians. And this is more or less the distribution in the different sectors that we cover of our students. But then, what other thing you can do if you want to be in touch with ICTP? Well, of course, you can apply. Every year, we have one or two, depending. I mean, for example, in this moment, there is an open application for visiting positions here. You can ask to come for any period of time, from one week to one year, you can come here to do your research or to open new research teams with us at ICTP or with the people at CISA or and so on. And, I mean, if you are already kind of an established scientist somewhere, from developing countries, okay? From developing countries, it's always a delicate definition. It's really important your nationality, okay? That's what distinguishes. And then we have an associate scheme, which is, again, very important because if you are actually an established scientist somewhere in a developing world, you would like probably to be kind of associated to ICTP for a longer period of time. And the associate scheme more or less means this. You can apply to our scheme to become an associate, which means that we support your visit for a period of between three and five years, for at least a month or two months, actually, 60 days. And we pay travel and we pay local expenses, we pay everything, and to, again, to work here at a more senior level. Well, lab, fortunately, we are all happy not to need them, okay? And this is more or less the distribution of our associates all around the world. As you can see, Europe is almost non-existing because this is a restricted to developing countries so that those little bars are for Eastern Europe countries in the list of UNESCO for the developing world, okay? And then there are other more specific projects that we run all over the world to achieve our mission. Okay, okay, we give prices. In mathematics we give, well, at the ICTP price, these are all prices restrict, well, except for the Dirac medal. The Dirac medal is open to everybody. But for the ICTP prize, the two things open for mathematicians are the ICTP prize, which is restricted for scientists in developing countries, and the Ramanujan prize, okay? Which is, again, Ramanujan prize is restricted to mathematician, of course. That's, okay. Then everything is on our webpage, plus the fact that we are very happy. The mathematics section is now made of five members, okay? And we are all, of course, happy to receive emails from people who are interested in any of these things for themselves or for their students, okay? Speaking about the diploma program, for example. Well, okay, so this tells you where you are, why you are here, and the other thing, of course, I would like to say is to thank the lecturers. I hope you will all stay, I mean, many of you will stay up to the end of the activity, which is a three-weeks activity. So we will start with a two-week school, as you know, and I would really like to thank the lecturers for their effort, okay? Each of them will tell you specifically what kind of things, if they have material, if they don't have material, or what can you do to take the best out of them, okay? So thanks to them, and let's see, what else? For any other practical problem, of course, refer to me or, now you know, everybody, you all received at least one email, presumably more than one, from Mrs. Mabilo Kutu, who is our fantastic secretarial help for this activity, okay? Any question you can think of? From the most stupid one, how do you go to the main center? How do I go to the library? How do I go ask us, okay? Up to the most delicate things. I mean, we are used to, I mean, we know that visa is always a problem, whatever, okay? We are here to help. The most important thing, the only, this is, I think, I'm new to ICTP in some sense. I really like it, and I think this machine works very well. You have to be focused on learning mathematics as much as you can, bother the lecturers. I should not say the lecturers are paid, okay? They receive a bit, not much, because of course we ask everybody to join our mission, at least for a limited part of time, okay? But please, ask them, ask them questions. Stay in touch with them, okay? That's the way, I mean, that's the way to make the best out of it. You will see the program is designed so that you have time to study. We are not stupid. We are on the sea. The sea is beautiful, okay? But it's an occasion for you, okay? Afternoons are free to study. If you want to study on the beach, you are welcome to do it, but please, study, okay? Study and ask questions. I can just tell you my purse, I was, of course, I'm Italian. I was a guest of one of these activities when I was an undergraduate, finishing my undergraduate degrees, and this is the place where I found my PhD advisor, okay? Just coming, I was sitting in one of those places and I started bothering one of these poor lecturers so much that at the end he said, okay, come to England, and we will work together, okay? In principle, that's what we hope it will happen also here, okay, also this time.