 This is a course, this is a course managed by ICTP and organized by the scientific committee. I welcome all the members of scientific committee. Well, I welcome Irina Swanson from Purdue. Yeah. Yeah. And then Marilina Rossi from Genoa, then Kishi Watanabe from Japan. And of course Lothar Gushi and then we have two young dynamic organizing committee members. Kyle Medox. Kyle, can you raise your hand. Yeah. And then Krithi Goel. So, scientific committee has been working for last one year to put together this course. And now it's the job of young people to take it forward for next 10 weeks and the speakers and the tutorial instructors a big exercise and I hope will be successful. So I invite Professor Lothar to to welcome everyone on behalf of ICTP. So, good afternoon or good morning or good evening depending on where you are. So I'm Lothar Gushi I work here in mathematics at ICTP. And it's a pleasure to welcome you to this credit course on type closure of ideals and its applications. I want to thank the organizers and also the scientific committee for all the hard work over as long time to prepare this program and to make this event possible. Also, I very much want to thank the lectures and tutors that will make these courses and do exercise sessions with with you. And this is a 10 week school. So it also requires a certain amount of stamina from the participants so I hope you will all be able to follow and enjoy it for the whole time and enjoy it until the end and learn a lot. So I also wanted to give a brief introduction to ICTP if this is possible and it's programs because some of them might interest you. So I hope you can see it. Yes. So this is ICTP here you can see a bird's eye view of the campus so it's a rather beautiful campus I hope you will all sometime be able to come here. We still have the pandemic so it's not so easy but we are slowly restarting our programs. And so I wanted to show you what we have here so this ICTP has been here for almost 60 years and the ideas that one here has both high level research and also the mission of capacity building in the developing world. So this consists of research education and outreach. So what happens. So there are five major research directions at ICTP. So high energy and cosmology, condensed matter and statistical physics, mathematics which we have here. There's physics and quantitative life sciences. There's also some activity in applied physics. Doesn't want to be the next. Okay, so one program which is particular close to our heart is the it doesn't work so well. So there are several programs I think here for, you know, for PhD and graduate studies for people here maybe most of interest would be the joint ICTP CISA mathematics program, PhD program. And so CISA is a graduate school here in TESTA, one of the best institutions in Italy. And there are also other things one can do for instance, the master and high engineering, high performance computing, things like that. And all that comes the diploma program, which is one of our, I mean, maybe favored programs and also think a big success story. So here we have students from the developing world which come for one year after they finish their undergraduate studies and study, say, getting credit courses. The theme is to prepare them for PhD program. So, every year we have 10 students and I think until now it has worked very well and most of them do get their PhD. It's very sad that it's so difficult. Okay. Anyway, so in addition, we organize many conferences. Every year they're about 60 conferences and workshops per year. This one is in some sense, one of them, although the format is very different from the usual. I mean, usually it would be one week conferences, workshops or two weeks. But this time it's 10 and it's all virtual, but we hope that soon we will have again many more also such programs here again. In normal years we would welcome about up to 5000 scientists per year to these activities and also as visitors and postdocs. Okay, you can see where people come from. So, as you can see, they come from all over the world. It's maybe not so important. That's the precise numbers, but you know, it's always many people from all over the world for coming here to our programs. So, one thing that is important is that somehow we want to offer something for everybody in every stage of their career. So it starts with a diploma program which prepares for PhD as a student. Then there is this PhD program, so the joint PhD program. We also have a step program where people come to, I mean, we already have an advisor in the home country with a PhD there, but they also get the addition, a second advisor here and come a few times during their studies here to discuss with him and do the PhD also with the help of somebody from here. And then after the PhD, you can come as a postdoc and as a visitor. And there's also the associate program where people after they are selected would come for maybe over a period of five years. They can come more or less every year for one or two months to visit us and to do work here and continue with the research. It's where it comes in different levels, junior, regular and senior, depending on the seniority. In addition, we have this Office of External Activities. So if you want to organize a school in your home country, you can ask for some limited funds from them to help you support some of the participants. There are also some partner institutes in Brazil, China and Mexico, which have recently been founded. So here, here, you can see a map of the different activities. There are these different partner institutes which you can see. And if you look at the blue and the yellow, you can see for instance in the year 2000 what scientific meetings in what places of the world scientific meetings and schools and workshops have been organized. So thank you. That was all I wanted to say. So you should look.