 So, thank you very much. It's a great honor for me to be able to say a few words at this opening. It's also emotional, I should say, and especially moved to see all of these daughters sitting at home, Johanna, that I haven't seen for so many years. Anyway, of course, the name of Alexander Rothenberg given to this lab is for one obvious reason. Well, I think the fame that the IHE has acquired from the very beginning, international fame, is largely due to Rothenberg's seminar here. And in fact, next to the Simon's auditorium, you have this room at the entrance, which was formerly a music room, a music pavilion, and then a library, and it is the room in which Rothenberg held his seminars. There were long seminars lasting one year, sometimes two. The seminar was in the tradition of Hadamard and Carton, and then combined somehow the advantage of making it possible to develop full-fledged theory at length and starting from scratch. And of course, the usual social role of making people meet and interact, but in this case, of course, with a stronger common interest and motivation. Of course, these long seminars are gone, but somehow their spirit survives in some intensive workbooks and devoted to a special topic. But while I remember, I started attending a seminar, in the fall of 1964, which was bad because I had already missed SGA 1, 2, 3 and 4. There were almost more than one and a half of the seminars. And in fact, I nearly missed SGA 5. Certainly, I would have missed SGA 5. And that didn't mean for Rothenberg's insistence on my attending and even what was worse, writing out notes for his talks. In fact, the problem is that at the time my background in algebraic geometry was near zero. I said, well, of course, it's so high-brow and I will never follow. But to my surprise, I could. So it was because of Rothenberg's style. Certainly those who had the privilege of listening to him remember. So the blackboard, it was, of course, extremely energetic and dynamic, but above all, it was methodically clear and rigorous. Remember, he neatly reviewed the material he needed for his talks. He set the goal clearly. He set the plan. And then he started with precise definitions and statements and full proofs and sometimes integrations. When I set full proofs, it might happen that at times he would say, well, this is a routine verification and the reader will make it. So, for example, old diagrams should commute. So no reader should check that. Sometimes it was not so obvious. Sometimes it would be the diagram of the entire community. But anyway. So in fact, it was easiest to take down notes. And I had no problem, in fact, in following, at least formally. But this substance was rich, you see. At the beginning, so, in the fall of 1964, he started by discussing local duality for torsion cheese prime to the characteristic. And it's at this time that he formulated this famous conjecture of absolute purity and also his conjecture on the existence of dualizing complexes which, in fact, in the most general form demanded by Rothenlich, was put only much later by Gaber in 1994 for absolute purity and in 2005 for dualizing complexes. And after that, we had the cycle class, homology, left and right trace formula. Rothenlich's old trace formula using Nielsen-Vecken method. And we had the Rothenlich-Ochafaris formula, and then the Laddick sheaves, and then the rationality of the L function. So it was a huge seminar. And from the very beginning, Rothenlich, of course, was using the language of the right categories and funtions. And I was discovering that with delight. And in fact, just playing with it with pleasure, it was a really fantastic new breeze which was blowing. And it's so much pleasure that, in fact, I became what Rothenlich described in Revenant Soaring, I was a homology student. And in any case, look, 50 years have elapsed. And this formalism, we use it every day. It doesn't have a wrinkle somehow. Of course, some constructions have been proven, there have been progress in many places, but still the formalism doesn't look old. Even maybe five years before Rothenlich, the material of the homological algebra, 10 years before Rothenlich, material of the homological algebra, I prefer not to look at it. And in the audience at that time, I remember, well, of course, there was the measure, Rothenlich student, the measure, Giro, Verdié, the Renault's, Joannoulou, and also remember, of course, older ones, which were, of course, much younger than I am now. There was Giudonni, there was Samuel, Sarah would come from time to time, and Tate, of course, who visited from 65 to 66. And of course, many others I can't mention. As for DeLing, he arrived in January 65. In fact, it's Tate who introduced him to Rothenlich at the Bovagi seminar on December 64. And as far as I remember, during the seminar, he had sort of a low profile. He didn't say much. But soon I heard of him as the person who could solve any puzzle, any seemingly intractable puzzle. He said, find a non-empty topos without poems, for example. Poems are two ways of defining a basic map of the same. So intractable. I mean, the Rothenlich had tried for four hours and then went nowhere. So, in a minute or so, DeLing could solve that. Anyway, these were the participants of the seminar. But the tools were mostly given by Rothenlich in SGFI, at least. And in the second part, at least in the first part. In the second part, we had talks by students. We had talks by Joannelou and Hélédic Corpology. And we had talks by Boucault and Rothenlich-Gochararis formula. And also, we had a talk by Serre and the Swann conductor. But mostly, Rothenlich left his students with the rising of the North of Hélédic Corp. So they had to learn the trade. That was a hard lesson somehow. In several pieces, I recalled these long afternoons I spent with him at his place. Going over all the remarks he had made, the remarks and suggestions and criticism he had made on my writing. And maybe you might even remember that we had dinner after a very long discussion. And that was not finished because after dinner we had more discussion and eventually Rothenlich would accompany me to the train and then I would take the last train to Paris just before midnight. So these were extraordinary experiences. And the talks, the seminar, they started, I think at 2.30 according to Renewal, it wasn't true of 2.15 or 2.30. I think 2.30, the last one hour and a half and then we had tea afterwards and more discussions of course. But one thing I remember is that often we had lunch at the cafeteria, the same cafeteria that you all know. But you see, there was Rothenlich, Rasser, State and maybe tea to other people and what I remember is that I understood nothing because the conversation was not about the present seminar but topics for future seminars like semi-stable reductions, the date curve, the geometry, I think. But it was beautiful anyway. Then next year we had the SGS6. So SGS6 was Riemann-Rohr and the Intersection Theory and I think it was a vacation for Rothenlich. Somehow it was old stuff. So he quietly let Dertelo and myself run the seminar from Lothi, he had given us and as good students of course we wanted to do much more general than what he had proposed or it's in cases we succeeded and Rothenlich was happy. He even said once that Dertelo was more functional than he was. Anyway, this was the SGS6 and I said Rothenlich may be not so much interested in Riemann-Rohr any longer but he was still interested in the development of Intersection Theory. Intersection Theory and singular schemes but not moving the cycles but using case theoretic methods instead. I think a very good approach somehow in the 70s eclipsed by Fulton's work but it's still, I think, more powerful. And then in 67, so that was the end of the SGS6 and Rothenlich thought the demobilizing at this time. So first he invented the crystalline chromology and he discussed, so then he invented the crystalline chromology, he gave some talks there and he let Bertelow write in his series a full-fledged theory for that and also Rothenlich was really interested in the connection of that with the work of Seyre and Tate on physical groups and also the links due to his theory. But also at the same time he formulated his famous standard conjectures so I'm not standard at all, I think, and you are still widely open today except for the first one, the hard-nature theory which was put quite a bit much later and then, of course, the subsequent theory of motives so it was quite an occupation and how about the next seminar, SGA8? But yes, Rothenlich had told me that he wanted an SGA8 and he wanted to have it on a billion schemes and certainly, so it would have been a fantastic seminar maybe under the spirit of SGA3 and we certainly missed it. Of course, we had Manfred's book but maybe it's not so functionalized that Rothenlich would have liked. But anyway, Rothenlich, after 67-68 was still working on Christel's and Jordanais theory and, of course, he talked at ICM in 1970 and certainly he proposed the problem of mysterious function which is something interesting that occupied Fontaine for some years and maybe other people in Piedic Hall's theory but still I had the impression that mathematics that seems to be the main focus of his interest and that he was slowly drifting away from mathematics. Somehow, I think the theories of politics had snatched him and maybe lured him into radical ecology. Anyway, in this respect, looking back this year, the 60s of seminars so obviously a golden age of algebraic geometry. The wind was blowing. We were discovering beautiful new territories and exploring them boldly, happily. Really a golden age. But today, in this auditorium, the Simon's auditorium there is one person who has never met Rothenlich. For one good reason, that person was born the same year as et alchromology. But this person is probably the one on Earth who knows EGA and SGA best. One who is really the few who have fully assimilated Rothenlich's philosophy. So this person is the director of research at CNRS and has visited the IHES for over 30 years. So this is Ofer Gabber and I am pleased to introduce him for the first talk. This title is writing out of rigid analytic families and observations on PLE theory. Ofer Gabber.