Entretien avec Nick Katz (Princeton University)
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| Lizenz | CC-Namensnennung 3.0 Unported: Sie dürfen das Werk bzw. den Inhalt zu jedem legalen Zweck nutzen, verändern und in unveränderter oder veränderter Form vervielfältigen, verbreiten und öffentlich zugänglich machen, sofern Sie den Namen des Autors/Rechteinhabers in der von ihm festgelegten Weise nennen. | |
| Identifikatoren | 10.5446/51187 (DOI) | |
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00:00
GrundraumMathematikNeunzehnZahlentheorieVierzigFrequenzAlgebraisches ModellGeometrieBesprechung/Interview
01:33
KombinatorLeistung <Physik>MathematikAbgeschlossene MengeNuklearer RaumMultiplikationsoperatorVerschiebungsoperatorSortierte LogikNeunzehnParametersystemBesprechung/Interview
04:40
Algebraisches ModellNichtlineares GleichungssystemNumerische MathematikMathematikerTopologieDifferenteRechter WinkelMathematikMultiplikationsoperatorMengenlehreGeometrieVorlesung/KonferenzBesprechung/Interview
06:36
Vollständiger VerbandAlgebraisches ModellKartesische KoordinatenTopologieMathematikNumerische MathematikSortierte LogikZweiEinsFunktionalWasserdampftafelt-TestBeweistheorieGrenzschichtablösungGeometriePunktMultiplikationsoperatorNeunzehnProjektive EbeneVarietät <Mathematik>Körper <Algebra>Familie <Mathematik>Glattheit <Mathematik>Figurierte ZahlAutomorphismusKohomologieGalois-FeldComputeranimation
Transkript: Englisch(automatisch erzeugt)
00:20
I'm Nick Katz, I teach mathematics at Princeton University, I'm interested in number theory and algebraic geometry and have been ever since I learned that these subjects existed. I came by boat in 1968, June of 1968, so I had just
00:44
missed the nice Évenement de May and it was very exciting to be here. Well so I
01:02
first came in 1968, stayed for a year and in over the next 20 years I think with one exception I spent every summer here and every once every four years
01:22
I had a sabbatical and I would spend the entire year here. So in in in this 20 year period I think something like 40% of my life was physically spent here. There's so many fond memories. So my first year here was turned out to be
01:47
the last year that Grotendieck was fully engaged in mathematics and he asked me to give some lectures in the SGA seminar and a very young, one year
02:09
younger than I and that remains the case. Deline was also here and he was perfectly helpful to me in preparing these these lectures that I was going to
02:20
give and so this forming a close relationship with Deline in those that very early time was sort of very important experience. So this combination of Deline and Grotendieck both so to speak at the height of
02:43
their powers in this one year I mean it completely changed my mathematical life the way I thought about mathematics it was amazing. Grotendieck after the
03:02
academic year in 1968-69 basically stopped being very mathematically active because his interest shifted. He founded a movement called Cerviv which was concerned with problems of nuclear disarmament or the absence of that
03:25
disarmament and so Deline became the person for some time it was the main reason that people wanted to come here but starting I would say around 1980 or
03:48
82 Ofer Gaber became the other important reason to come here and Deline left here to go to the Institute in Princeton in 1983 I think
04:03
84 and after that Ofer became for me the reason to want to come here and so it's completely appropriate that there's a conference honoring him because well he had tremendous impact on my own work and as we've heard from
04:24
the other people giving lectures far from the only person on whom Ofer had a terrific impact. So it really starts with Descartes who understood
04:47
really for the first time that on the one hand people had if you like drawn pictures of things and a completely different set of people had written down equations and Descartes saw that the pictures were pictures of equations
05:06
and that that's algebraic geometry this interaction between the pictures and the equations. IHS was founded in 1958 largely under the so to speak scientific
05:29
influence of Diodanay who understood that Grondik was this tremendous talent and that he Diodanay who was a very fine mathematician in his own right he
05:46
decided that the best thing he could do for mathematics would be to basically stop his own work and become Grondik's scribe and which is already a terrific terrifically selfless thing to have done and he
06:02
convinced Mochan who was the administrative founder of the institution that what they had to do was hire Grondik immediately as a permanent member so I believe at the beginning the two permanent members were Diodanay and Grondik and that put IHS on the map as the world center of algebraic
06:27
geometry and it remained that way for the eleven years that Grondik was both here and completely active in algebraic geometry. Well I first met him must have
06:44
been 1981 or 82 I actually looked at some old papers of mine to find the earliest one where I explicitly thank Ofer Gabor for telling me something and that was a paper if I look carefully enough I think the earliest one was a
07:06
paper that was published in 1982 and since it typically takes a year or a year and a half between when you write a paper and when it actually is published that would say that already starting in 1980 or 81 I was that we
07:23
were both here at the same time and I was already able to benefit from his tremendous insight into all sorts of aspects of mathematics. No all I mean he's made a number of contributions the ones that have had the most impact on
07:48
me he gave a proof that for projective smooth varieties over well over finite fields but projective smooth varieties over algebraically closed fields the L
08:03
attic the ZL attic cohomology is torsion free for all but finitely many L that it sounds like a very technical thing but for lots of applications it's very important thing to know but if you ask a hundred
08:21
different people the same question what what was the most important thing that Ofer Gabor did as it related to your own work you get a hundred different answers in almost a hundred different subjects. It started when I was an undergraduate and I stumbled across a book in the library at Johns Hopkins by
08:49
Segre which had a title something like arithmetic questions in algebraic geometry or I don't remember the exact title I should have looked this up for you but already this this concatenation of the words arithmetic
09:06
and algebraic geometry it just seemed fascinating to me. What motivated me to pursue my interest well I think it's a general fact that people start off
09:28
doing something they find interesting and if it turns out by luck that they're good at it they and they can keep doing it they keep enjoying it
09:43
they can be employed to do it which is sort of miraculously wonderful thing people pay you to do something you want to do anyway I don't know that it's it's what I'm gonna say is special to mathematics but you've been
10:03
thinking about a problem trying to figure something out and when assuming that you eventually do when you do when you realize how it all works
10:21
typically this realization the actual realization the awareness takes place in in a matter of minutes or seconds of course you've been thinking about it for a long time but this actual realization is tremendously powerfully
10:40
pleasant experience there's a famous essay by Poincare where he talks about how he discovered the concept of automorphic functions stepping off a bus on his way to do compulsory military service and I'm not comparing myself to Poincare but this this experience of suddenly realizing something it's very
11:01
powerful I spent the academic year in 1968-69 here that was my first year here Luke and was one of a few of Groton Deak students who I would
11:22
physically see every Tuesday afternoon at Groton Deak's Tuesday afternoon seminar but I didn't really get to know him but then I think it was two years later Luke spent one semester that year as a visitor at MIT and in
11:42
the course of that visit we invited him to Princeton to give a lecture and after this lecture there was a dinner for the lecture where the the attendees
12:04
were myself Luke and Bill Messing and it was a long and pleasant evening several hours although it certainly wasn't a restaurant worthy of several
12:22
hours from a gastronomical point of view so and that that's when I think I would say I first really got to know Luke and then subsequently the academic year 1971-72 I was again back for the entire year and I think it was in the course of that year that I met Luke's family and so I would say I've known him
12:48
well for 46 years
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