![]() The classification theorem here is that there is basically only one representation, but it is one with an unusually rich structure. This case is a very unusual example where there is effectively a unique structure. Typically mathematicians develop theories with an eye to classifying all structures of a given kind. One thing that struck me when thinking about this and teaching the class is that this is a central topic in representation theory, but one that often doesn’t make it into the textbooks or courses. There are other much less well understood aspects of this unity, but the topic here is something well-understood. In the past I’ve often made claims about the deep unity of fundamental physics and mathematics, One goal of this document is to lay out precisely one aspect of what I mean when making these claims. The basic relationship between quantum mechanics and representation theory explained here is something that I’ve always felt deserves a lot more attention than it has gotten. There’s nothing really new in these notes, but this is material I’ve always found both fascinating and challenging, so writing it up has clarified things for me, and I hope will be of use to others. ![]() In a few days I’m heading off for a ten-day vacation in northern California, and one thing I don’t want to be thinking about then is things like how to get formulas involving modular forms correct. This is still a work-in-progress, but I’ve decided today to step away from it a little while, work on other things, and then come back later perhaps with a clearer perspective on what I’d like to do with these notes. I’m posting the current version, working title From Quantum Mechanics to Number Theory via the Oscillator Representation. Since the end of the semester I’ve been trying to clean up and expand this part of my class notes. This past semester I taught our graduate class on Lie groups and representations, and spent part of the course on the Heisenberg group and the oscillator representation. From everything I have seen, that number has always been and remains zero. The problem with this subject though is not the number of people who understand IUTT, but the number who can explain to others in a convincing way the proof of corollary 3.12 in the third IUTT paper. I hope that you will boldly take on the challenge of researching IUT theory together with me so that you can be one of the next. We plan to prepare prizes for such young people and encourage them to continue to participate in the community that seriously researches IUT theory…Īlthough it is difficult to understand, there are already more than 20 mathematicians in the world who understand and develop the IUT theory. ![]() A student who blooms his talents that emerges from within. If you pass all of our courses, you will be better equipped with IUT theory than any mathematics student in any university in the world. The website seems to be Japanese-only, here’s what I get via Google Translate: The Center will offer an introductory course on IUTT. One component of the new university will be the Inter Universal Geometry Center, with Fumiharu Kato as director, Ivan Fesenko as deputy director. The establishment of a new university in Japan has been announced, to be called ZEN University.
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