![]() 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. ![]() Visualized this means that every pair of elements forms either has one element above and one below, or forms a diamond with some pair of elements, one above and one below.The establishment of a new university in Japan has been announced, to be called ZEN University. (Note that they are not comparable because neither is a superset of the other)Īnother example of a lattice would be the powers of a set with set theoretic inclusion.Ī way to think of lattices would be as a sort of structure where every pair of elements has one element above it that is smaller than every other element above it, and one bigger then every below it. A greatest lower bound is an element $l_0$ such that for every lower bound $l$, $l \leq l_0$.Īn example would be $A = \mathbb$ are not comparable. A lower bound is an element $l$ such that for every $b \in B, l \leq b$. ![]() Consider a partially ordered set $(A,\leq)$, and a non-empty subset $B$.
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