Olga
  • Member for 9 years, 11 months
  • Last seen more than 1 year ago
Research-level mathematical bookstores
12 votes

I think, some less known shops need an advertisement. Independent University of Moscow (here is a link http://ium.mccme.ru/english/ to an English web-site) is a wonderful place itself and also runs ...

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How do you not forget old math?
6 votes

In general, the math I do use -- I do not forget [here I think I repeat everybody who commented above], the only kind of math I do really forget is the math I do not use at all. This is not as sad, ...

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Atiyah-Guillemin-Sternberg convexity theorem
5 votes

For this topic in general, I really recommend a book of Anna Cannas da Silva Lectures on Symplectic Geometry. It's wonderfully written and very clear. You can read a proof of the theorem in the book ...

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Writing Mathematics : Linking words
4 votes

If you are Russian, everything was done for us by A.B. Sosinsky in his great book "How to write a mathematical article in English". Here is a link (http://www.ega-math.narod.ru/Quant/ABS.htm). The ...

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Surfaces filled densely by a geodesic
4 votes

I feel there is some implicit idea here but nobody formulated it, so let me try: a smooth closed surface has no filling geodesic if and only if its geodesic flow is integrable What do you think ...

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Sign problem in a Calogero-Moser system: proof of integrability?
Accepted answer
4 votes

The answer to my question (provided by BS) is the following: We have to change the action by looking at the group $G=U(n, \mathbb{C})$ and its action by conjugacy on pairs of Hermitian matrices. The ...

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Zoll sphere which is not a surface of revolution
4 votes

I'm repeating what was said above and adding some details for completeness. A little chunk of historiography: Zoll found all the surfaces with periodic geodesic flow in the case of the isometry group ...

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Why do dynamicists worry so much about differentiability hypotheses in smooth dynamics?
3 votes

I will probably say a banal thing but the interesting degree of regularity depends on the problem you consider. In the theory of foliations, the foliations themselves are usually considered smooth ...

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An example of a beautiful proof that would be accessible at the high school level?
3 votes

I actually think that Hilbert's Third problem is one of the explainable for school guys. It's even more cool that it exists in such a famous list close to the problems that are so tempting and not yet ...

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Metric on tangent bundle
2 votes

One of the ways of defining naturally a metric on the tangent bundle $TM$ is indeed (as Peter says above) a Sasaki metric defined in 1968. You can prove that $(TM, g_{\mathrm{Sas}})$ is flat if and ...

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Probabilistic method used to prove existence theorems
2 votes

Thinking about my own question, I had another question that came to my mind. Take any real number and write its binary representation. With probability $1$ the proportion of zeroes and ones is the ...

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Is this Riccati equation ("Josephson junction") always phase-locked at integer rotation numbers?
1 votes

The answer to your question is YES, and you can look up the proof in our article with A. Klimenko https://arxiv.org/pdf/1305.6746.pdf for example. The key idea is to mix monotonicity with Moebius ...

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Can a periodically additively perturbed sinusoidal vector field on the circle have a stable periodic orbit of higher least period?
1 votes

I feel that this is important that I answer you that one third of my thesis was devoted to this equation. :) I have two published articles on this equation (one in Russian though) and I am not alone. ...

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Journals for undergraduates
1 votes

If you read French, you should certainly look at this site : http://images.math.cnrs.fr/?lang=fr This was first aimed at teachers and large audience interested in maths but on practice this is read by ...

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Is the 'massive' Calogero-Moser system still integrable?
1 votes

This is more a remark than an answer since it gives an answer to the question that Greg didn't ask but I find it a very interesting and less popular property of Calogero-Moser system! Wojciechowski ...

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math circles video lectures for school children?
-1 votes

These videos are fun: http://www.etudes.ru/en/ Although they do not explain what the proof is but they show some wonderful mathmatical ideas: Arnold's rouble problem, polyhedra, etc... Lots of ...

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