My 2 selected answers:
Finding a 1-form adapted to a smooth flow
Proposals for polymath projects
My offered bounties:
https://mathoverflow.net/users/36688/ali-taghavi?tab=bounties&sort=offered
Some selected questions:
PhD dissertations that solve an established open problem
Limit cycles as closed geodesics (in negatively or positively curved space)
The error in Petrovski and Landis' proof of the 16th Hilbert problem
Does $P_xP_y+Q_xQ_y=0 \implies$ "non-existence of limit cycle" for $P\partial_x+Q\partial_y$"? (Complex dilatation and limit cycle theory)
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Il est bien plus beau de savoir quelque chose de tout que de savoir tout d’une chose (Blaise Pascal)
What would be the fate of the Hilbert 16th problem?
$$\text{Is} \; H(n)< \infty?$$
When I was a PHD student, working on limit cycle theory, my supervisor encouraged me to learn the elements and basics of Noncommutative Geometry in order to find some new interpretations for the concept of "The number of limit cycles". I have deep admiration to him, since he was a different supervisor among other mathematicians in Iran.
The second part of this note (http://arxiv.org/abs/1302.0001) is an $\varepsilon$- try to find a possible new interpretation for this concept, a possible relation to (Fredholm) index theory.
In particular I am interested to find a generalisation and an
abstract version of the remark 2 and its consecutive example in
page 5 of the above note
Moreover I am interested in the fate of the following question:
Limit cycles of quadratic systems and closed geodesics(Finitness of $H(2)$)
I am also interested to know the answers to the questions listed in this post:
Proposals for polymath projects
My email address is "[email protected]"
My papers:
1)(Pythagorean triples) https://arxiv.org/abs/2403.17966
2)https://link.springer.com/article/10.1007/s41980-023-00771-x
3)https://www.sciencedirect.com/science/article/pii/S0723086914000036
4)http://bims.iranjournals.ir/article_872_fd7287eb7f1365d9156e9da3ccb25196.pdf
5)https://arxiv.org/abs/math/0409594
6)http://mcs.qut.ac.ir/article_243944.html
7)https://maco.lu.ac.ir/article-1-86-en.html
8)https://maco.lu.ac.ir/article-1-113-en.html
9)(Some Questions around the Hilbert 16th problem) https://arxiv.org/abs/math/0507516
