Möbius strips and differential equations One of the most…
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Möbius strips and differential equations
One of the most important theorems in my area of research is the Riemann--Hilbert correspondence. Roughly, it tells you that you can convert differential equations into certain geometric objects, and that this conversion process loses no information. In particular, one can convert questions about differential equations into geometric questions, and conversely one can convert certain geometric questions into problems about differential equations.
In https://hidden-phenomena.com/articles/monodromy , my friend and I wrote a blog post showing this example in a very simple case. The differential equation in question is very simple: f'(x) = f(x)/2x, and the geometric object is related to the Möbius strip!
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One of the most important theorems in my area of research is the Riemann--Hilbert correspondence. Roughly, it tells you that you can convert differential equations into certain geometric objects, and that this conversion process loses no information. In particular, one can convert questions about differential equations into geometric questions, and conversely one can convert certain geometric questions into problems about differential equations.
In https://hidden-phenomena.com/articles/monodromy , my friend and I wrote a blog post showing this example in a very simple case. The differential equation in question is very simple: f'(x) = f(x)/2x, and the geometric object is related to the Möbius strip!
#science
source
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