11:33 AM
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We can write rational Ramanujan-like series with rational parameters in the following form: $$\sum_{n=0}^{\infty} \left( \prod_{i=0}^{2m} \frac{(s_i)_{n}}{(1)_{n}} \right) z_0^{n} \sum_{k=0}^m a_k n^k = \frac{\sqrt{(-1)^m \chi}}{\pi^m},$$ where $\chi$ is the character (an integer). Zudilin's s...

4 hours later…
3:31 PM
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When students learn multivariable calculus they're typically barraged with a collection of examples of the type "given surface X with boundary curve Y, evaluate the line integral of a vector field Y by evaluating the surface integral of the curl of the vector field over the surface X" or vice ver...

Based on Wayback Machine, it seems that was originally . February 2013 and December 2013.
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Stacks qua moduli spaces were introduced to keep track of nontrivial automorphisms of the objects they parameterize. In essence they are groupoids of objects with some form geometric cohesion. The classic example is principal bundles/torsors, the whole category of which is actually a groupoid. B...

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The category theoretical definition of stacks (as given for instance in Giraud: Cohomologie non-abĂ©lienne) allow for arbitrary categories as targets (the stack condition only involves isomorphisms however). A natural example is the category of quasi-coherent sheaves (which has the category of vec...

> One can more or less arrive at the idea of a groupoid by thinking of bereasoned equivalence relations, elements do not just happen to be equivalent but there are specific, in general several, reasons for them to be equivalent.
I thought that it is a typo, but it seems that bereasoned indeed is a word.
The question was bumped recently by David Roberts - so I checked whether there are some things which can be improved. (Since it was bumped to the frontpage anyway.)