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...

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...

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...