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Hitchin’s Moduli Space in Geometric Langlands is obtained by a reduction from an infinite-dimensional space of connections. See the original paper by Hitchin Stable bundles and integrable systems (th …

The philosophy I subscribe to: tangent vector is an object defined by a base point and a direction. When you want to make a formal definition out of it you do the following things: for schemes, you …

Eh, it depends on what you need to know about orbifolds. Here are the basic facts you certainly need to know: orbifold is a smooth manifold X together with a very good finite group G action — it shou …

I've never seen such an interesting analysis problem :) Here is my current state, which I post because I like this form in itself and because I hope somebody finishes it. We can reformulate what we w …

If your question is about complex line bundles up to an algebraic isomorphism, such bundles are classified by [the group of divisors](http://en.wikipedia.org/wiki/Divisor_(algebraic_geometry) for any …

I think the question Is it possible to capture a sphere in a knot? is an excellent one-step problem.

The definition of symbol as presented in Wikipedia is not invariant — only the highest order terms. Some textbooks call those higher order terms symbols (Wikipedia suggests the name principal symbol), …

What's the most natural way to establish the asymptotics of $\Delta$ on a compact Riemannian manifold $M$ of dimension $N$? The asymptotics should be $$ \#\{v < A^2\} = \mathrm{const}\ast\mathrm{vol …