MathOverflow

A complex manifold is said to admit a holomorphic coordinate chart around a point if there exists a neighborhood (U) of the point and a map[\phi : U \to \mathbb{C}^n]such that (\phi) is a homeomorphism onto its image and the transition maps between overlapping...

In 09.2020 by pure chance I discovered the YouTube channel of Richard Borcherds where he gives graduate courses in Group Theory, Algebraic Geometry, Schemes, Commutative Algebra, Galois Theory, Lie Groups, and Modular forms! (and an undergraduate courses...

I am looking for reference for inequalities of the following form where all spaces are taken on bounded domains subset of $\mathbb{R}^d$ with regular boundaries:
$$|u|_{L^2}≤C|u|_{H^1}^{\theta}|u|_{L^{\phi}}^{1-\theta}.$$
E.g. generalized Gagliardo–Nirenberg inequalities using Orlicz spaces in a very special case....

Can you give me an example of a quandle $Q$ and a knot $K$ such that $K$ only has trivial $Q$-colorings but $K\#K$ has nontrivial $Q$-colorings?