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The notation $*/\!/G$ refers to the topological groupoid with a single object, whose morphisms are described by the compact Lie group $G$. The double slash in this context means groupoid quotient, an …

The half-edges incident to a 4-valent vertex can be labeled 1,2,3,4. There are three ways to split them into pairs: 12-34, 13-24, and 14-23. Another way to think of the three pairings is by consider …

The ring of functions on your supermanifold is $C^\infty(\mathbb{R}) \otimes \mathbb{C}[a,b]$, where $a$ and $b$ are odd. The even part is then $C^\infty(\mathbb{R}) \oplus C^\infty(\mathbb{R})ab$, w …

If I'm not mistaken, this is the associative algebra of algebraic differential operators on the torus $\mathbb{G}_{m,\mathbb{C}}^2$. It is the tensor product of two copies of $w_\infty$, not the dire …

I'm not a mathematical physicist, so parts of this may be wrong. In quantum field theory, one encounters operators that are supported at points in spacetime, or at least are very local. For example …

The Feigin-Frenkel isomorphism is globalized by the global quantum geometric Langlands conjecture, proposed by Stoyanovsky, and refined by Gaitsgory and his collaborators. See Gaitsgory's 2016 collec …

I'm not an expert in this area, but I've heard that algebraic topologists run into congruences quite often. For example, the stable homotopy groups of spheres are almost always finite abelian groups, …

I think the suggested example is not a good fit for illustrating a tensor product decomposition, because $L^2$ functions on an interval are most naturally identified with states of a single particle i …

I'm not an expert on black holes, but I can give you a couple pointers. From work of Bekenstein and Hawking in the 1970s, we are pretty sure that macroscopic black holes in our 3+1 dimensional univer …

You get (approximately) elliptic trajectories in 2D phase space whenever you are close to a nondegenerate stable equilibrium. This is one way to explain why harmonic oscillators are so universal. Si …

I don't know what paper you are reading, but you can find examples in most textbooks. For example, Frenkel and Ben-Zvi's book "Vertex algebras and algebraic curves" has a treatment of modules in chap …

$S^3 \times S^5$ has isometry group $SO_4(\mathbb{R}) \times SO_6(\mathbb{R})$, which has $SU(2) \times SU(2) \times SU(4)$ as a four-fold cover. Since it appears that you aren't worrying too much ab …

I suspect the expected structure of $Rep(V)$ common to all vertex algebras $V$ is something like "abelian pseudomonoidal category" and I don't think you can say much else. The abelian structure follo …

This "example" may seem like rather weak sauce, but I think you could take any smooth quasi-projective family $X \to S$ for $S$ any scheme, since you can pull back a fiberwise symplectic form from pro …

If your VOA $V$ is not rational, then it is quite unlikely that its category of representations is a modular tensor category. That is, you can safely conclude that Theorem 3 contains an unstated assu …