The Calogero-Sutherland operator on the space of homogeneous symmetric polynomials in $n$ variables is defined by $$ \frac{\alpha}{2}\sum_{i=1}^n x_i^2\frac{\partial^2}{\partial x_i^2} + \frac{1}{2}\sum_{1\leqslant i < j \leqslant n} \left(\frac{x_i+x_j}{x_i-x_j}\right)\left(x_i\frac{\partial}{\p...

For someone who is new to Lie $\infty$-algebras, the title looks confusing. This is how Lie $\infty$-algebras are commonly described, for example, see What is a homotopy between $L_\infty$-algebra morphisms Many people think of Lie algebroids as NQ-manifolds with the excuse that it is easy to wri...

Let $X\subset \mathbb{P}^3$ be the surface defined by the equation $xy-zw=0$, and consider the curve $E \subset X$ defined by the equation $x=z=0$. Question. Can $E$ be contracted to a point?

We know for two vector bundles $E$ and $F$ over compact manifold $M$,an elliptic operator $D:\Gamma(\mathrm{E})\to \Gamma(\mathrm{F})$ is automatically Fredholm. And for the case $M$ is noncompact, in particular manifolds with cylindrical ends,in this paper: http://www.numdam.org/article/ASNSP_19...

Given a monic irreducible polynomial f in Z[x], I'd like to know for how many primes p we have that f mod p is irreducible. In the link: How many primes stay inert in a finite (non-cyclic) extension of number fields?, the analyzation gives rise to a characterisation in the case Q[x]/(f) is Galois...