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It's a two part question about higher genus open gromov witten theory:
What is the current status and how far are we from a general theory in higher genus?
What are the directions that are being pursued or can be pursued?

Let $\mathcal H = L^2(\mathbb{R}_+^\times, d^\times x)$, and let$$(Df)(x) = x \frac{d}{dx}f(x)$$denote the infinitesimal generator of the scaling action$$f(x) \mapsto f(e^t x).$$
It is well known that:
$D$ is not essentiallyself-adjoint on natural densedomains in $\mathcal H$,...

In HoTT book we have definition of a category, consisting a groupoid as the core of category and Hom sets between objects. In simplicial HoTT, we have Rezk types modeling internal $\infty$-categories in any $\infty$-topos. My question is, can we define...

I have been investigating the existence of non-trivial integer solutions to the Diophantine equation:$A^{4}+B^{4}+C^{4}=2n^{2}D^{4}$where $n$ is a square-free positive integer.
Through extensive computational search (covering $n$ up to $1013$), I have found that this equation possesses extremely large primitive integer solutions for many values of $n$. For instance, when $n=101$, the smallest solution involves integers with...