9 problems

The QALE Laplacian index-set and Fredholm conjecture. The displayed description of $\mathcal{I}_X$ holds, and the displayed map is Fredholm, with finite-dimensional kernel and coke…

Rational degree conjecture. There exists a $\mathbb{Q}$-valued topological degree ${\rm deg}(f)$ such that

Boundary-image conjecture. For any component ${\mathcal E}_{0}$ of ${\mathcal E}$, $\bar{\Pi}(\partial {\mathcal E}_{0})$ has empty interior in ${\mathcal C}$.

Adiabatic Fredholm family conjecture. The data

Let $P=\Delta+V-\lambda^2$ be the Helmholtz operator on $\mathbb{R}^n$, where $\lambda^2>0$ and $V=\sum_{\alpha\in I}\pi_\alpha^*(V^\alpha)$ is a three-body potential with…

Let $\operatorname{R}(W_{\phi})$ and $\operatorname{N}(W_{\phi})$ denote the range and null space of the operator $W_{\phi}$ on $L^1([0,L])$, and let…

Equivalence-representation conjecture. If $\mathfrak{a}:X\Longrightarrow Y$ is invertible in the category $\mathfrak{Ep}$, then it can be represented by a diagram

The Fredholm property conjecture. The section $\bar{\partial}$ is Fredholm in the following sense: $\mathfrak M_{g,n}(\mathfrak B,\omega)$ has a cover by exploded coordinate neighb…

The exploded Dolbeault-bundle conjecture. The space $\mathfrak E_{g,n}(\mathfrak B,\omega)$ has the structure of a Fréchet orbifold exploded fibration and is a vector bundle over…