10 problems

Computational characterization conjecture. (a) There exists an $S\in\mathbb{S}$ such that both $S$ and $\partial S$ are integer density rectifiable. (b) $\Phi\neq\emptyset$. (c)…

Equidistribution conjecture. For every generic $H$, one has

Let $T$ be a metric current with compact support on $\mathbb{R}^d$, and let $\widetilde{T}$ be the classical current it induces. Flat chain conjecture. One has … This conjecture as…

Asymptotic empirical-current conjecture. The total variation measures $\lVert T^{(r)}\rVert$ converge to $\mu_E$ in the weak$^*$ topology of measures supported on $E$. Moreover, if…

Let $X$ be a smooth ambient space and let $Z(f)\subset X$ be the zero locus of $f$. Model chains on $Z(f)$ using currents on $X$, and call a current smooth when it is represented b…

Let $X$ be a smooth space, let $\boldsymbol{Z}(f)$ be the derived zero locus associated to $f$, let $d4aa^f_{\Lambda}$ denote the microlocal homology object associated to…

Let $T$ be a $d$-closed integral current of type $(k,k)$ on a complex manifold. Harvey and Shiffman’s result characterizes such currents as holomorphic chains under an additional h…

Let $Y$ be a three-manifold, let $(A_i,Psi_i)$ be a sequence of solutions of the HaydysWitten equations with $\|\Psi_i\|_{L^2}\to\infty$, and let $Z\subset Y$ be the closed nowhere…

In the Euclidean setting, consider the Gilbert–Steiner minimization problem (P2) and its formulations over normal and integral currents. A mass gap means that the infimum among nor…

Generic algebraic-set convergence conjecture. For a very generic algebraic set of dimension $k-s$, the iterates