9 problems

Logarithmic action conjecture. The formula above remains true for general smooth subordination evolution. This is posed as an open question concerning the extension of the variatio…

Let $\mathcal{G}$ be a graph with fields $\phi_i,\tilde\phi_i$ describing branching trees, and let $\mathfrak{r}$ and $\mathfrak{t}$ be graph points. Write…

Consider the Hastings–Levitov random aggregation model with parameter $\alpha\in\mathbb{R}$, where $\alpha$ controls the regularization of the growth dynamics. The regimes…

Let $G$ be a nested fractal graph, and let $o$ be a starting vertex such that every graph-metric ball $B_o(n)$ has spatial symmetry. Consider the four single-source Laplacian growt…

Let a fixed state space support four Laplacian growth models: internal diffusion-limited aggregation (IDLA), rotor-router aggregation, divisible sandpiles, and abelian sandpiles. F…

In Laplacian growth, the interface evolves under zero-surface-tension dynamics, and a nonsingular solution is one that remains free of singularities during the evolution. In the si…

Laplacian growth is interface evolution driven by Laplacian fields, including Hele-Shaw flow, and the domain may have arbitrary connectivity. Surface tension is assumed to be small…

A Hele-Shaw flow describes viscous fluid motion in a narrow cell, and its connectivity is the connectivity of the fluid domain. Surface tension is neglected, so the interface evolv…

In Laplacian growth, let the weak solution be defined through the equivalence between the distribution of zeros of the orthogonal polynomials and the branch cut of the Schwarz func…