7 problems

Bullett–Freiberger general mating conjecture. All polynomials with connected Julia set can be mated with Hecke groups as correspondences.

Let $K$ be a nonarchimedean local field with residue characteristic $p$, let $X/K$ be a proper smooth variety purely of dimension $n$, let $\sigma \in W_K$, and let…

Bullett–Penrose conjecture. The connectedness locus of this family of algebraic correspondences is homeomorphic to the Mandelbrot set.

Let $d$ be the parameter defining the Hurwitz space $\mathcal{H}_{2d-1}$, and let $P_1,P_2\in\mathcal{H}_{2d-1}$. For each $P_i$, let $\mathfrak{B}(P_i)$ be the corresponding Bers…

The dynamics of Kleinian groups and rational maps are two classes of conformal dynamical systems. Fatou's conjecture. These classes may fit into a general theory of algebraic corre…

Correspondence homomorphism conjecture. (i) For any $\alpha\in c_{\mathrm{equi}}(X\times Y/X,0)$, $\mathrm{tr}_{\alpha}$ satisfies (M1). (ii) For any…

Let $X$ be a strictly semistable scheme over ${\mathcal O}$, and let $\Gamma_{1,K}$ and $\Gamma_{2,K}$ be correspondences on $X_K$. Write $\Gamma_K=\Gamma_{2,K}\circ\Gamma_{1,K}$,…