6 problems

Let ${\mathcal{A}}$ be a primitive Apollonian circle packing. Let $S_{\mathcal{A}}$ be the set of missing curvatures that do not lie in any of the quadratic or quartic obstruction…

The local-global multiplicity conjecture. If $t\asymp X$ is admissible, then

Let $\Gamma(2)'$ be the commutator subgroup of the level-2 principal congruence subgroup $\Gamma(2)\subset\operatorname{SL}_2(\mathbb{Z})$, and let an integer $t$ be admissible if,…

Consider the periodic continued fractions $[\overline{a_1,\ldots,a_k}]$ with entries in $\mathbb{Q}(\sqrt{5})$ satisfying $a_i\leq 2$. McMullen's exponential-growth conjecture. The…

Cohen's refined Zaremba conjecture. The multiplicity satisfies

Let $H(\alpha,\beta)$ denote a hyperbolic hypergeometric monodromy group, where $\alpha$ and $\beta$ are the parameter tuples defining the corresponding hypergeometric equation. A…