7 problems

For each genus $g$, let $\delta_{g,0}$ denote the minimum dilatation among pseudo-Anosov maps on the closed surface of genus $g$, and let $\mu$ be the golden ratio. Hironaka's gold…

Fix $m\geq 2$, and let $f_1,f_2\in\operatorname{PA}(m)$ be $m$-modal standard PCP zig-zags of pseudo-Anosov type. Let $\lambda_i$ be the growth rate of $f_i$, and let…

A real number $bb>1$ is a bi-Perron unit if it is a positive real algebraic unit whose Galois conjugates lie in the annulus … except possibly for $bb$ and $bb^{-1}$. Bi-Perron suff…

McMullen's conjecture. Every bi-Perron unit is the dilatation of some pseudo-Anosov homeomorphism.

Let $\delta_g^+$ be the minimum dilatation for orientable pseudo-Anosov mapping classes on the closed surface of genus $g$. For a polynomial $p(t)$, let … and define … The Lanneau–…

Let $S$ be a closed surface and let $\phi$ be a pseudo-Anosov mapping class with dilatation $\lambda(\phi)$. For a fibered cohomology class, let $L(S,\phi)$ denote the correspondin…

Thurston's conjecture. The pseudo-Anosov dilatations are precisely the algebraic units that are Perron and larger than the Galois conjugates of their inverses.