Versions of the following preprints might also be available on the arXiv

[1] Tightness and computing distances in the curve complex pdf
"We offer an explicit algorithm for computing the distance between two curves in the $1$-skeleton of Harvey's curve complex. On the way, we address the non-local finiteness of the curve complex by computational means."

[2] An obstruction to the strong relative hyperbolicity of a group (with J. W. Anderson and J. Aramayona) pdf
"We give a combinatorial criterion that implies both the non-strong relative hyperbolicity and the one-endedness of a finitely generated group. We use this to show that many important classes of groups do not admit a strong relatively hyperbolic group structure and have one end. Applications include surface mapping class groups, the Torelli group, (special) automorphism and outer automorphism groups of most free groups and to Thompson's group F."

[3] Combinatorial rigidity in curve complexes and mapping class groups pdf (correction)
"In all possible cases, we prove that local embeddings between two curve complexes whose complexities do not increase from domain to codomain are induced by surface homeomorphism. This is our first main result. From this we can deduce our second, a strong local co-Hopfian result for mapping class groups."

[4] Uniformly exponential growth and mapping class groups of surfaces (with J. W. Anderson and J. Aramayona) pdf "We show that the mapping class group (as well as closely related groups) of an orientable surface with finitely generated fundamental group has uniformly exponential growth. We further demonstrate the uniformly non-amenability of many of these mapping class groups."

[5] On the distance between two Seifert surfaces of a knot (with M. Sakuma) pdf
"For a knot $K$ in $\B{S}^{3}$, Kakimizu introduced a simplicial complex whose vertices are all the isotopy classes of minimal genus spanning surfaces for $K$. The first purpose of this paper is to prove the $1$-skeleton of this complex has diameter bounded by a function quadratic in knot genus, whenever $K$ is atoroidal. The second purpose of this paper is to prove the intersection number of two minimal genus spanning surfaces for $K$ is also bounded by a function quadratic in knot genus, whenever $K$ is atoroidal. As one application, we prove the simple connectivity of Kakimizu's complex among all atoroidal genus $1$ knots."

[6] Totally geodesic subgraphs of the pants complex (with J. Aramayona and H. Parlier) pdf
"Our main theorem asserts that every Farey graph embedded in the $1$-skeleton of the pants complex of any finite type surface is totally geodesic."

[7] Constructing convex planes in the pants complex (with J. Aramayona and H. Parlier) pdf
"Our main theorem identifies a class of totally geodesic subgraphs of the $1$-skeleton of the pants complex, each isomorphic to the product of two Farey graphs. We deduce the existence of many convex planes in the $1$-skeleton of the pants complex."

[8] An acylindricity theorem for the mapping class group pdf
"We study the usual action of the mapping class group of a surface on the $1$-skeleton of the curve complex from a computational perspective."

[9] Computing distances in two pants complexes revising pdf
"We offer an explicit algorithm for the computing of distances between any two vertices in the 1-skeleton of the pants complex of the 5-holed sphere and the 2-holed torus. On the way, we address the lack of local finiteness in these graphs by computational means."