2 citations · 2 across the 3 of their papers we have counts for
7 papers
Twisting cubic rabbits
Justin Lanier, Rebecca R. Winarski
We solve an infinite family of twisted polynomial problems that are cubic generalizations of Hubbard's twisted rabbit problem. We show how the result of twisting by a power of a ce…
Curve graphs of surfaces with finite-invariance index 1
Justin Lanier, Marissa Loving
In this note we make progress toward a conjecture of Durham--Fanoni--Vlamis, showing that every infinite-type surface with finite-invariance index 1 and no nondisplaceable compact…
Centers of subgroups of big mapping class groups and the Tits alternative
Justin Lanier, Marissa Loving
In this note we show that many subgroups of mapping class groups of infinite-type surfaces without boundary have trivial centers, including all normal subgroups. Using similar tech…
Adding a point to configurations in closed balls
Lei Chen, Nir Gadish, Justin Lanier
We answer the question of when a new point can be added in a continuous way to configurations of distinct points in a closed ball of arbitrary dimension. We show that this is p…
How to hear the shape of a billiard table
Aaron Calderon, Solly Coles, Diana Davis +2
The bounce spectrum of a polygonal billiard table is the collection of all bi-infinite sequences of edge labels corresponding to billiard trajectories on the table. We give methods…
Normal generators for mapping class groups are abundant
Justin Lanier, Dan Margalit
We provide a simple criterion for an element of the mapping class group of a closed surface to have normal closure equal to the whole mapping class group. We apply this to show tha…