Research

Current Projects

1. (joint with George Shaji) Automorphisms of the Grand Arc Graph. 

Abstract: We answer a version of Ivanov's metaconjecture for the grand arc graph of a large class of infinite-type surfaces. Specifically, we prove that the extended mapping class group of these surfaces is isomorphic to the group of continuous automorphisms of the grand arc graph. 

2. (joint with Johanna Mangahas and Roberta Shapiro) Non-uniform-perfection of Homeo_0(S).

Abstract: Inspired by the work of Bowden, Hensel and Webb, we show that to show that if S has at least 3 ends or boundary components, then Homeo_0(S) (the identity component of the group of homeomorphisms of a surface S to itself) is not uniformly perfect. To do so, we study the action of Homeo_0(S) on the prescribed fine arc graph of S. 

Past Projects

1. (joint with Carolyn Abbott and Assaf Bar-Natan) Gromov Boundary of the Grand Arc Graph.

Abstract: We describe a dense subset of the Gromov boundary of the grand arc graph of an infinite-type surface as a space of geodesic laminations, analogous to Klarreich's description of the Gromov boundary of the curve complex. After showing that the grand arc graph satisfies a bounded geodesic image theorem, we also prove that the boundary is not compact.

2. A conjecture on the lengths of filling pairs - Bidyut Sanki, Arya Vadnere. Published in Geometriae Dedicata, November 2020. DOI - 10.1007/s10711-020-00586-8

Abstract: We prove a lower bound for the filling pair systolé function (which sums the hyperbolic lengths of a filling pair of curves, given a hyperbolic metric) for closed hyperbolic surfaces with genus at least 2. 

3. Isoperimetric Inequality for Disconnected Regions - Bidyut Sanki, Arya Vadnere. Published in Geometriae Dedicata, November 2024. DOI - 10.1007/s10711-024-00961-9

Abstract: We prove a version of the isoperimetric inequality for configurations of finitely many polygons.