10 citations · 14 across the 8 of their papers we have counts for
10 papers
On indefinite integral ternary quadratic forms
Alexander Gamburd, Amit Ghosh, Peter Sarnak +1
We resolve two problems pertaining to indefinite integral ternary quadratic forms, one highlighted by Margulis and the other initiated by Serre, both from 1990. To do so we develop…
Short words of infinite order
Junho Peter Whang
Given an infinite linear group with a finite set of generators, we show that the shortest word length of an element of infinite order has an upper bound that depends only on the nu…
On finite categories of algebraic varieties
Junho Peter Whang
We prove that the finiteness of a finitely generated category of irreducible algebraic varieties over a field of characteristic zero is decidable. We also obtain a Burnside finiten…
On periodic orbits of polynomial maps
Junho Peter Whang
We prove the existence of an effective universal upper bound for the order of any integral periodic orbit of any integral algebraic dynamical system in a fixed ambient space. Using…
Surfaces, braids, Stokes matrices, and points on spheres
Yu-Wei Fan, Junho Peter Whang
Moduli spaces of points on -spheres carry natural actions of braid groups. For , , and , we prove that these symmetries extend to actions of mapping class groups of p…
The rank two -curvature conjecture on generic curves
Anand Patel, Ananth N. Shankar, Junho Peter Whang
We prove the -curvature conjecture for rank two vector bundles with connection on generic curves, by combining deformation techniques for families of varieties and topological a…
Arithmetic of curves on moduli of local systems
Junho Peter Whang
We investigate the arithmetic of algebraic curves on coarse moduli spaces for special linear rank two local systems on surfaces with fixed boundary traces. We prove a structure the…
Nonlinear descent on moduli of local systems
Junho Peter Whang
We establish a structure theorem for the integral points on moduli of special linear rank two local systems over surfaces, using mapping class group descent and boundedness results…
Surface group representations in with finite mapping class orbits
Indranil Biswas, Subhojoy Gupta, Mahan Mj +1
Given an oriented surface of positive genus with finitely many punctures, we classify the finite orbits of the mapping class group action on the moduli space of semisimple complex…
Global geometry on moduli of local systems for surfaces with boundary
Junho Peter Whang
We show that every coarse moduli space, parametrizing complex special linear rank two local systems with fixed boundary traces on a surface with nonempty boundary, is log Calabi-Ya…