Mahan Mj

activity

20052023

most citedRelative Hyperbolicity, Trees of Spaces and Cannon-Thurston Maps

34 citations · 324 across the 55 of their papers we have counts for

collaborators

70 papers

math.GR2023

Commensurated hyperbolic subgroups

Nir Lazarovich, Alex Margolis, Mahan Mj

We show that if H is a non-elementary hyperbolic commensurated subgroup of infinite index in a hyperbolic group G, then H is virtually a free product of hyperbolic surface groups a…

math.GR2023

Greenberg-Shalom's Commensurator Hypothesis and Applications

Nic Brody, David Fisher, Mahan Mj +1

We discuss many surprising implications of a positive answer to a question raised in some cases by Greenberg in the $‘70$ s and more generally by Shalom in the early $2000$ s. We ref…

math.DS2023★ 1 cited

Matings, holomorphic correspondences, and a Bers slice

Mahan Mj, Sabyasachi Mukherjee

There are two frameworks for mating Kleinian groups with rational maps on the Riemann sphere: the algebraic correspondence framework due to Bullett-Penrose-Lomonaco \cite{BP94,BL20…

math.DS2023★ 2 cited

The Sullivan dictionary and Bowen-Series maps

Mahan Mj, Sabyasachi Mukherjee

The Sullivan dictionary between Kleinian groups and rational dynamics describes striking similarities between the fields, both in terms of the objects of study as well as the techn…

math.GR2022

Class number for pseudo-Anosovs

François Dahmani, Mahan Mj

Given two automorphisms of a group $G$ , one is interested in knowing whether they are conjugate in the automorphism group of $G$ , or in the abstract commensurator of $G$ , and how t…

math.PR2022★ 2 cited

Mixing Properties of Stable Random Fields Indexed by Amenable and Hyperbolic Groups

Mahan Mj, Parthanil Roy, Sourav Sarkar

We show that any stationary symmteric $α$ -stable ( $S α S$ ) random field indexed by a countable amenable group $G$ is weakly mixing if and only if it is generated by a null action, ex…

math.SG2022★ 1 cited

The Gromov-Tischler theorem for stratified spaces

Mahan Mj, Balarka Sen

We define a notion of a symplectic structure on stratified spaces, and demonstrate that given a symplectic structure on a stratified space $X$ with integral cohomology class, $X$ c…

math.GT2022

h-Principle for Stratified Spaces

Mahan Mj, Balarka Sen

We extend Gromov and Eliashberg-Mishachev's h-principle on manifolds to stratified spaces. This is done in both the sheaf-theoretic framework of Gromov and the smooth jets framewor…

math.GR2022

Commensurators of normal subgroups of lattices

David Fisher, Mahan Mj, Wouter Van Limbeek

We study a question of Greenberg-Shalom concerning arithmeticity of discrete subgroups of semisimple Lie groups with dense commensurators. We answer this question positively for no…

math.GT2021★ 1 cited

Combination Theorems in Groups, Geometry and Dynamics

Mahan Mj, Sabyasachi Mukherjee

The aim of this article is to give a survey of combination theorems occurring in hyperbolic geometry, geometric group theory and complex dynamics, with a particular focus on Thurst…

math.DS2021★ 4 cited

Combining Rational maps and Kleinian groups via orbit equivalence

Mahan Mj, Sabyasachi Mukherjee

We develop a new orbit equivalence framework for holomorphically mating the dynamics of complex polynomials with that of Kleinian surface groups. We show that the only torsion-free…

math.AG2021

One-relator Sasakian groups

Indranil Biswas, Mahan Mj

We prove that any one-relator group $G$ is the fundamental group of a compact Sasakian manifold if and only if $G$ is either finite cyclic or isomorphic to the fundamental group of…

math.GR2020★ 4 cited

Regluing graphs of Free Groups

Pritam Ghosh, Mahan Mj

Answering a question due to Min, we prove that a finite graph of roses admits a regluing such that the resulting graph of roses has hyperbolic fundamental group.

math.GT2020

Propagating quasiconvexity from fibers

Mahan Mj, Pranab Sardar

Let $1 \to K ⟶ G ⟶ π Q$ be an exact sequence of hyperbolic groups. Let $Q_{1} < Q$ be a quasiconvex subgroup and let $G_{1} = π^{- 1} (Q_{1})$ . Under rela…

math.GR2020

Property (T) for fiber products

Mahan Mj, Arghya Mondal

We study when the fiber product of groups with Property (T) has Property (T).

math.PR2019

First Passage Percolation on Hyperbolic groups

Riddhipratim Basu, Mahan Mj

We study first passage percolation (FPP) on a Gromov-hyperbolic group $G$ with boundary $\partial G$ equipped with the Patterson-Sullivan measure $ν$ . We associate an i.i.d.\ colle…

math.GT2019★ 2 cited

Cubulating Surface-by-free Groups

Jason F. Manning, Mahan Mj, Michah Sageev

Let $1 \to H \to G \to Q \to 1$ be an exact sequence where $H = π_{1} (S)$ is the fundamental group of a closed surface $S$ of genus greater than one, $G$ is hyperbolic and $Q$ is fi…

math.GT2019★ 2 cited

Commensurators of thin normal subgroups and abelian quotients

Thomas Koberda, Mahan Mj

We give an affirmative answer to many cases of a question due to Shalom, which asks if the commensurator of a thin subgroup of a Lie group is discrete. In this paper, let $K < Γ < G$ b…

math.GT2019

Monodromy representations of meromorphic projective structures

Subhojoy Gupta, Mahan Mj

We determine the image of the monodromy map for meromorphic projective structures with poles of orders greater than two. This proves the analogue of a theorem of Gallo-Kapovich-Mar…

math.GT2019

Meromorphic projective structures, grafting and the monodromy map

Subhojoy Gupta, Mahan Mj

A meromorphic projective structure on a punctured Riemann surface $X ∖ P$ is determined, after fixing a standard projective structure on $X$ , by a meromorphic quadratic diff…

math.GT2019★ 3 cited

Tight trees and model geometries of surface bundles over graphs

Mahan Mj

We generalize the notion of tight geodesics in the curve complex to tight trees. We then use tight trees to construct model geometries for certain surface bundles over graphs. This…

math.GR2018★ 3 cited

Commutators, commensurators, and $PSL_{2} (Z)$

Thomas Koberda, Mahan Mj

Let $H < PSL_{2} (Z)$ be a finite index normal subgroup which is contained in a principal congruence subgroup, and let $Φ (H) \neq = H$ denote a term of the lower central…

math.DS2018★ 1 cited

Stable Random Fields, Patterson-Sullivan measures and Extremal Cocycle Growth

Jayadev Athreya, Mahan Mj, Parthanil Roy

We study extreme values of group-indexed stable random fields for discrete groups $G$ acting geometrically on spaces $X$ in the following cases: 1) $G$ acts freely, properly discon…

math.GT2018

Cheeger inequalities for graph limits

Abhishek Khetan, Mahan Mj

We introduce notions of Cheeger constants for graphons and graphings. We prove Cheeger and Buser inequalities for these. On the way we prove co-area formulae for graphons and graph…

Commensurated hyperbolic subgroups

Greenberg-Shalom's Commensurator Hypothesis and Applications

Matings, holomorphic correspondences, and a Bers slice

The Sullivan dictionary and Bowen-Series maps

Class number for pseudo-Anosovs

Mixing Properties of Stable Random Fields Indexed by Amenable and Hyperbolic Groups

The Gromov-Tischler theorem for stratified spaces

h-Principle for Stratified Spaces

Commensurators of normal subgroups of lattices

Combination Theorems in Groups, Geometry and Dynamics

Combining Rational maps and Kleinian groups via orbit equivalence

One-relator Sasakian groups

Regluing graphs of Free Groups

Propagating quasiconvexity from fibers

Property (T) for fiber products

First Passage Percolation on Hyperbolic groups

Cubulating Surface-by-free Groups

Commensurators of thin normal subgroups and abelian quotients

Monodromy representations of meromorphic projective structures

Meromorphic projective structures, grafting and the monodromy map

Tight trees and model geometries of surface bundles over graphs

Commutators, commensurators, and PSL2​(Z)

Stable Random Fields, Patterson-Sullivan measures and Extremal Cocycle Growth

Cheeger inequalities for graph limits

Commutators, commensurators, and $PSL_{2} (Z)$