56 citations · 120 across the 14 of their papers we have counts for
6 papers · 1 filter
Conjugation curvature for Cayley graphs
Assaf Bar-Natan, Moon Duchin, Robert Kropholler
We introduce a notion of Ricci curvature for Cayley graphs that can be thought of as "medium-scale" because it is neither infinitesimal nor asymptotic, but based on a chosen finite…
Random nilpotent groups I
Matthew Cordes, Moon Duchin, Yen Duong +2
We study random nilpotent groups in the well-established style of random groups, by choosing relators uniformly among freely reduced words of (nearly) equal length and letting the…
Rational growth in the Heisenberg group
Moon Duchin, Michael Shapiro
A group presentation is said to have rational growth if the generating series associated to its growth function represents a rational function. A long-standing open question asks w…
Equations in nilpotent groups
Moon Duchin, Hao Liang, Michael Shapiro
We show that there exists an algorithm to decide any single equation in the Heisenberg group in finite time. The method works for all two-step nilpotent groups with rank-one commut…
Filling loops at infinity in the mapping class group
Aaron Abrams, Noel Brady, Pallavi Dani +2
We study the Dehn function at infinity in the mapping class group, finding a polynomial upper bound of degree four. This is the same upper bound that holds for arbitrary right-angl…
Pushing fillings in right-angled Artin groups
Aaron Abrams, Noel Brady, Pallavi Dani +2
We construct "pushing maps" on the cube complexes that model right-angled Artin groups (RAAGs) in order to study filling problems in certain subsets of these cube complexes. We use…