15 citations · 18 across the 8 of their papers we have counts for
9 papers
Stratified Gradient Hamiltonian Vector Fields and Collective Integrable Systems
Benjamin Hoffman, Jeremy Lane
We construct completely integrable systems on the dual of the Lie algebra of any compact Lie group with respect to the standard Lie-Poisson structure. These systems generalize…
Action-angle coordinates on coadjoint orbits and multiplicity free spaces from partial tropicalization
Anton Alekseev, Benjamin Hoffman, Jeremy Lane +1
Coadjoint orbits and multiplicity free spaces of compact Lie groups are important examples of symplectic manifolds with Hamiltonian groups actions. Constructing action-angle variab…
Toric Symplectic Stacks
Benjamin Hoffman
We give an intrinsic definition of toric symplectic stacks, and show that they are classified by simple convex polytopes equipped with some additional combinatorial data. This gene…
Concentration of symplectic volumes on Poisson homogeneous spaces
Anton Alekseev, Benjamin Hoffman, Jeremy Lane +1
For a compact Poisson-Lie group , the homogeneous space carries a family of symplectic forms , where is in the positive Weyl chamber and $s…
Stacky Hamiltonian actions and symplectic reduction
Benjamin Hoffman, Reyer Sjamaar, Chenchang Zhu
We introduce the notion of a Hamiltonian action of an étale Lie group stack on an étale symplectic stack and establish versions of the Kirwan convexity theorem, the Meyer-Marsden-W…
Langlands Duality and Poisson-Lie Duality via Cluster Theory and Tropicalization
Anton Alekseev, Arkady Berenstein, Benjamin Hoffman +1
Let be a connected semisimple Lie group. There are two natural duality constructions that assign to it the Langlands dual group and the Poisson-Lie dual group . T…
Poisson Structures and Potentials
Anton Alekseev, Arkady Berenstein, Benjamin Hoffman +1
We introduce a notion of weakly log-canonical Poisson structures on positive varieties with potentials. Such a Poisson structure is log-canonical up to terms dominated by the poten…
Iterated functions and the Cantor set in one dimension
Benjamin Hoffman
In this paper we consider the long-term behavior of points in under iterations of continuous functions. We show that, given any Cantor set embedded in ${\mathbb…
A note on triangulations of sum sets
Karoly J. Boroczky, Benjamin Hoffman
For finite sets A and B in the plane, we write A+B to denote the set of sums of the elements of A and B. In addition, we write tr(A) to denote the common number of triangles in any…