21 citations · 105 across the 17 of their papers we have counts for
22 papers
Minimal subdynamics and minimal flows without characteristic measures
Joshua Frisch, Brandon Seward, Andy Zucker
Given a countable group and a -flow , a measure is called characteristic if it is -invariant. Frisch and Tamuz asked about the existence o…
Borel asymptotic dimension and hyperfinite equivalence relations
Clinton Conley, Steve Jackson, Andrew Marks +2
A long standing open problem in the theory of hyperfinite equivalence relations asks if the orbit equivalence relation generated by a Borel action of a countable amenable group is…
Bernoulli shifts with bases of equal entropy are isomorphic
Brandon Seward
We prove that if is a countably infinite group and and are probability spaces having equal Shannon entropy, then the Bernoulli shifts $G \curvearrowright (L^G…
The Koopman representation and positive Rokhlin entropy
Brandon Seward
In a prior paper, the author generalized the classical factor theorem of Sinai to actions of arbitrary countably infinite groups. In the present paper, we use this theorem and the…
Positive entropy actions of countable groups factor onto Bernoulli shifts
Brandon Seward
We prove that if a free ergodic action of a countably infinite group has positive Rokhlin entropy (or, less generally, positive sofic entropy) then it factors onto all Bernoulli sh…
Continuous Combinatorics of Abelian Group Actions
Su Gao, Steve Jackson, Edward Krohne +1
This paper develops techniques which are used to answer a number of questions in the theory of equivalence relations generated by continuous actions of abelian groups. The methods…
Folner tilings for actions of amenable groups
Clinton T. Conley, Steve Jackson, David Kerr +3
We show that every probability-measure-preserving action of a countable amenable group G can be tiled, modulo a null set, using finitely many finite subsets of G ("shapes") with pr…
Hyperfiniteness and Borel combinatorics
Clinton Conley, Steve Jackson, Andrew Marks +2
We study the relationship between hyperfiniteness and problems in Borel graph combinatorics by adapting game-theoretic techniques introduced by Marks to the hyperfinite setting. We…
Weak containment and Rokhlin entropy
Brandon Seward
We define a new notion of weak containment for joinings, and we show that this notion implies an inequality between relative Rokhlin entropies. This leads to new upper bounds to Ro…
Cost, -Betti numbers and the sofic entropy of some algebraic actions
Damien Gaboriau, Brandon Seward
In 1987, Ornstein and Weiss discovered that the Bernoulli -shift over the rank two free group factors onto the seemingly larger Bernoulli -shift. With the recent creation of…
Forcing constructions and countable Borel equivalence relations
Su Gao, Steve Jackson, Edward Krohne +1
We prove a number of results about countable Borel equivalence relations with forcing constructions and arguments. These results reveal hidden regularity properties of Borel comple…
Krieger's finite generator theorem for actions of countable groups I
Brandon Seward
For an ergodic probability-measure-preserving action of a countable group , we define the Rokhlin entropy to be the infimu…
Borel structurability on the 2-shift of a countable group
Brandon Seward, Robin D. Tucker-Drob
We show that for any infinite countable group and for any free Borel action there exists an equivariant class-bijective Borel map from to the free pa…
Every action of a non-amenable group is the factor of a small action
Brandon Seward
It is well known that if is a countable amenable group and factors onto , then the entropy of the first action must be gr…
Locally Nilpotent Groups and Hyperfinite Equivalence Relations
Scott Schneider, Brandon Seward
A long standing open problem in the theory of hyperfinite equivalence relations asks if the orbit equivalence relation generated by a Borel action of a countable amenable group is…
Arbitrarily Large Residual Finiteness Growth
Khalid Bou-Rabee, Brandon Seward
The residual finiteness growth of a group quantifies how well approximated the group is by its finite quotients. In this paper, we construct groups with arbitrarily large residual…
Ergodic actions of countable groups and finite generating partitions
Brandon Seward
We prove that if an ergodic action of a countable group on a probability space admits a generating partition having finite Shannon entropy then it admits a finite generating partit…
Finite entropy actions of free groups, rigidity of stabilizers, and a Howe-Moore type phenomenon
Brandon Seward
We study a notion of entropy for probability measure preserving actions of finitely generated free groups, called f-invariant entropy, introduced by Lewis Bowen. In the degenerate…
A subgroup formula for f-invariant entropy
Brandon Seward
We study a measure entropy for finitely generated free group actions called f-invariant entropy. The f-invariant entropy was developed by Lewis Bowen and is essentially a special c…
Group Colorings and Bernoulli Subflows
Su Gao, Steve Jackson, Brandon Seward
In this paper we study the dynamics of Bernoulli flows and their subflows over general countable groups from the symbolic and topological perspectives. We study free subflows (subf…
Burnside's Problem, spanning trees, and tilings
Brandon Seward
In this paper we study geometric versions of Burnside's Problem and the von Neumann Conjecture. This is done by considering the notion of a translation-like action. Translation-lik…
Generalizing Magnus' characterization of free groups to some free products
Khalid Bou-Rabee, Brandon Seward
A residually nilpotent group is \emph{-parafree} if all of its lower central series quotients match those of a free group of rank . Magnus proved that -parafree groups of…