Lewis Bowen

Measure conjugacy invariants for actions of countable sofic groups

Sofic groups were defined implicitly by Gromov in [Gr99] and explicitly by Weiss in [We00]. All residually finite groups (and hence every linear group) is sofic. The purpose of this paper is to introduce, for every countable sofic group

Entropy for expansive algebraic actions of residually finite groups

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The ergodic theory of free group actions: entropy and the f -invariant

, a family of measure-conjugacy invariants for measure-preserving

Sofic entropy and amenable groups

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Densest Packing of Equal Spheres in Hyperbolic Space

-actions on probability spaces. These invariants generalize Kolmogorov-Sinai entropy for actions of amenable groups. They are computed exactly for Bernoulli shifts over

Invariant random subgroups of lamplighter groups

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Fluid-Solid Transition in a Hard-Core System

, leading to a complete classification of Bernoulli systems up to measure-conjugacy for many groups including all countable linear groups. Recent rigidity results of Y. Kida and S. Popa are utilized to classify Bernoulli shifts over mapping class groups and property T groups up to orbit equivalence and von Neumann equivalence respectively.

Geometric covering arguments and ergodic theorems for free groups

We prove a formula for the sofic entropy of expansive principal algebraic actions of residually finite groups, extending recent work of Deninger and Schmidt.

Pointwise ergodic theorems beyond amenable groups

Previous work introduced two measure-conjugacy invariants: the

Free groups in lattices

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