About

Lewis Bowen is a professor of mathematics at The University of Texas at Austin, holding the Jane and Roland Blumberg Centennial Professorship in Mathematics. He earned both his bachelor's degree in 1997 and his Ph.D. in 2002 from UT Austin. Before returning to UT Austin in 2012, Bowen held academic positions at institutions including the University of Hawai'i, Texas A&M University, and Indiana University. His research focuses on ergodic theory, probability theory, and dynamical systems, with particular interest in the ergodic theory of non-amenable group actions and geometric group theory. Bowen's work has been recognized with several honors, including being named a fellow of the American Mathematical Society in its inaugural class in 2012 and receiving the Brin Prize in Dynamical Systems in 2017.

Research topics

• Data Mining
• Computer Science
• Mathematics
• Pure mathematics
• Econometrics
• Discrete mathematics
• Physics
• Thermodynamics
• Statistics
• Mathematical analysis

Selected publications

• Metric criteria for fixed price of countable groups

  ArXiv.org · 2025-10-06

  preprintOpen accessSenior author

  We establish general criteria for a countable group $Γ$ to have fixed price 1 depending on a choice of left-invariant proper metric on $Γ$. We apply this criterion to show that if $Γ_1,Γ_2$ are two countable groups satisfying a certain growth condition then $Γ_1\times Γ_2$ has fixed price 1. For example, $Γ\times Γ$ has fixed price 1 for any countable group $Γ$.

  PublisherOA PDFDOI

• Locally compact sofic entropy theory

  Transactions of the American Mathematical Society Series B · 2025-02-06

  articleOpen access1st authorCorresponding

  This paper generalizes sofic entropy theory, in both the topological and measure-theory settings, to actions of locally compact groups. We prove invariance under topological and measure conjugacy of these entropies and establish the variational principle.

  PublisherOA PDFDOI

• Surjunctivity does not characterize cosoficity of invariant random subgroups

  ArXiv.org · 2025-11-10

  preprintOpen access1st authorCorresponding

  A group is surjunctive if every injective cellular automaton on it is also surjective. Gottschalk famously conjectured that all groups are surjunctive. This remains a central open problem in symbolic dynamics and descriptive set theory. Gromov and Weiss termed the notion of sofic groups, and proved that all such groups are surjunctive, providing the largest class of groups which satisfy Gottschalk's conjecture. It is still open to decide whether all groups are sofic. This became a major open problem in group theory, and is related to other well known problems such as the Aldous--Lyons conjecture in probability theory and to Connes' embedding problem in the theory of operator algebras. A complementary natural question to ask is: Does the reverse implication to Gromov and Weiss' result holds? Namely, are all surjunctive groups sofic? As currently there are no known non-sofic groups, answering this problem in the negative in the category of groups is still out of reach. This paper resolves this problem in the generalized setup of invariant random subgroups of free groups (IRSs), where non (co)sofic objects were recently shown to exist by Lubotzky, Vidick and the two authors. Specifically, we prove that there exists a surjunctive non (co)sofic IRS, resolving the aforementioned problem in the negative. Our proof uses a complexity theoretic approach, and in particular a recent development due to Manzoor, as well as the theory of Rokhlin entropy developed by Seward and others. As a byproduct of our proof technique, the non (co)sofic IRS we provide satisfies a condition stronger than surjunctivity; it satisfies a version of Seward's maximal Rokhlin entropy of Bernoulli Shifts (RBS) criterion.

  PublisherOA PDFDOI

• ALGEBRAIC DYNAMICAL SYSTEMS FROM LDPC CODES SATISFY A STRONG NEGATION OF THE WEAK PINSKER PROPERTY

  Journal of the Institute of Mathematics of Jussieu · 2025-06-09

  articleOpen accessCorresponding

  Abstract We construct an explicit algebraic example of a subshift of finite type over a group $\Gamma $ with an invariant Markov measure which has completely positive sofic entropy (with respect to ‘most’ sofic approximations) and yet does not have a direct Bernoulli factor because its model spaces shatter into exponentially many clusters of sub-exponential size. The example and its analysis are related to random low-density parity-check (LDPC) codes.

  PublisherDOI

• The Aldous--Lyons Conjecture II: Undecidability

  arXiv (Cornell University) · 2024-12-30

  preprintOpen access1st authorCorresponding

  This paper, and its companion [BCLV24], are devoted to a negative resolution of the Aldous--Lyons Conjecture [AL07, Ald07]. In this part we study tailored non-local games. This is a subclass of non-local games -- combinatorial objects which model certain experiments in quantum mechanics, as well as interactive proofs in complexity theory. Our main result is that, given a tailored non-local game $G$, it is undecidable to distinguish between the case where $G$ has a special kind of perfect strategy, and the case where every strategy for $G$ is far from being perfect. Using a reduction introduced in the companion paper [BCLV24], this undecidability result implies a negative answer to the Aldous--Lyons conjecture. Namely, it implies the existence of unimodular networks that are non-sofic. To prove our result, we use a variant of the compression technique developed in MIP*=RE [JNV+21]. Our main technical contribution is to adapt this technique to the class of tailored non-local games. The main difficulty is in establishing answer reduction, which requires a very careful adaptation of existing techniques in the construction of probabilistically checkable proofs. As a byproduct, we are reproving the negation of Connes' embedding problem [Con76] -- i.e., the existence of a $\mathrm{II}_1$-factor which cannot be embedded in an ultrapower of the hyperfinite $\mathrm{II}_1$-factor -- first proved in [JNV+21], using an arguably more streamlined proof. In particular, we incorporate recent simplifications from the literature [dlS22b, Vid22] due to de la Salle and the third author.

  PublisherOA PDFDOI

• Entropy for actions of free groups under bounded orbit-equivalence

  Israel Journal of Mathematics · 2024-08-04 · 1 citations

  article1st author
  PublisherDOI

• The Aldous--Lyons Conjecture I: Subgroup Tests

  arXiv (Cornell University) · 2024-07-31 · 1 citations

  preprintOpen access1st authorCorresponding

  This paper, and its companion [BCV24], are devoted to a negative resolution of the Aldous--Lyons Conjecture [AL07, Ald07]. This conjecture, originated in probability theory, is well known (cf. [Gel18]) to be equivalent to the statement that every invariant random subgroup of the free group is co-sofic. We disprove this last statement. In this part we introduce subgroup tests. These tests are finite distributions over continuous functions from the space of subgroups of the free group to $\{0,1\}$. Subgroup tests provide a general framework in which one can study invariant random subgroups of the free group. Classical notions such as group soficity and group stability arise naturally in this framework. By the correspondence between subgroups of the free group and Schreier graphs, one can view subgroup tests as a property testing model for certain edge-labeled graphs. This correspondence also provides the connection to random networks. Subgroup tests have values, which are their asymptotic optimal expectations when integrated against co-sofic invariant random subgroups. Our first main result is that, if every invariant random subgroup of the free group is co-sofic, then one can approximate the value of a subgroup test up to any positive additive constant. Our second main result is an essentially value preserving correspondence between certain non-local games and subgroup tests. By composing this correspondence with a stronger variant of the reduction in MIP*=RE [JNV+21], proved in the companion paper [BCV24], we deduce that approximating the sofic value of a subgroup test is as hard as the Halting Problem, and in particular, undecidable. The combination of our two main results proves the existence of non co-sofic invariant random subgroups of the free group.

  PublisherOA PDFDOI

• Locally compact sofic entropy theory

  arXiv (Cornell University) · 2023-11-04

  preprintOpen access1st authorCorresponding

  This paper generalizes sofic entropy theory, in both the topological and measure-theory settings, to actions of locally compact groups. We prove invariance under topological and measure conjugacy of these entropies and establish the variational principle.

  PublisherOA PDFDOI

• Algebraic dynamical systems from LDPC codes satisfy a strong negation of the weak Pinsker property

  arXiv (Cornell University) · 2023-12-28 · 1 citations

  preprintOpen access

  We construct an explicit algebraic example of a subshift of finite type over a group $Γ$ with an invariant Markov measure which has completely positive sofic entropy (with respect to `most' sofic approximations) and yet does not have a direct Bernoulli factor, because its model spaces shatter into exponentially many clusters of sub-exponential size. The example and its analysis are related to random low-density parity-check (LDPC) codes.

  PublisherOA PDFDOI

• A topological dynamical system with two different positive sofic entropies

  Transactions of the American Mathematical Society Series B · 2022 · 7 citations

  • Mathematics
  • Pure mathematics
  • Mathematical analysis

  A sofic approximation to a countable group is a sequence of partial actions on finite sets that asymptotically approximates the action of the group on itself by left-translations. A group is sofic if it admits a sofic approximation. Sofic entropy theory is a generalization of classical entropy theory in dynamics to actions by sofic groups. However, the sofic entropy of an action may depend on a choice of sofic approximation. All previously known examples showing this dependence rely on degenerate behavior. This paper exhibits an explicit example of a mixing subshift of finite type with two different positive sofic entropies. The example is inspired by statistical physics literature on 2-colorings of random hyper-graphs.

  PublisherOA PDFDOI

Recent grants

• Ergodic Theory of Non-Amenable Group Actions

  NSF · $330k · 2019–2022

• The Ergodic Theory of Nonamenable Group Actions

  NSF · $123k · 2012–2014

• CAREER: Ergodic Theory of Nonamenable Group Actions

  NSF · $500k · 2010–2013

• CAREER: Ergodic Theory of Nonamenable Group Actions

  NSF · $382k · 2012–2016

• The Ergodic Theory of Nonamenable Group Actions

  NSF · $171k · 2009–2012

Frequent coauthors

• Amos Nevo

  Technion – Israel Institute of Technology

  18 shared

• Robin Tucker-Drob

  12 shared

• Charles Radin

  12 shared

• Alexander I. Bufetov

  9 shared

• Peter Burton

  8 shared

• Rostyslav Kravchenko

  7 shared

• Peter Winkler

  6 shared

• Rostislav Grigorchuk

  Texas A&M University

  5 shared

Awards & honors

• Frank E. Gerth III Faculty Fellowships (Holder)
• Brin Prize in Dynamical Systems (2017)
• Fellow of the American Mathematical Society (2012)
• Livingston Fellowship (1999-2000)
• John L. and Anne Crawford Endowed Presidential Scholarship R…