Professor

**Contact Information**

- Office: RLM 9.154
- Phone: 471-1132
- Mail:
Mathematics Department

1 University Station C1200

University of Texas at Austin

78712 - email: lpbowen (at) math.utexas.edu

- Ph.D. in Mathematics, University of Texas at Austin, 2002.
- B.S. with Honors in Mathematics, University of Texas at Austin, 1997.

- Spring 2017: Professor of Mathematics, UT Austin
- Fall 2015: Miverva Distinguished Visiting Professorship at Princeton
- 2012-Spring 2017, Associate Professor of Mathematics, UT Austin.
- 2011-2012, Associate Professor of Mathematics, Texas A&M.
- 2009-2011, Assistant Professor of Mathematics, Texas A&M.
- 2007-2009, Assistant Professor of Mathematics, University of Hawai'i.
- Summer 2007, Visiting Professor of Mathematics, University of Texas at Austin.
- Fall 2004-Spring 2007, Zorn Postdoctoral Fellow, Indiana University.
- Fall 2002-Spring 2004, VIGRE Postdoctoral Fellow, UC Davis.
- Summer 2001, Assistant Instructor, University of Texas at Austin.

My research is in the ergodic theory of non-amenable group actions and in geometric group theory.

- 2017: Simons Fellow.

- Fall 2017: Faculty Research Assignment from UT.

- 2017: Brin Prize in Dynamical Systems.

- Fall 2015-Spring 2017: Gerth Faculty Fellow at UT.
- January 2016: Bourbaki article on my work:
- Fall 2015: Miverva Distinguished Visiting Professorship at Princeton
- Fall 2012: Fellow of the AMS.
- Spring 2002: Frank Gerth III Dissertation Award.
- Fall 1999 - Spring 2000: Livingston Fellowship.
- Fall 1997 - Spring 1998: John L. and Anne Crawford Endowed Presidential Scholarship Recipient.

- BSF Grant #2008274, Ergodic theory beyond amenable groups, co-PI, Sept 2009 to Aug 2013. $52,000.
- NSF Grant DMS--0968762, Ergodic theory of non-amenable group actions, PI, Sept 2009 to Aug 2012. $170,760.
- NSF CAREER Grant DMS--0954606, CAREER: Ergodic theory of non-amenable group actions, PI, May 2010 to May 2015. $499,993.
- NSF Grant DMS--1500389, Ergodic Theory of Non-amenable Group Actions, PI, May 2015-April 2018. $373,411.

- Lewis Bowen, Circle Packing in Hyperbolic Space, Math. Phys. Electron. J. 6 (2000), Paper 6, 10 pp. (electronic).
- Lewis Bowen, Periodicity and Circle Packing in the Hyperbolic Plane, Geom. Dedicata 102 (2003), 213--236.
- Lewis Bowen, On the existence of completely saturated packings and completely reduced coverings, Geom. Dedicata 98 (2003), 211--226.
- Lewis Bowen and Charles Radin, Densest Packing of Equal Spheres in Hyperbolic Space, Discrete Comput. Geom. 29 (2003), no. 1, 23--39.
- Lewis Bowen, Couplings of Uniform Spanning Forests, Proc. Amer. Math. Soc. 132 (2004), no. 7, 2151--2158.
- Lewis Bowen and Charles Radin, Optimally Dense Packings of Hyperbolic Space, Geom. Dedicata 104 (2004), 37--59.
- Lewis Bowen, Charles Holton, Charles Radin and Lorenzo Sadun, Uniqueness and symmetry in problems of optimally dense packings, Math. Phys. Electron. J. 11 (2005), Paper 1, 34 pp.
- Lewis Bowen, Mike Develin, Jesus De Loera and Francisco Santos, On the Gromov Norm of the Product of Two Surfaces, Topology 44 (2005), no. 2, 321--339. erratum: Topology 47 (2008), no. 6, 471--472.
- Lewis Bowen, Russell Lyons, Charles Radin and Peter Winkler, A Solidification Phenomenon in Random Packings, SIAM J. Math. Anal. 38 (2006), no. 4, 1075--1089.
- Lewis Bowen, Russell Lyons, Charles Radin and Peter Winkler, Fluid/Solid Transition in a Hard-Core System, Phys. Rev. Lett. 96, 025701 (2006).
- Lewis Bowen, A generalization of the prime geodesic theorem to counting conjugacy classes of free subgroups. Geom. Dedicata, 124, (2007), 37--67.
- Lewis Bowen, Free groups in lattices, Geometry & Topology, 13, (2009), 3021--3054.
- Lewis Bowen, Nonabelian free group actions: Markov processes, the Abramov-Rohlin formula and Yuzvinskii's formula, Ergodic Theory Dynam. Systems 30 (2010), no. 6, 1629--1663.
- Lewis Bowen, The ergodic theory of free group actions: entropy and the f-invariant. Groups Geom. Dyn. 4 (2010), no. 3, 419--432
- Lewis Bowen, A new measure conjugacy invariant for actions of free groups, Ann. of Math., vol. 171 (2010), No. 2, 1387--1400.
- Lewis Bowen, Measure conjugacy invariants for actions of countable sofic groups, J. Amer. Math. Soc., 23 (2010), 217-245.
- Lewis Bowen, Invariant measures on the space of horofunctions of a word hyperbolic group, Ergodic Theory Dynam. Systems. 30 (2010), no. 1, 97--129.
- Lewis Bowen, Entropy for expansive algebraic actions of residually finite groups, Ergodic Theory Dynam. Systems. 31 (2011), no. 3, 703--718.
- Lewis Bowen, Weak isomorphisms between Bernoulli shifts, Israel J. of Math, (2011) Volume 183, Number 1, 93-102.
- Lewis Bowen, Orbit equivalence, coinduced actions and free products, Groups Geom. Dyn. 5 (2011), no. 1, 1–15.
- Lewis Bowen, Stable orbit equivalence of Bernoulli shifts over free groups, Groups Geom. Dyn. 5 (2011), no. 1, 17–38.
- Lewis Bowen and Hanfeng Li, Harmonic models and spanning forests of residually finite groups, Journal of Functional Analysis, Volume 263, Issue 7, 1 October 2012, 1769--1808.
- Lewis Bowen, Every countably infinite group is almost Ornstein, Contemp. Mathematics, 567, (2012), 67–78.
- Lewis Bowen, Sofic entropy and amenable groups, Ergodic Theory Dynam. Systems 32 (2012), no. 2, 427–466.
- Lewis Bowen and Amos Nevo, Pointwise ergodic theorems beyond amenable groups, Ergod. Th. and Dynam. Sys. (2013), 33, 777--820.
- Lewis Bowen and Robin Tucker-Drob, On a co-induction question of Kechris, Israel J. of Math. March 2013, Volume 194, Issue 1, pp 209--224.
- Lewis Bowen and Yonatan Gutman, Corrigendum to "Nonabelian free group actions: Markov processes, the Abramov-Rohlin formula and Yuzvinskii's formula", Ergodic Theory and Dynam. Systems 33 Issue 02 / April 2013, pp 643 - 645.
- Lewis Bowen and Amos Nevo, Geometric covering arguments and ergodic theorems for free groups, L’Enseignement Mathématique, Volume 59, Issue 1/2, 2013, pp. 133--164.
- Lewis Bowen, Random walks on coset spaces with applications to Furstenberg entropy. Invent. Math. Volume 196, Issue 2 (2014), Page 485-510
- Lewis Bowen and Amos Nevo, A horospherical ratio ergodic theorem for actions of free groups. Groups Geom. Dyn. 8(2):331--353, 2014.
- Lewis Bowen and Yonatan Gutman, A Juzvinskiĭ Addition Theorem for Finitely Generated Free Group Actions, Ergodic Theory Dynam. Systems 34 (2014), no. 1, 95--109.
- Lewis Bowen, Review of Entropy in dynamical systems by Tomasz Downarowicz, Bulletins of the AMS, Vol 51, No 4, October 2014, 669-674.
- Lewis Bowen, The type and stable type of the boundary of a Gromov hyperbolic group. Geometriae Dedicata, October 2014, Volume 172, Issue 1, pp 363--386.
- Lewis Bowen, Entropy theory for sofic groupoids I: the foundations. Journal d'Analyse Mathématique October 2014, Volume 124, Issue 1, pp 149--233.
- Lewis Bowen, Cheeger constants and L2 Betti numbers. Duke Math. J. 164 (2015), no. 3, 569–615.
- Lewis Bowen, Rostislav Grigorchuk and Rostyslav Kravchenko, Invariant random subgroups of lamplighter groups. Israel J. Math. 207 (2015), no. 2, 763–782.
- Lewis Bowen and Amos Nevo, Amenable equivalence relations and the construction of ergodic averages for group actions. J. Anal. Math. 126 (2015), 359–388.
- Lewis Bowen, Yair Hartman and Omer Tamuz, Property (T) and the Furstenberg entropy of nonsingular actions. Proc. Amer. Math. Soc. 144 (2016), no. 1, 31–39.
- Lewis Bowen, Invariant random subgroups of the free group. Groups Geom. Dyn. 9 (2015), no. 3, 891–916.
- Lewis Bowen and Amos Nevo, von-Neumann and Birkhoff ergodic theorems for negatively curved groups. Ann. Sci. Éc. Norm. Supér. (4) 48 (2015), no. 5, 1113–1147.
- Lewis Bowen, Alexander Bufetov and Olga Romaskevich, Mean convergence of Markovian spherical averages for measure-preserving actions of the free group. Geom. Dedicata 181 (2016), 293–306.
- Lewis Bowen, Weak density of orbit equivalence classes of free group actions. Groups Geom. Dyn. 9 (2015), no. 3, 811–830.
- Lewis Bowen, L1-measure equivalence and group growth, in the appendix of: Integrable measure equivalence for groups of polynomial growth by Tim Austin. Groups Geom. Dyn. 10 (2016), no. 1, 117–154.
- Lewis Bowen, Zero entropy is generic. Entropy 18 (2016), no. 6, Paper No. 220, 20 pp.
- Lewis Bowen, Simple and large equivalence relations. Proc. Amer. Math. Soc. 145 (2017), no. 1, 215–224.
- Lewis Bowen, Rostislav Grigorchuk and Rostyslav Kravchenko, Characteristic random subgroups of geometric groups and free abelian groups of infinite rank. Trans. Amer. Math. Soc. 369 (2017), no. 2, 755–781.

- Lewis Bowen, Yair Hartman and Omer Tamuz, Generic stationary measures and actions. To appear in Transactions of the AMS.
- Lewis Bowen, Integrable orbit equivalence rigidity for free groups. To appear in Israel J. of Math.
- Lewis Bowen, Review of Introduction to Sofic and Hyperlinear Groups and Connes' Embedding Conjecture by Valerio Capraro and Martino Lupini. To appear in the Bulletin for Symbolic Logic.
- Lewis Bowen, Equivalence relations that act on bundles of hyperbolic spaces. To appear in Ergodic Theory and Dynamical Systems.
- Lewis Bowen, Daniel Hoff and Adrian Ioana, von Neumann's problem and extensions of non-amenable equivalence relations. To appear in Groups, Geometry and Dynamics.

- Lewis Bowen and Amos Nevo, Hyperbolic geometry and pointwise ergodic theorems.
- Ian Biringer, Lewis Bowen and Omer Tamuz, Invariant random subgroups of semidirect products.
- Lewis Bowen, Examples in the entropy theory of countable group actions.
- Lewis Bowen and Robin Tucker-Drob, The space of stable weak equivalence classes of measure-preserving actions.
- Lewis Bowen, All properly ergodic Markov chains over a free group are orbit equivalent.
- Lewis Bowen, Finitary random interlacements and the Gaboriau-Lyons problem.

**Conference, workshops and seminars
organized**

- Member of the Scientific Committee for the workshop "Entropies and soficity" to be held in Lyon, France, January 2018.
- Co-organizer of the "Ergodic Theory and Operator Algebras" workshop at Texas A&M, June 2017.
- Organizer of the Focused Research Group ``Entropy Theory in Dynamics’’ at the Banff International Research Station, August 2016.
- Co-organizer of the "Groups & Dynamics" workshop at UT Austin, March 2015.
- Co-organizer of the Arbeitsgemeinschaft on Sofic Entropy at Oberwolfach, Germany, October 2013.
- Organizer of the "Dynamical Systems of Algebraic Origin" workshop at UW, August 2013.
- Organizer of the "L^1-Orbit Equivalence" workshop at UIC, July 2013.
- Co-organizer of the "Group Actions and Dynamics seminar" at UT Austin, Fall 2012 - present.
- Co-organizer of "Groups, Geometry and Random Structures" a workshop held in March 2012 at Texas A&M University.
- Co-organizer of a special session on Dynamical Systems and Operator Algebras at the 2011 Fall Central Section Meeting of the AMS at the University of Nebraska-Lincoln.
- Co-organizer of "Group actions on measure spaces" a workshop held in March 2011 at Texas A&M University.
- Co-organizer of "Workshop on Groups, Embeddings and Applications", March 2009 at the University of Hawai'i.
- Co-organizer, Undergraduate seminar, 2007-2009 at the University of Hawai'i.

- Invited speaker at the Undergraduate Math Club at UT, February 2013.
- Invited speaker at MCTP (Mentoring through critical transition points) at Texas A&M, July 2010, July 2011, July 2012.
- Invited speaker at Texas A&M Undergraduate Math Club, April 2011.
- Keynote speaker at Aggieland Saturday, Feb 2011.
- Mentored two undergraduates as part of the Research Experiences for Undergraduates program at Indiana University during the summer of 2006.

**Volumes edited**

- Co-editor of a special volume of Contemporary
Mathematics in honor of A. M. Stepin
*: Dynamical systems and group actions*, Contemp. Math., 567, Amer. Math. Soc., Providence, RI, 2012.

**Committees & other service
within the UT math department**

- Chair Committee, UT Austin, 2017.
- Hiring Committee, UT Austin, 2016.
- Candidacy Committee for James Murphy, UT Austin, Spring 2017.
- Phd supervisor for Alice Mark (UT Austin, Spring 2015-) and Kathyrn Dabbs (UT Austin, Fall 2016-)
- Phd Committee for Michael Kelly, UT Austin, Fall 2013.
- Third Year Review Committee, UT Austin, Fall 2013 - Spring 2014.
- ASGSC, UT Austin, Fall 2013 - present.
- Tenure Committee, UT Austin, Spring 2013 and Spring 2015.
- Analysis Prelim Exam Committee, UT Austin, Summer 2013, Summer 2014, Summer 2015, Winter 2016.
- Postdoctoral hiring committee, UT Austin, 2012 and 2013.
- Graduate application reviewer, UT Austin, 2012-2014.

**Committees & other service
outside the UT math department**

- Phd Committee for Jan Cannizzo, University of Ottawa, Spring 2014.
- Teaching Committee Member, Texas A&M, Fall 2011-Spring 2012.

**Recent Invited Conference Talks
and Outside Seminar Talks (2009-present)**

- Simons Collaboration on Algorithms & Geometry Meeting (at the Simons Foundation in NYC) Oct 13, 2017, Invited Talk. Title: Measure-conjugacy invariants inspired by constraint satisfaction problems and a counterexample to the Weak Pinsker conjecture for free group actions.
- Probability Seminar at Princeton,
Oct 11, 2017. Title: Random interlacements and the
Gaboriau-Lyons problem.

- 2017 Workshop in Dynamical Systems and Related Topics at Penn State, Oct 5-8, 2017, Invited Talk. Title: Pointwise ergodic theorems for hyperbolic groups.
- Clay Research
Conference special session on Ergodic Theory (at Oxford),
Sept 24-29, 2017, Invited talk. Title: A counterexample
to the Weak Pinsker conjecture for free group actions
*.*

- Current Trends in Dynamical Systems and the Mathematical Legacy of Rufus Bowen, UBC, July 30-Aug 4, 2017. Title: Entropy theory in the nonamenable setting.
- von Neumann Algebras and Measured Group Theory, IHP, Paris, July 3-7, 2017. Title: Random interlacements and the von Neumann-Day problem.
- Baylor University Colloquium, May 2017. Title: Entropy theory in the non-amenable setting.
- Spring School on Analysis on Groups and Measured Group Theory, Northwester, April 3-7, 2017, invited talk. Title: Random Interlacements and the von Neumann-Day problem.
- University of Houston Colloquium, Feb 22 2017. Title: Entropy theory in the non-amenable setting.
- University of Kansas Colloquium, Sept 22 2016. Title: Entropy theory in the non-amenable setting.
- Canadian Annual Symposium on Operator Algebras and their Applications (COSy), CRM, June 13-17, 2016, invited speaker. Titles: Introduction to sofic invariants, The Weak Pinsker Conjecture, Cheeger constants and L2-Betti numbers.
- Random Spatial Processes and Dynamics, Texas A&M, April 11-15, 2016, invited speaker. Titles: 1. Entropy and processes on regular trees, 2. More examples, factors and isomorphisms of Bernoulli shifts, 3. Zero entropy is generic.
- Ergodic Theory and Logic mini-workshop, UCLA, Jan 2016. Title: the space of stable weak equivalence classes of measure-preserving group actions
- UCLA functional analysis seminar, Jan 2016. Title: Zero entropy is generic
- SUNY Stony Brook colloquium, Dec 2015. Title: Entropy for Sofic Group Actions
- Geometric and Probabilistic Methods in Group Theory and Dynamical Systems, Texas A&M, invited talk, Nov 2015. Title: Cheeger constants and L^2 Betti numbers
- CUNY Geometry and topology seminar, Nov 2015. Title: Cheeger constants and L^2 Betti numbers
- Miverva lecture series, Princeton University, Oct-Dec 2015. Title: Benjamini-Schramm convergence in Groups & Dynamics.
- Technion Colloquium, Haifa, Israel, Oct 2015. Title: Entropy and processes on regular trees.
- Ergodic Theory, Fractals and Groups, Hebrew University, Jerusalem, Oct 2015. Title: Entropy theory for actions of nonamenable groups.
- Statistical physics on transitive graphs, the Bernoulli Center, Lausanne, Switzerland, Oct 2015. Title: Entropy and processes on regular trees.
- SUNY Buffalo Colloquium, Oct 2015. Title: Entropy for Sofic Group Actions
- Groups, Graphs and Stochastic processes, Banff International Research Center, June 2015. Title: F-entropy, random graphs and Markov chains.
- Caltech-UCLA joint analysis seminar, May 2015. Title: Pointwise ergodic theorems beyond amenable groups.
- University of Iowa Colloquium, May 2015. Title: Entropy for Sofic Group Actions
- Indiana University Colloquium, April 2015. Title: Cheeger constants and L^2 Betti numbers
- Workshop von Neumann algebras and ergodic theory, UCLA, invited talk, September 2014. Title: Hyperbolic equivalence relations.
- Dynamics and Numbers, Max Planck Institute for Mathematics, invited talk, July 2014. Title: Sofic entropy and algebraic dynamics.
- IHES, Invited talk, July 2014. Title: Entropy for Sofic Group Actions.
- Graph limits, groups and stochastic processes, Renyi Institute, Budapest, July 2014. Title: Approximation properties of graphs, groups and symbolic actions
- Groups, Groupoids and Dynamics Workshop, Texas A&M, June 2014. Title: 3 part Lecture series on measured equivalence relations.
- Workshop on Dynamical Systems and Related Topics, University of Maryland, April 2014. Title: Stationary actions.
- Northwestern Colloquium, February 2014. Title: Entropy for Sofic Group Actions
- A mini-course on sofic groups (4 one hour lectures) given during the Group Structure, Group Actions and Ergodic Theory workshop at the Fields Institute, February 2014.
- Random Walks on Groups, Institut Henri Poincare, January 2014. Title: Random walks on coset spaces of random subgroups.
- Dynamics, Geometry and Operator Algebras, Texas A&M, August 2013.
- Group Theory, Measure, and Asymptotic Invariants, Oberwolfach, August 2013.
- Dynamical Systems of Algebraic Origin Workshop, UW, July 2013.
- L^1-Orbit Equivalence Workshop, UIC, July 2013.
- Courant Institute Colloquium, May 2013.
- Von Neumann Algebras and Ergodic Theory Workshop, invited talk, Vanderbilt University, April 2013.
- Workshop II: Dynamics of Groups and Rational Map, Institute for Pure & Applied Mathematics, invited talk, April 2013.
- "Logic, Dynamics and their Interactions, with a celebration of the work of Dan Mauldin", U. of North Texas, plenary address, June 2012.
- Geometry and Topology seminar, Caltech, May 2012.
- Workshop on von Neumann algebras and ergodic theory, UCLA, May 2012.
- Group Theory International Webinar, May 2012.
- Vanderbilt Colloquium, March 2012.
- Laminations and Symbolic Dynamics, 3 talks, CIRM, Luminy, France, March 2012.
- Workshop on Invariant Random Subgroups in Sde-Boker, Israel, 2 talks, Februrary-March 2012.
- Rice University Colloquium, October 2011.
- 2011 Fall Central AMS Meeting, University of Nebraska-Lincoln, Invited address, October 2011.
- ``Groups, graphs and stochastic processes'', BIRS, June 2011.
- Workshop on II_1 factors: rigidity, symmetries and classification, IHP, May 2011.
- ``Finite-dimensional approximations to discrete groups'', Oberwolfach, May 2011.
- Trends in Dynamics, Northwestern University, April 2011.
- Dynamics seminar, University of Houston, April 2011.
- ``Workshop on Concentration Phenomenon, Transformation Groups and Ramsey Theory'', Fields Institute, Oct 12-15, 2010.
- Topology Seminar, UT Austin, Sept 27, 2010.
- ``Workshop on Geometric, Asymptotic and Combinatorial Group Theory with Applications'', Centre de recherches mathematiques, Aug 15-19, 2010.
- Midwest Dynamics, University of Illinois, Chicago, Nov 6-8, 2009.
- Group Theory Seminar, UIUC, Nov 2009.
- Princeton Colloquium, Oct 2009.
- 3 talks at the Center for Dynamics and Geometry seminar, PSU, Oct 2009.
- East Coast Operator Algebras Symposium, Texas A&M, Oct 24-25 2009.
- Informal Regional Functional Analysis Seminar, Texas A&M, Aug 7-9 2009.
- 2nd Pingree Dynamics Workshop, Pingree Park, Aug 3-8 2009.
- Dynamical Systems and Randomness, Institut Henri Poincare, May 11-15 2009.
- Residually finite groups, graph limits and dynamics, Banff International Research Station, Apr 12-19, 2009.
- Probability seminar, University of Washington, April 2009.
- Rice University Colloquium, Feb 2009.
- UT Austin Colloquium, Feb 2009.
- U. of Houston Colloquium, Feb 2009.

- Sukhpreet Singh (Summer 2011-present)
- Yuqing (Frank) Lin (Spring 2016-present)
- Isaac Smith (Fall 2016-present)

- Dylan Airey (Fall 2014-Spring 2017). Dylan was a Dean’s Honors Graduate and is currently a graduate student at Princeton U.

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