Lewis Bowen
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

Education

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

In the Profession

• 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.

Research or Scholarly Interests

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

Awards and Honors

• 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.

Notable Recent Grants

• 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.

Publications

1. Lewis Bowen, Circle Packing in Hyperbolic Space, Math. Phys. Electron. J. 6 (2000), Paper 6, 10 pp. (electronic).
2. Lewis Bowen, Periodicity and Circle Packing in the Hyperbolic Plane, Geom. Dedicata 102 (2003), 213--236.
3. Lewis Bowen, On the existence of completely saturated packings and completely reduced coverings, Geom. Dedicata 98 (2003), 211--226.
4. Lewis Bowen and Charles Radin, Densest Packing of Equal Spheres in Hyperbolic Space, Discrete Comput. Geom. 29 (2003), no. 1, 23--39.  
5. Lewis Bowen, Couplings of Uniform Spanning Forests, Proc. Amer. Math. Soc. 132 (2004), no. 7, 2151--2158.
6. Lewis Bowen and Charles Radin, Optimally Dense Packings of Hyperbolic Space, Geom. Dedicata 104 (2004), 37--59. 
7. 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.
8. 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.
9. 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. 
10. Lewis Bowen, Russell Lyons, Charles Radin and Peter Winkler, Fluid/Solid Transition in a Hard-Core System, Phys. Rev. Lett. 96, 025701 (2006).
11. Lewis Bowen, A generalization of the prime geodesic theorem to counting conjugacy classes of free subgroups. Geom. Dedicata, 124, (2007), 37--67.
12. Lewis Bowen, Free groups in lattices, Geometry & Topology, 13, (2009), 3021--3054.
13. 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.
14. Lewis Bowen, The ergodic theory of free group actions: entropy and the f-invariant. Groups Geom. Dyn. 4 (2010), no. 3, 419--432
15. Lewis Bowen, A new measure conjugacy invariant for actions of free groups, Ann. of Math., vol. 171 (2010), No. 2, 1387--1400.
16. Lewis Bowen, Measure conjugacy invariants for actions of countable sofic groups,  J. Amer. Math. Soc., 23 (2010), 217-245.
17. Lewis Bowen, Invariant measures on the space of horofunctions of a word hyperbolic group, Ergodic Theory Dynam. Systems. 30 (2010), no. 1, 97--129.
18. Lewis Bowen, Entropy for expansive algebraic actions of residually finite groups, Ergodic Theory Dynam. Systems. 31 (2011), no. 3, 703--718.
19. Lewis Bowen, Weak isomorphisms between Bernoulli shifts, Israel J. of Math, (2011) Volume 183, Number 1, 93-102.
20. Lewis Bowen, Orbit equivalence, coinduced actions and free products, Groups Geom. Dyn. 5 (2011), no. 1, 1–15.
21. Lewis Bowen, Stable orbit equivalence of Bernoulli shifts over free groups, Groups Geom. Dyn. 5 (2011), no. 1, 17–38.
22. 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.
23. Lewis Bowen, Every countably infinite group is almost Ornstein, Contemp. Mathematics, 567, (2012), 67–78. 
24. Lewis Bowen, Sofic entropy and amenable groups, Ergodic Theory Dynam. Systems 32 (2012), no. 2, 427–466.
25. Lewis Bowen and Amos Nevo, Pointwise ergodic theorems beyond amenable groups, Ergod. Th. and Dynam. Sys. (2013), 33, 777--820.
26. 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.
27. 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.
28. 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.
29. Lewis Bowen, Random walks on coset spaces with applications to Furstenberg entropy. Invent. Math.  Volume 196, Issue 2 (2014), Page 485-510
30. Lewis Bowen and Amos Nevo, A horospherical ratio ergodic theorem for actions of free groups. Groups Geom. Dyn. 8(2):331--353, 2014.
31. 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.
32. Lewis Bowen, Review of Entropy in dynamical systems by Tomasz Downarowicz, Bulletins of the AMS, Vol 51, No 4, October 2014, 669-674. 
33. 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.
34. Lewis Bowen, Entropy theory for sofic groupoids I: the foundations. Journal d'Analyse Mathématique October 2014, Volume 124, Issue 1, pp 149--233.
35. Lewis Bowen, Cheeger constants and L2 Betti numbers. Duke Math. J. 164 (2015), no. 3, 569–615.
36. Lewis Bowen, Rostislav Grigorchuk and Rostyslav Kravchenko, Invariant random subgroups of lamplighter groups. Israel J. Math. 207 (2015), no. 2, 763–782. 
37. Lewis Bowen and Amos Nevo, Amenable equivalence relations and the construction of ergodic averages for group actions. J. Anal. Math. 126 (2015), 359–388.
38. 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.
39. Lewis Bowen, Invariant random subgroups of the free group. Groups Geom. Dyn. 9 (2015), no. 3, 891–916.
40. 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.
41. 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.
42. Lewis Bowen, Weak density of orbit equivalence classes of free group actions. Groups Geom. Dyn. 9 (2015), no. 3, 811–830.
43. 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.
44. Lewis Bowen, Zero entropy is generic. Entropy 18 (2016), no. 6, Paper No. 220, 20 pp.
45. Lewis Bowen, Simple and large equivalence relations. Proc. Amer. Math. Soc. 145 (2017), no. 1, 215–224.
46. 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.

Papers Accepted

• 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.

Papers Submitted

• Lewis Bowen, Daniel Hoff and Adrian Ioana, von Neumann's problem and extensions of non-amenable equivalence relations.
• 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.

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.

Extra-curricular teaching & lectures

• 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) 

• Clay Research Conference special session on Ergodic Theory, 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.

Recent Graduate Students and/or Postdocs

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

Undergraduate research assistants

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

Teaching Experience