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Lewis P Bowen

Department of Mathematics

Jane and Roland Blumberg Centennial Professorship in Mathematics (Holder)


Phone: 512-471-1132

Office Location
PMA 9.154

Postal Address
AUSTIN, TX 78712
Ph.D., University of Texas at Austin (2002)
B.S., University of Texas at Austin (1997)


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.

Papers Accepted

Lewis Bowen and Robin Tucker-Drob, On a co-induction question of Kechris, Israel J. of Math., (15 pages).

Lewis Bowen and Yonatan Gutman, Corrigendum to "Nonabelian free group actions: Markov processes, the Abramov-Rohlin formula and Yuzvinskii's formula", Ergodic Theory Dynam. Systems, (6 pages). 

Lewis Bowen and Amos Nevo, Geometric covering arguments and ergodic theorems for free groups, L’Enseignement Mathématique, (24 pages).

Lewis Bowen and Yonatan Gutman, A Juzvinskiĭ Addition Theorem for Finitely Generated Free Group Actions, Ergodic Theory Dynam. Systems, (20 pages).

Lewis Bowen and Amos Nevo, A horospherical ratio ergodic theorem for actions of free groups. To appear in Groups, Geometry and Dynamics.

Lewis Bowen, Entropy theory for sofic groupoids I: the foundations. To appear in Journal d'Analyse Mathematique.

Lewis Bowen, Random walks on coset spaces with applications to Furstenberg entropy. To appear in Inventiones Mathematicae.

Papers Submitted

Lewis Bowen, Invariant random subgroups of the free group.

Lewis Bowen, The type and stable type of the boundary of a Gromov hyperbolic group.

Lewis Bowen and Amos Nevo, von-Neumann and Birkhoff ergodic theorems for negatively curved groups.

Lewis Bowen and Amos Nevo, Amenable equivalence relations and the construction of ergodic averages for group actions.

Lewis Bowen, Cheeger constants and L2 Betti numbers.

  • 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.