Professor

- 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-Summer 19: Gerth
Faculty Fellow at UT.
- January 2016: Bourbaki article on
my work: Gaboriau,
Damien Entropie sofique. (French) [Sofic
entropy] Séminaire Bourbaki. Vol. 2015/2016. Exposés
1104–1119. Astérisque No.
390 (2017), Exp.
No. 1108, 101–138.

- Fall 2015: Miverva
Distinguished Visiting Professorship at Princeton
- Fall 2012: Fellow of the AMS (inaugural
class).
- Fall 2011: Invited address at the Central AMS
Meeting, University of Nebraska-Lincoln.
- 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.

- NSF Grant DMS--1937215, Research
Training Group in Groups and Dynamics, PI. August 2020-August
2025. $2,325,503.

- NSF Grant DMS--1900386, Ergodic Theory of
Non-amenable Group Actions, PI,
May 2019-April 2022. $329,726.

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

2000

- Lewis Bowen, Circle Packing in Hyperbolic
Space, Math. Phys. Electron. J. 6 (2000), Paper 6, 10 pp.
(electronic).

2003

- 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.

2004

- 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.

2005

- 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.

2006

- 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).

2007

- Lewis Bowen, A
generalization of the prime geodesic theorem to counting
conjugacy classes of free subgroups. Geom. Dedicata, 124, (2007), 37--67.

2009

- Lewis Bowen, Free groups in lattices,
Geometry & Topology, 13, (2009), 3021--3054.

2010

- 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.

2011

- 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.

2012

- 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.

2013

- 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.

2014

- 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, 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.

2015

- 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, 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, Weak density of orbit
equivalence classes of free group actions. Groups Geom. Dyn. 9 (2015), no. 3, 811–830.

2016

- 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, 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, 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.

2017

- 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. Trans.
Amer. Math. Soc. 369 (2017), no. 7, 4889–4929.
- Lewis Bowen, Integrable
orbit equivalence rigidity for free groups.
Israel
J. Math. 221 (2017), no.
1, 471–480.

2018

- Bowen, Lewis; Hoff, Daniel; Ioana, Adrian; von Neumann's problem and extensions of non-amenable equivalence relations. Groups Geom. Dyn. 12 (2018), no. 2, 399–448.
- Bowen, Lewis; Tucker-Drob, Robin The space of stable weak equivalence classes of measure-preserving actions. J. Funct. Anal. 274 (2018), no. 11, 3170–3196.
- Lewis Bowen, Equivalence relations that act on bundles of hyperbolic spaces. Ergodic Theory Dynam. Systems 38 (2018), no. 7, 2447–2492.
- Lewis Bowen, All properly ergodic Markov chains over a free group are orbit equivalent. Unimodularity in randomly generated graphs, 155–174, Contemp. Math., 719, Amer. Math. Soc., Providence, RI, 2018.
- Lewis Bowen, A brief introduction to sofic entropy theory. Proceedings of the International Congress of Mathematicians—Rio de Janeiro 2018. Vol. III. Invited lectures, 1847–1866, World Sci. Publ., Hackensack, NJ, 2018

2019

- Bowen, Lewis, Finitary random interlacements and the Gaboriau-Lyons problem. Geom. Funct. Anal. 29 (2019), no. 3, 659–689.
- Bowen, Lewis; Nevo, Amos Hyperbolic geometry and pointwise ergodic theorems. Ergodic Theory Dynam. Systems 39 (2019), no. 10, 2689–2716.

2020

- Ian Biringer, Lewis Bowen and Omer Tamuz, Invariant random subgroups of semidirect products. Ergodic Theory Dynam. Systems 40 (2020), no. 2, 353–366.
- Bowen, Lewis; Examples in the entropy theory
of countable group actions.
*Ergodic Theory Dynam. Systems*40 (2020), no. 10, 2593–2680. - Bowen, Lewis; Burton, Peter; Failure
of the
L1 pointwise ergodic theorem forPSL(ℝ) .*Geom. Dedicata*207 (2020), 61–80. - Bowen, Lewis; Burton, Peter Flexible
stability and nonsoficity.
*Trans. Amer. Math. Soc.*373 (2020), no. 6, 4469–4481.

2021

- Lewis Bowen, Ben Hayes and Frank Lin, A multiplicative
ergodic theorem for von Neumann algebra valued cocycles.
*Comm. Math. Phys.*384 (2021), no. 2, 1291–1350.

- Lewis Bowen, Sofic homological invariants and the Weak Pinsker Property. To appear in Amer. J. Math.
- Lewis Bowen and Robin Tucker-Drob, Superrigidity, measure equivalence, and weak Pinsker entropy. To appear in Groups, Geometry and Dynamics.
- Dylan Airey, Lewis Bowen and Frank Lin, A topological dynamical system with two different positive sofic entropies. To appear in Trans. Amer. Math. Soc.
- Peter Burton, Lewis Bowen, Locally compact sofic groups. To appear in Israel J. of Math.

**Book Reviews**

- 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, Book review of Introduction to sofic and hyperlinear groups and Connes' embedding conjecture. Bull. Symb. Log. 22 (2016), no. 3, 356--358.

- Co-organizer of the 3-day
Groups & Dynamics workshop at U. of Texas, September 2018.

- 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.

- I gave a talk on the work of
recent Fields Medalist Akshay Venkatesh, Sept 2018.

- 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

- 2020-21: Dissertation Committees (for Maksym Chaudkari, Max Riestenberg and Gillian Grindstaff), reviewed applications for Graduate admissions, Algebra prelim committee, co-organized the summer DRP, managed the Groups & Dynamics RTG.
- 2019-20: Candidacy Committee
(for Gillian Grindstaff, Austin Alderete, Maksym Chaudkhari),
Dissertation Committee (for Frank Lin), Tenure Committee (for
Jeff Danciger), postdoc hiring committee, FAR committee, OIT
(Online Instruction Team).

- 2018-19:
Chair committee, ASGCS, Candidacy Committee
(for Neza Zager Korenjak, Isaac Smith and Theodore Weisman),
PhD Committee (for James Murphy), Tenure Committee,

- 2017-18:
Faculty Annual Review Committee, Chair committee, Hiring
Committee (Bing and aP), ASGCS,
Algebra Prelim Exam (both Summer & Winter), Graduate
admissions, Candidacy Committee (for James Murphy, Max
Riestenberg and Yuqing Lin),
PhD Committee (for Yuqing Lin).
- 2016-17:
Hiring Committee, ASGSC, Analysis Prelim Exam Committee
(Winter), PhD Committee (for Alice Mark, Kathyrn Dabbs, Sukhpreet
Singh),
- 2015-16:
ASGSC, Analysis Prelim Exam Committee (Summer), Tenure
Committee, Candidacy Committee (for Alice Mark)
- 2014-15:
ASGSC, Analysis Prelim Exam Committee (Summer), Third Year
Review Committee, Graduate admissions committee.
- 2013-14:
ASGSC, Analysis Prelim Exam Committee (Summer), Third Year
Review Committee, PhD Committee (for Michael Kelly), Tenure
Committee, Postdoctoral hiring committee, Graduate
admissions committee.
- 2012-13: Postdoctoral hiring committee, Graduate admissions committee.

Committees & other service outside the UT math
department

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

**Professional Service**

- Editor for
Journal of Modern Dynamics since 2018.

- Committee
member of the Dynamical Systems Prize for Young Mathematicians
since Jaunary 2018.

- NSF panel reviewer (four times, the last time was 2016).
- (2019-2020)
reviewed for MathSciNet, Swiss National Science Foundation,
Binational Science Foundation, KU Leuven, Annals of Math,

- (2019-2020)
quick reviews for: Duke Math. J., many others

- Previously reviewed for Reviewer for MathSciNet, Annals of Math, Publications of the IHES, Journal of Functional Analysis, Ergodic Theory and Dynamical Systems, Groups, Geometry and Dynamics, etc.
- Reviewer for KU
Leuven, FONDECYT, AGIRA, Binational Science Foundation, Swiss
National Science Foundation

**Lecture Series**

- Quantitative
Linear Algebra tutorials, IPAM March 2018. Title: Amenability,
soficity and entropy theory (4 50-minute lectures).

- L2 invariants
and their analogues in positive characteristic, ICMAT, April
2018. Title: Fuglede-Kadison Determinants and Sofic entropy.
(8 1.25-hour lectures).

- Advanced School: Entropies and Soficity. Universite de Lyon, January 2018. Title: Sofic entropy theory (5 lectures).
- 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.
- Miverva lecture series, Princeton University, Oct-Dec 2015. Title: Benjamini-Schramm convergence in Groups & Dynamics (5 lectures).
- 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.

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

- SUMIRFAS (Texas A&M online). July 30. Title: Symmetric spaces
for von Neumann algebras with applications to the
invariant subspace problem and the multiplicative ergodic
theorem
Symmetric spaces for von Neumann algebras with applications to the invariant subspace problem and the multiplicative ergodic theore - Actions! (ENS-Lyon online). June 22. Title: Entropy,
orbit-equivalence and free groups

- Expanding Dynamics summer school (online). June 17. Title:
Weak Pinsker Entropy.

- Midwest Dynamics Seminar. January 25 (online). Title: A Multiplicative Ergodic Theorem with
continuous Lyapunov distribution.

- UTGD online seminar. March 26. Title: From sofic groups to
MIP*=RE. Attended by over 140 people.

- CDSNS Colloquium (Georgia Tech, online seminar). July 22. Title: A Multiplicative Ergodic Theorem with continuous Lyapunov distribution.
- One Day Symbolic Dynamics seminar (U. of
Chile, online seminar). Sept 10. Title: Sofic entropy of
subshifts.

2019

- Rice Colloquium, October 2019. Title: The Weak Pinsker
Problem.

- Measurability, Ergodic Theory and
Combinatorics, July 12, 2019, at Warwick University. Title:
A topological dynamical system with two different positive
sofic entropies.

- Geometry seminar, Sept 27, 2018. Title: Lecture 4 on the work of the 2018 Fields Medalists: Akshay Venkatesh.
- ICM invited lecture. August 8, 2018. Title: A brief introduction to sofic entropy theory.
- Caltech Colloquium. June 5, 2018. Title: Sofic entropy theory.
- UCLA/Caltech Joint Logic seminar, April 27, 2018, UCLA. Title: Weak Pinsker entropy.
- UCLA Colloquium, April 5,
2018. Title: Random interlacements, forests and walks.

- Workshop II: Approximation
Properties in Operator Algebras and Ergodic Theory, IPAM, May
1, 2018. Title: Sofic homology invariants and the Weak Pinsker
Property.

2017

- 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.

2016

- 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.
- 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

2015

- 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
- 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

2014

- 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
- Random Walks on Groups, Institut Henri Poincare, January 2014. Title: Random walks on coset spaces of random subgroups.

2013

- 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.

2012

- "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.

2011

- 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.

2010

- ``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.

2009

- 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-Summer 2016). Sukhpreet received his PhD in Summer 2016 and gained employment at Goldman Sachs.
- Kathyrn Dabbs (Fall 2016-Summer 2017, co-advised with Amir Mohammadi). Kathryn received her PhD in Summer 2017 and became a lecturer in the UT math dept.
- Yuqing (Frank) Lin (Spring
2016-Spring 2020). Frank received his PhD in May 2020, has a 1
year postdoc at Ben-Gurion University and afterwards a 2 year
postdoc at TAMU.

- Isaac Smith (Fall 2016-present)

- Rostislav Kravchenko (Fall 2014-Spring 2015, currently a lecturer at Northwestern U.)
- Peter Burton (Fall 2017-present)

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

Fall 2020: Hunter Vallejos**,**** **Lilly Alexander & Ryan
Chatterjee

Spring 2020: Hunter Vallejos (Teichmuller
dynamics)

Spring 2019: Yan Cheng (Mezard-Montanari's book)

Teaching Experience

Spring 2019: Yan Cheng (Mezard-Montanari's book)

Spring 2021 |
Curves and Surfaces |
M365G |
UT Austin |

Fall 2020 |
Topics in Dynamics (graduate course) |
M392C |
UT Austin |

Spring 2020 |
Introduction to Dynamics |
M375T |
UT Austin |

Fall 2019 |
Algebra |
M380C |
UT Austin |

Spring 2019 |
Reading Course (undergraduate) |
M175 | UT Austin |

Spring 2019 |
Algebraic Structures I |
M373K |
UT Austin |

Fall 2018 | Random graphs and Gibbs measures |
M393C | UT Austin |

Fall 2018 | Probability I | M362K | UT Austin |

Spring 2017 |
Curves and Surfaces |
M365G |
UT Austin |

Fall 2016 |
Probability I |
M362K |
UT Austin |

Fall 2016 |
Algebra |
M380C |
UT Austin |

Spring 2016 |
Reading course (graduate) |
M396D |
UT Austin |

Spring 2016 |
Probability I |
M362K |
UT Austin |

Fall 2015 |
Reading course (undergraduate) |
M175 |
UT Austin |

Spring 2015 |
Introduction to Dynamics and Ergodic Theory |
M393C |
UT Austin |

Spring 2015 |
Probability I |
M362K |
UT Austin |

Fall 2014 |
Real Analysis |
M381C |
UT Austin |

Spring 2014 |
Probability I |
M362K |
UT Austin |

Fall 2013 |
Topics in Ergodic Theory |
M393C |
UT Austin |

Spring 2013 |
Algebraic Structures I |
M373K |
UT Austin |

Fall 2012 |
Advanced Calculus for Applications I |
M427k |
UT Austin |

Summer 2012 |
Directed Studies |
M685 |
Texas A&M |

Spring 2012 |
Directed Studies |
M685 |
Texas A&M |

Fall 2011 |
Structures and Methods of Combinatorics |
M431 |
Texas A&M |

Fall 2011 |
Directed Studies |
M685 |
Texas A&M |

Summer 2011 |
Directed Studies |
M685 |
Texas A&M |

Spring 2011 |
Seminar in Analysis (topics in ergodic theory) |
M633 |
Texas A&M |

Fall 2010 |
Introduction to Probability Theory |
M411 |
Texas A&M |

Fall 2010 |
Engineering Calculus III |
M251 |
Texas A&M |

Spring 2010 |
Advanced Engineering Mathematics |
M401 |
Texas A&M |

Spring 2010 |
Engineering Calculus III |
M251 |
Texas A&M |

Spring 2009 |
Graduate Real Analysis II |
M632 |
University of Hawai'i |

Fall 2009 |
Graduate Real Analysis I |
M631 |
University of Hawai'i |

Fall 2009 |
Calculus IV |
M244 |
University of Hawai'i |

Spring 2008 |
Introduction to Discrete Mathematics (for education majors) |
M301 |
University of Hawai'i |

Fall 2007 |
Calculus I |
M241 |
University of Hawai'i |

Fall 2007 |
Calculus for Business and Social Sciences |
M203 |
University of Hawai'i |

Summer 2007 |
Probability Theory |
Mf362K |
UT Austin |

Spring 2007 |
Calculus III |
M311 |
Indiana University |

Fall 2006 |
Finite Mathematics (two sections) |
M118 |
Indiana University |

Spring 2006 |
Complex Analysis |
M415 |
Indiana University |

Spring 2006 |
Calculus III |
M311 |
Indiana University |

Fall 2005 |
Calculus I (two sections) |
M211 |
Indiana University |

Spring 2005 |
Numerical Analysis (for education majors) |
M371 |
Indiana University |

Fall 2004 |
Calculus I (two sections) |
M211 |
Indiana University |

Summer 2004 |
Calculus II |
M212 |
Indiana University |

Spring 2004 |
Probability Theory |
M131 |
UC Davis |

Winter 2004 |
Differential Equations |
M22B |
UC Davis |

Fall 2003 |
Calculus I |
M21A |
UC Davis |

Spring 2003 |
Differential Geometry |
M116 |
UC Davis |

Winter 2003 |
Linear Algebra |
M22A |
UC Davis |

Fall 2002 |
Calculus I |
M21A |
UC Davis |

Summer 2001 |
Coordinate Geometry |
M305G |
UT Austin |