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

• 2022-2024: holder of the Blumberg Professorship, UT Austin
  
• 2017: Simons Fellow.
• Fall 2017: Faculty Research Assignment from UT.
• 2017: Brin Prize in Dynamical Systems.
• Fall 2015-2024: 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.

Notable Recent Grants

• NSF Grant DMS--2154680, Ergodic Theory Beyond Amenability, PI, May 2022-April 2025. $425,512.
  
• 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.

Research Publications

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 for PSL(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.

2022

• Lewis Bowen and Robin Tucker-Drob, Superrigidity, measure equivalence, and weak Pinsker entropy. Groups Geom. Dyn. 16 (2022), no. 1, 247–286.
• Airey, Dylan; Bowen, Lewis; Lin, Yuqing Frank A topological dynamical system with two different positive sofic entropies. Trans. Amer. Math. Soc. Ser. B 9 (2022), 35–98.
• Bowen, Lewis Sofic homological invariants and the weak Pinsker property. Amer. J. Math. 144 (2022), no. 1, 169–226.
• Bowen, Lewis; Burton, Peter Locally compact sofic groups. Israel J. Math. 251 (2022), no. 1, 239–270.
  

Papers Accepted

• Lewis Bowen and Yuqing Frank Lin, Entropy for actions of free groups under bounded orbit equivalence. To appear in Israel J. of Math.
• Lewis Bowen, Locally compact sofic entropy theory, part I. To appear in Trans. Amer. Math. Soc.

Papers Submitted

• Tim Austin, Lewis Bowen and Chris Shriver. Algebraic dynamical systems from LDPC codes satisfy a strong negation of the weak Pinsker property.
• Lewis Bowen, Michael Chapman, Alexander Lubotzky and Thomas Vidick. The Aldous-Lyons Conjecture I: Subgroup Tests.

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.

Conference, workshops and seminars organized

• Co-organizer of the 5-day Graduate mini-school in Groups & Dynamics at UT Austin, May 2023.
• Co-organizer of the 5-day Graduate mini-school in Groups & Dynamics at UT Austin, July 2022.
  
• 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.

Extra-curricular teaching & lectures

• 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

• 2023-24: managed the Groups & Dynamics RTG, promotion committee (for Lisa Piccirillo and Kate Juschenko), PhD Committee (for Erin Belivacqua, Luis Torres), co-organized the summer DRP (directed reading program), managed the Groups & Dynamics RTG.
• 2022-23: FAR committee,  PhD Committee (for Neza Zager Korenjak and Maksym Chaudkari), Candidacy Committee (for Allie Embry and Colin Walker), review committee (for Rostislav Kravchenko), co-organized the summer DRP (directed reading program), managed the Groups & Dynamics RTG.
  
• 2021-22: Triad for Maks Radziwill, Committee for faculty hiring, Committee for CNS Diversity faculty position search, ASGCS, reviewed applications for Graduate admissions, Dissertation Committee for Theodore Weisman, co-organized the summer DRP (directed reading program), managed the Groups & Dynamics RTG, 
• 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).
• (2022-2023) reviewed for the US-Israel Binational Science Foundation.
  
• (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)

2024

• Groups and Dynamics Workshop at Texas A&M, March 1. Title "An approach to the Aldous-Lyons Conjecture". (This workshop was organized by N. Goncharuk and R. Grigorchuk. It featured talks by Yaroslav Vorobets, myself, Alan Reid and Alex Lubotzky).
  
• Brazos Analysis Seminar, Nov 16-17 at the University of Houston. Title "An approach to the Aldous-Lyons Conjecture".

2023

• Long Feng Science Forum in the School of Science and Engineering (SSE) at The Chinese University of Hong Kong, Shenzhen (CUHK-Shenzhen), February 13, title: How the topology of hyperbolic manifolds influences geometry.
• INRIA Paris online seminar, April 17, title: Finitary random interlacements and the Gaboriau-Lyons problem

2022

• UCLA Functional Analysis seminar, March 9, title: Entropy, orbit-equivalence and free groups
• Ergodic Theory and its Connections: A Conference in Honor of the Legacy of Michael Boshernitzan, May 19-22, Rice U. Title: Pointwise Ergodic Theorems for PSL(2,R)
• Online seminar at the Chinese university of Hong Kong, July 2022, Title: Sofic groups
  

2021

• 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
• 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.
  

2020

• 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.
  

2018

• 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.

Recent Graduate Students

• 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-Summer 2020). Isaac received a Masters degree in Summer 2020.
  
• Hunter Vallejos. semester of candidacy: Spring 2022. Expected PhD: Fall 2024.
• Alexandra Embry. semester of candidacy: Spring 2023. Expected PhD: Fall 2024
• Erin Belivacqua, Expected semester of candidacy: Spring 2024.
  

Recent Postdocs

• Rostislav Kravchenko (Fall 2014-Spring 2015)
• Peter Burton (Fall 2017-Spring 2021)
• Amanda Wilkens (Fall 2021- Spring 2024)
  
• Chris Shriver (Fall 2021- Spring 2024)

Undergraduate mentoring

• Dylan Airey (Fall 2014-Spring 2017). Dylan was a Dean’s Honors Graduate and was accepted to graduate school in mathematics at Princeton U.
• Ryan Chatterjee (Fall 2020-Fall 2021). Ryan wrote an excellent Honors Thesis on Selberg's Trace Formula. He has been accepted to several graduate mathematics programs.
  

Reading Courses
Fall 2023: Aaron Benda, Erin Bevilacqua
Spring 2021: Hunter Vallejos, Lilly Alexander & Ryan Chatterjee

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 2024	Introduction to Dynamics	M375T	UT Austin
Fall 2023	Graduate Real Analysis	M381C	UT Austin
Spring 2023	Curves and Surfaces	M365G	UT Austin
Fall 2022	Graduate Real Analysis	M381C	UT Austin
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