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Darren Creutz

  • Visiting Professor, Vanderbilt University
    Associate Professor, U.S. Naval Academy

Positions

  • Visiting Professor of Mathematics, Vanderbilt University
  • Associate Professor of Mathematics, U.S. Naval Academy
  • Assistant Professor of Mathematics, U.S. Naval Academy
  • Assistant Professor of Mathematics, Vanderbilt University
  • Research Assistant, University of California: Los Angeles
  • 2024–2025
  • 2023–
  • 2016–2023
  • 2011–2016
  • 2007–2011

Education

  • PhD Pure Mathematics, University of California: Los Angeles
  • M.A. Mathematics, University of California: Los Angeles
  • B.A. Mathematics with Honors & Computer Science, Williams College
  • 2011
  • 2006
  • 2003

Research

Research Areas: Ergodic Theory, Symbolic Dynamics, Lattices in Lie Groups, Rank-One Transformations

Publications

  • On Minimal Subshifts of Linear Word Complexity with Slope less than 3/2
    Darren Creutz and Ronnie Pavlov
  • Measure-Theoretically Mixing Subshifts of Minimal Word Complexity
    Darren Creutz
  • Low Complexity Subshifts have Discrete Spectrum 2023
    Darren Creutz and Ronnie Pavlov Forum of Mathematics, Sigma
  • Word Complexity of (Measure-Theoretically) Weakly Mixing Rank-One Subshifts 2023
    Darren Creutz Ergodic Theory and Dynamical Systems
  • Stabilizers of Stationary Actions of Lattices in Semisimple Groups 2023
    Darren Creutz Groups, Geometry and Dynamics
  • Measure-Theoretically Mixing Subshifts with Low Complexity 2022
    Darren Creutz, Ronnie Pavlov and Shaun Rodock Ergodic Theory and Dynamical Systems
  • Character Rigidity for Lattices and Commensurators 2022
    Darren Creutz and Jesse Peterson American Journal of Mathematics
  • Harmonic Functions on Compactly Generated Groups 2022
    Darren Creutz International Journal of Mathematics
  • Mixing on Stochastic Staircase Transformations 2021
    Darren Creutz Studia Mathematica
  • Stabilizers of Actions of Lattices in Products of Groups 2017
    Darren Creutz Ergodic Theory and Dynamical Systems
  • Stabilizers of Ergodic Actions of Lattices and Commensurators 2017
    Darren Creutz and Jesse Peterson Transactions of the AMS
  • Contractive Spaces and Relatively Contractive Maps 2016
    Darren Creutz AMS Contemporary Mathematics
  • A Normal Subgroup Theorem for Commensurators of Lattices 2014
    Darren Creutz and Yehuda Shalom Groups, Geometry and Dynamics
  • Mixing on Rank-One Transformations 2010
    Darren Creutz and Cesar Silva Studia Mathematica
  • Mixing on a Class of Rank-One Transformations 2004
    Darren Creutz and Cesar Silva Ergodic Theory and Dynamical Systems
  • Ergodic Theory of Group Actions
    Darren Creutz Lecture Notes
  • Commensurated Subgroups and the Dynamics of Group Actions on Quasi-Invariant Measure Spaces 2011
    Darren Creutz Doctoral Dissertation
  • Rank-One Mixing and Dynamical Averaging 2001
    Darren Creutz Honors Thesis

Talks

  • Word Complexity Cutoffs for Mixing Properties (focused on Partial Mixing) Vanderbilt University 1 Nov 2024
  • Adelic Subshifts Pennsylvania State University 29 Mar 2024
  • Adelic Structure of Low Complexity Subshifts Vanderbilt University 22 Mar 2024
  • Mixing Properties of Subshifts and Word Complexity Cutoffs University of Denver Colloquium 8 Mar 2024
  • Actions of Lattices in Semisimple Lie Groups University of Denver 1 Mar 2024
  • Word Complexity Cutoffs for Mixing Properties of Subshifts University of California: San Diego 8 Feb 2024
  • Word Complexity Cutoffs for Mixing Properties of Subshifts Pennsylvania State University 12 Dec 2023
  • Actions of Lattices in Semisimple Lie Groups Pennsylvania State University 8 Dec 2023
  • Subshift Word Complexity and Mixing Properties University of Denver 14 Nov 2023
  • Workshop on Low Complexity Dynamical Systems (co-organizer) University of Maryland 2-6 Oct 2023
  • Low Complexity Systems U.S. Naval Academy 18 Apr 2023
  • Word Complexity Cutoffs for Mixing Properties of Subshifts University of Maryland 13 Oct 2022
  • Word Complexity Cutoffs for Mixing Properties of Subshifts U.S. Naval Academy 3 Oct 2022
  • Word Complexity of Rank-One Subshifts University of Denver 26 May 2022
  • Low Complexity Subshifts admitting Mixing Measures AMS Special Session on Zero-Dimensional Dynamics, University of Denver (Virtual) 14 May 2022
  • Mixing Subshifts with Low Word Complexity Univeristy of Virginia 11 May 2022
  • Low Complexity Subshifts U.S. Naval Academy 11 Apr 2022
  • Continuous Actions of Lattices (in Higher-Rank Semisimple Groups) are Free U.S. Naval Academy 14 Oct 2021
  • Continuous Actions of Lattices (in Higher-Rank Semisimple Groups) are Free University of Maryland 30 Sep 2021
  • Complexity from Simplicity: Dimensions, Fractals and Chaos U.S. Naval Academy (online) 23 Feb 2021
  • Ergodic Theory: The Mathematics of Experiment, Probability and Time Colloquium, U.S. Naval Academy 13 Nov 2019
  • Mixing of Stochastic Staircase Transformations U.S. Naval Academy 21 Oct 2019
  • Fractals and Dimension Annapolis Civitan Club 15 Aug 2019
  • Mathematical Existence: A Philosophical Discussion U.S. Naval Academy 16 Apr 2019
  • Harmonicity and energy of cocycles: (T) without ultraproducts nor conditionally negative type University of Virginia 5 Apr 2019
  • Rigidity for actions and characters of lattices (in products of Lie groups) Colloquium, University of Virginia 4 Apr 2019
  • Relative Entropy and an Entropy Gap for Some Groups Without (T) Purdue University 15 Feb 2019
  • How discontinuous can an integrable function be? U.S. Naval Academy 22 Jan 2019
  • Completeness, Incompleteness, Consistency and Independence: Gödel's revolutionizing of logic U.S. Naval Academy 11 Oct 2018
  • Amenability of Stationary Actions of Lattices Vanderbilt University 6 Apr 2018
  • Amenability of Stationary Actions of Lattices University of Virginia 30 Mar 2018
  • A (potential) topological/C*-algebra approach to rigidity for lattices (joint w/ M. Kalantar) U.S. Naval Academy 5 Mar 2018
  • Stationary Actions of Lattices Brazos Analysis Seminar, University of Houston 4 Nov 2017
  • Relativized Furstenberg Entropy and an Information Theory of Joinings U.S. Naval Academy 16 Oct 2017
  • Set Theory Past ZFC: Large Cardinals, Forcing, and Independence U.S. Naval Academy 3 Apr 2017
  • The Normal Subgroup Theorem for Lattices in Products (Property (T)) U.S. Naval Academy 6 Feb 2017
  • The Normal Subgroup Theorem for Lattices in Products (Amenability) U.S. Naval Academy 23 Jan 2017
  • Random Walks and Harmonic Functions on Groups U.S. Naval Academy 7 Nov 2016
  • Ergodic Actions of Lattices in Higher-Rank Semisimple Groups University of Maryland 6 Oct 2016
  • Mixing and Rank-One Transformations U.S. Naval Academy 3 Oct 2016
  • Character Rigidity for Lattices in Lie Groups U.S. Naval Academy 26 Aug 2016
  • Rigidty Theory of Lattices in Semisimple Groups U.S. Naval Academy 3 Feb 2016
  • The Information Theory of Joinings Vanderbilt University 22 Jan 2016
  • Harmonic Maps on Groups and Property (T) Noncommutative Geometry and Operator Algebras Spring Institute 6 May 2015
  • Co-Organizer, Special Session: Classification Problems in Operator Algebras AMS Joint Mathematics Meetings 11 Jan 2015
  • Operator-Algebraic Superrigidity for Lattices AMS Special Session on Classification Problems in Operator Algebras, Baltimore Maryland 15 Jan 2014
  • Operator Algebraic Superrigidity for Lattices and Commensurators Northwestern University 3 Dec 2013
  • Rigidity for Characters on Lattices and Commensurators Vanderbilt University 30 Oct 2013
  • Character Rigidity for Lattices and Commensurators Vanderbilt University 27 Sep 2013
  • Stabilizers of Ergodic Actions of Product Groups and Lattices in Products Shanks Workshop on von Neumann Algebras and Ergodic Theory, Vanderbilt University 28 Apr 2013
  • Stabilizers of Actions of Groups and Invariant Random Subgroups Vanderbilt University 26 Apr 2013
  • Stabilizers of Actions of Product Groups and Lattices in Product Groups Vanderbilt University 5 Apr 2013
  • Mixing on Rank-One Transformations Vanderbilt University 25 Jan 2013
  • Stabilizers of Ergodic Actions of Lattices and Commensurators University of California: San Diego 16 Nov 2012
  • Poisson Boundaries, Harmonic Functions and Random Walks on Groups Vanderbilt University 9 Nov & 5 Dec 2012
  • Stabilizers of Ergodic Actions of Lattices and Commensurators Vanderbilt University 19 Sep 2012
  • Stabilizers of Ergodic Actions of Lattices and Commensurators Williams College Ergodic Theory Conference 28 Jul 2012
  • Stabilizers of Ergodic Actions of Lattices and Commensurators UCLA Workshop on von Neumann Algebras and Ergodic Theory 26 May 2012
  • Stabilizers for Ergodic Actions of Commensurators Vanderbilt University 6 Apr 2012
  • The Property (T) “Half” of the Margulis-Zimmer Conjecture Vanderbilt University 29 Feb 2012
  • Property (T) for Certain Totally Disconnected Groups Related to a Conjecture of Margulis and Zimmer Vanderbilt University 17 Feb 2012
  • SAT Actions and Rigidity of Lattices Vanderbilt University 30 Nov 2011
  • Normal Subgroups of Commensurators of Lattices Vanderbilt University 9 Nov 2011
  • Normal Subgroups of Commensurators and Rigidity of SAT Actions Vanderbilt University 26 Aug & 2 & 9 Sep 2011
  • Dynamics of SAT Actions CalTech 2 May 2011
  • Normal Subgroups of Commensurators and Rigidity of SAT Actions University of California: Los Angeles 6 Apr & 13 Apr 2011
  • Normal Subgroups and Rigidity for Commensurators Vanderbilt University 28 Feb 2011
  • Quasi-Invariant Group Actions University of California: Los Angeles 18 Feb 2011
  • Normal Subgroups of Commensurators and SAT Actions CalTech 20 Jan 2011
  • A Normal Subgroup Theorem for Commensurators Yale University 15 Nov 2010
  • Mixing, Random Sequences and Rank-One Transformations Northwestern University 9 Nov 2010
  • Normal Subgroup and Factor Theorems for Commensurators University of Illinois: Chicago 8 Nov 2010
  • A Normal Subgroup Theorem for Commensurators of Lattices AMS Western Meeting 9 Oct 2010
  • Superstability and Finite-Time Extinction for Semigroups University of California: Los Angeles 27 Apr 2010
  • Poisson Boundaries and Their Applications University of California: Los Angeles Jan 2009
  • Rank-One Actions, Mixing and Singular Spectra University of California: Los Angeles Mar 2007

Conferences and Seminars Organized

  • Co-Organizer, Workshop on Low Complexity Dynamical Systems Brin Mathematics Research Institute at the University of Maryland 2023
  • Seminar Lead, Operator Algebras and Dynamics Seminar U.S. Naval Academy 2018–2023
  • Co-Organizer, AMS Special Session on Classification Problems in Operator Algebras Joint Mathematics Meetings 2015
  • Co-Organizer, Shanks Workshop: von Neumann Algebras and Ergodic Theory Vanderbilt University 2013

Teaching Experience

  • Single Variable Calculus Vanderbilt University Fall 2024
  • Calculus III U.S. Naval Academy Spring 2023
  • Calculus III U.S. Naval Academy Fall 2022
  • Calculus III U.S. Naval Academy Spring 2022
  • Complex Variables U.S. Naval Academy Spring 2022
  • Calculus III U.S. Naval Academy Fall 2021
  • Calculus III (split classroom hybrid) U.S. Naval Academy Spring 2021
  • Calculus II (online) U.S. Naval Academy Fall 2020
  • Calculus III (online) U.S. Naval Academy Summer 2020
  • Calculus III U.S. Naval Academy Spring 2020
  • Calculus II U.S. Naval Academy Fall 2019
  • Real Analysis (Honors) U.S. Naval Academy Fall 2019
  • Calculus III U.S. Naval Academy Spring 2019
  • Calculus II U.S. Naval Academy Fall 2018
  • Calculus II U.S. Naval Academy Spring 2018
  • Calculus I U.S. Naval Academy Fall 2017
  • Differential Equations U.S. Naval Academy Spring 2017
  • Calculus III with Vector Fields U.S. Naval Academy Fall 2016
  • Modern Algebra U.S. Naval Academy Fall 2016
  • Mathematical Theory of Statistics Vanderbilt University Spring 2016
  • Probability and Statistical Inference Vanderbilt University Fall 2015
  • Single-Variable Calculus I Vanderbilt University Fall 2015
  • Probability and Statistics for Engineering Vanderbilt University Summer 2015
  • Probability and Statistical Inference Vanderbilt University Spring 2015
  • Differential Equations with Linear Alegbra Vanderbilt University Spring 2015
  • Probability and Statistical Inference Vanderbilt University Fall 2014
  • Differential Equations with Linear Alegbra Vanderbilt University Fall 2014
  • Single Variable Calculus Vanderbilt University Summer 2014
  • Ergodic Theory of Group Actions Vanderbilt University Spring 2014
  • Multivariable Calculus Vanderbilt University Fall 2013
  • Single-Variable Calculus Vanderbilt University Summer 2013
  • Introduction to Analysis Vanderbilt University Spring 2013
  • Ordinary Differential Equations Vanderbilt University Fall 2012
  • Introduction to Analysis Vanderbilt University Spring 2012
  • Accelerated Single-Variable Calculus II Vanderbilt University Fall 2011
  • Probability & Programming Review University of California: Los Angeles Winter 2011
  • Advanced Topics for Undergraduates University of California: Los Angeles Summer 2010
  • Integration and Infinite Series University of California: Los Angeles Spring 2010
  • Robert Sorgenfrey Distinguished Teaching Award UCLA Spring 2010
  • Teaching Assistant, Linear Algebra UCLA Winter 2010
  • Teaching Assistant, Theory of Numbers UCLA Spring 2009
  • Teaching Assistant, Intro. Programming UCLA Winter 2009
  • Teaching Assistant, Nonlinear Differential Equations UCLA Fall 2008
  • Teaching Assistant, Intro. Probability Theory UCLA Spring 2008
  • Teaching Assistant, Game Theory UCLA Winter 2008
  • Teaching Assistant, Combinatorics UCLA Fall 2007
  • Teaching Assistant, Stochastic Processes UCLA Spring 2007
  • Teaching Assistant, Intro. Probability Theory UCLA Winter 2007
  • Teaching Assistant, Intro. Probability Theory UCLA Fall 2006
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