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Charles H. Conley

Professor

University of North Texas

Department of Mathematics

(940) 565-3326

Email: conley@unt.edu

Education

  • PhD, University of California, Los Angeles, 1991
    Major: Mathematics
    Dissertation: Representations of Finite Length of Semidirect Product Lie Groups
  • MS, California Institute of Technology, 1987
    Major: Physics
  • SB, Massachusetts Institute of Technology, 1985
    Major: Mathematics

Professional Positions

    Academic - Post-Secondary

  • Professor, University of North Texas. University of North Texas. (2011 - Present).
  • Associate Professor, University of North Texas. University of North Texas. (2002 - 2011).
  • Assistant Professor, University of North Texas. University of North Texas. (1997 - 2002).
  • Visiting Assistant Professor, Oklahoma State University. Oklahoma State University. (1995 - 1997).
  • Adjunct Assistant Professor, University of California. University of California. (1994 - 1995).
  • C.L.E. Moore Instructor, Massachusetts Institute of Technology. Massachusetts Institute of Technology. (1992 - 1994).
  • Member, The Institute for Advanced Study. The Institute for Advanced Study. (1991 - 1992).

Professional Memberships

  • American Mathematical Society. (1987 - Present).

Development Activities

  • Faculty Development Leave, Lie algebras, University of Lyon I. Lyon,France. (2012).
  • Faculty Development Leave, Representations of Virasoro-type Lie algebras, University of Bourgogne. Dijon,France. (2005).

Teaching

Teaching Experience

    University of North Texas

  • MATH 1190 - Business Calculus, 1 course.
  • MATH 1650 - Pre Calculus, 4 courses.
  • MATH 1710 - Calculus I, 2 courses.
  • MATH 1720 - Calculus II, 1 course.
  • MATH 2700 - Linear Algebra and Vector Geometry, 1 course.
  • MATH 3400 - Number Theory, 1 course.
  • MATH 3410 - Differential Equations I, 8 courses.
  • MATH 3510 - Abstract Algebra I, 5 courses.
  • MATH 3740 - Vector Calculus, 1 course.
  • MATH 4450 - Introduction to the Theory of Matrices, 5 courses.
  • MATH 4500 - Introduction to Topology, 1 course.
  • MATH 4520 - Introduction to Functions of a Complex Variable, 5 courses.
  • MATH 4900 - Special Problems, 9 courses.
  • MATH 4910 - Special Problems, 2 courses.
  • MATH 5000 - Instructional Issues for the Professional Mathematician, 1 course.
  • MATH 5400 - Introduction to Functions of a Complex Variable, 5 courses.
  • MATH 5500 - Introduction to the Theory of Matrices, 4 courses.
  • MATH 5520 - Modern Algebra, 7 courses.
  • MATH 5530 - Modern Algebra, 4 courses.
  • MATH 5600 - Introduction to Topology, 1 course.
  • MATH 5900 - Special Problems, 11 courses.
  • MATH 5950 - Master's Thesis, 1 course.
  • MATH 6510 - Topics in Algebra, 6 courses.
  • MATH 6700 - Selected Topics in Advanced Mathematics, 1 course.
  • MATH 6900 - Special Problems, 11 courses.
  • MATH 6950 - Doctoral Dissertation, 24 courses.

Directed Student Learning

  • Doctoral Advisory Committee Chair, "Annihilators of tensor density modules of K(1|1)," Mathematics. (2019 - May 2023).
  • Master's Thesis Committee Chair, "Simplicial molecules," Mathematics. (January 2020 - May 2021).
  • Doctoral Advisory Committee Chair, "Annihilators of indecomposable bounded modules of Vec(R)," Mathematics. (2016 - 2019).
  • Doctoral Advisory Committee Chair, "Non-resonant uniserial representations of Vec(R)," Mathematics. (2014 - 2018).
  • Doctoral Advisory Committee Chair, "Uniserial representations of Vec(R) with a single Casimir eigenvalue," Mathematics. (2014 - 2018).
  • Major Professor, "Centers of invariant differential operator algebras over higher rank Jacobi groups," Mathematics. (2010 - 2013).
  • Major Professor, "Subquotients of differential operator modules over Vec(R)," Mathematics. (2009 - 2012).
  • Major Professor, "Level curves of the angle function of positive definite symmetric matrices," Mathematics. (2006 - 2009).
  • Major Professor, "Representations of sl(2) and sl(3)," Mathematics. (2006 - 2008).
  • Major Professor, "Cryptography," Mathematics. (1999 - 2001).

Research

Published Intellectual Contributions

    Conference Proceeding

  • C. Conley. (1994). Extensions of the mass 0 helicity 0 representation of the Poincaré group. Other. Non‑compact Lie Groups and Some of Their Applications. 429 315-324. Dordrecht, Kluwer.

    • Journal Article

  • Conley, C.H., Ovsienko, V. (2023). Counting quiddities of polygon dissections. The Mathematical Intelligencer. 45 (3) 256-262.
  • Conley, C.H., Ovsienko, V. (2023). Quiddities of polygon dissections and the Conway-Coxeter frieze equation. Annali della Scuola Normale Superiore di Pisa. 24 2125-2170.
  • Conley, C.H., Ovsienko, V. (2023). Shadows of rationals and irrationals: supersymmetric continued fractions and the super modular group. Journal of Geometry and Physics. 190 paper 104866, 18 pages.
  • Conley, C.H., Erickson, J. (2022). The vibrational modes of simplicial molecules. The Mathematical Intelligencer. 44 (4) 364-370.
  • Conley, C.H., Ovsienko, V. (2019). Lagrangian configurations and symplectic cross-ratios. Mathematische Annalen. 375 (3-4) 1105-1145. arXiv:1812.04271
  • Conley, C.H., Ovsienko, V. (2018). Rotundus: triangulations, Chebyshev polynomials, and Pfaffians. The Mathematical Intelligencer. 40 (3) 45-50.
  • C. Conley, D. Grantcharov. (2017). Quantization and injective submodules of differential operator modules. Advances in Mathematics. 316 216-254.
  • C. Conley, M. Raum. (2016). Harmonic Maaß-Jacobi forms of degree 1 with higher rank indices. International Journal of Number Theory. 12 (7) 1871-1897.
  • C. Conley, V. Ovsienko. (2016). Linear differential operators on contact manifolds. International Mathematics Research Notices. 2016 (22) 6884-6920.
  • C. Conley, R. Dahal. (2015). Centers and characters of Jacobi group-invariant differential operator algebras. Journal of Number Theory. 148 40-61.
  • C. Conley, J. Larsen. (2015). Equivalence classes of subquotients of pseudodifferential operator modules. Transactions of the American Mathematical Society. 367 (12) 8809-8842.
  • C. Conley. (2015). Equivalence classes of subquotients of supersymmetric pseudodifferential operator modules. Algebras and Representation Theory. 18 (3) 665-692.
  • C. Conley, M. Sepanski. (2015). Factorizations of relative extremal projectors. P-Adic Numbers, Ultrametric Analysis, and Applications. 7 (4) 276-290.
  • Bringmann, K., Conley, C.H., Richter, O.K. (2012). Jacobi forms over complex quadratic fields via the cubic Casimir operators. Commentarii Mathematici Helvetici. 87 (4) 825-859.
  • C. Conley. (2009). Conformal symbols and the action of contact vector fields over the superline. Journal fur die reine und angewandte Mathematik. 633 115-163.
  • C. Conley. (2009). Quantizations of modules of differential operators. Contemporary Mathematics. 490 61-81.
  • C. Conley, C. Martin. (2007). Annihilators of tensor density modules. Journal of Algebra. 312 (1) 495-526.
  • Bringmann, K., Conley, C.H., Richter, O.K. (2007). Maass-Jacobi forms over complex quadratic fields. Mathematical Research Letters. 14 (1) 137-156.
  • C. Conley. (2005). Bounded subquotients of pseudodifferential operator modules. Communications in Mathematical Physics. 257 (3) 641-657.
  • C. Conley, P. Pucci, J. Serrin. (2005). Elliptic equations and products of positive definite matrices. Mathematische Nachrichten. 278 (12-13) 1490-1508.
  • C. Conley, M. Sepanski. (2005). Infinite commutative product formulas for relative extremal projectors. Advances in Mathematics. 196 (1) 52-77.
  • C. Conley, M. Sepanski. (2004). Singular projective bases and the affine Bol operator. Advances in Applied Mathematics. 33 (1) 158-191.
  • C. Conley, M. Sepanski. (2003). Relative extremal projectors. Advances in Mathematics. 174 (2) 155-166.
  • C. Conley, C. Martin. (2001). A family of irreducible representations of the Witt Lie algebra with infinite dimensional weight spaces. Compositio Mathematica. 128 (2) 153-175.
  • C. Conley. (2001). Bounded length 3 representations of the Virasoro Lie algebra. International Mathematics Research Notices. 2001 (12) 609-628.
  • C. Conley. (1999). Super multiplicative integrals. Letters in Mathematical Physics. 47 (1) 63-74.
  • C. Conley. (1998). Geometric realizations of representations of finite length II. Pacific Journal of Mathematics. 183 (2) 201-211.
  • C. Conley. (1997). Geometric realizations of representations of finite length. Reviews in Mathematical Physics. 9 (7) 821-851.
  • C. Conley. (1995). Little group method for smooth representations of finite length. Duke Mathematical Journal. 79 (3) 619-666.
  • C. Conley. (1993). Representations of finite length of semidirect product Lie groups. Journal of Functional Analysis. 114 (2) 421-457.

Presentations Given

    Invited Talk

  • Conley, C.H. (Presenter), Southwest Linear Algebra Meeting, Quiddities of polygon dissections, University of Baylor, Waco, United States of America. (2022).
  • Conley, C.H. (Author & Presenter), Group Theory, Probability, and the Structure of Space-Time, Relative extremal projectors, University of California, Los Angeles, United States of America. (2014).
  • Conley, C.H. (Presenter), Annual Texas Meeting of the Mathematical Association of America, Undergraduate projects in representation theory, Texas A&M International University, Laredo, United States of America. (2014).
  • Conley, C.H. (Presenter), Texas-Oklahoma Conference on Representation Theory and Automorphic Forms III, Cohomology of vector field Lie algebras, University of Oklahoma, Norman, United States of America. (2012).
  • Conley, C.H. (Presenter), Building Bridges: 1st EU-US Conference on Automorphic Forms and Related Topics, Invariant differential operators, RWTH Aachen University, Germany. (2012).
  • Conley, C.H. (Presenter), Texas-Oklahoma Conference on Representation Theory and Automorphic Forms II, Differential operators on contact manifolds, Oklahoma State University, Stillwater, United States of America. (2012).
  • Conley, C.H. (Presenter), Workshop on equivariant quantization, Applications of classical representation theory to quantization, University of Luxembourg, Luxembourg. (2011).
  • Conley, C.H. (Presenter), Red River Conference on Automorphic Forms and Representation Theory, Invariant differential operators, University of Oklahoma, Norman, United States of America. (2010).
  • Conley, C.H. (Presenter), Special Session on Integrability of Dynamical Systems, Annual Joint Meeting, Quantizations of differential operator modules, American Mathematical Society, Mathematical Association of America, San Francisco, United States of America. (2010).
  • Conley, C.H. (Presenter), Special Session on Representation Theory, Sectional Meeting, Quantizations of differential operator modules, American Mathematical Society, Waco, United States of America. (2009).
  • Conley, C.H. (Presenter), Conference on Symmetry in Mathematics and Physics, Projective quantizations of modules of differential operators, University of California, Los Angeles, United States of America. (2008).

    • Lecture

  • Conley, C.H. (Presenter), Algebra Seminar, Tensor field modules of vector field Lie algebras, University of North Texas, Denton, United States of America. (2023).
  • Conley, C.H. (Presenter), Algebra Seminar, Injective annihilators, University of North Texas, Denton, United States of America. (2022).
  • Conley, C.H. (Presenter), Laboratory Seminar, Annihilators of representations of vector field Lie algebras, University of Champagne-Ardennes, Reims, France. (2022).
  • Conley, C.H. (Presenter), Algebra Seminar, Polygon dissections, University of North Texas, Denton, United States of America. (2021).
  • Conley, C.H. (Presenter), Colloquium, Continuants, Pfaffians, cross-ratios, and Lagrangian polygons, University of Texas, Arlington, United States of America. (2019).
  • Conley, C.H. (Leader), Math Circle, Dissecting polygons, University of Texas, Arlington, United States of America. (2019).
  • Conley, C.H. (Presenter), Algebra Seminar, Introduction to Catalan Numbers II, University of North Texas, United States of America. (2019).
  • Conley, C.H. (Presenter), Colloquium, Continuants, Pfaffians, cross-ratios, and Lagrangian polygons, Idaho State University, Pocatello, United States of America. (2018).
  • Conley, C.H. (Presenter), Algebra Seminar, Cross-ratios, Pfaffians, and Lagrangian polygons, University of North Texas, United States of America. (2017).
  • Conley, C.H. (Presenter), Colloquium, Cross-ratios, Pfaffians, and Lagrangian polygons, Sam Houston State University, Huntsville, United States of America. (2017).
  • Conley, C.H. (Presenter), Colloquium, Tetrahedral molecules, Baylor University, Waco, United States of America. (2016).
  • Conley, C.H. (Presenter), Colloquium, Relative extremal projectors, University of Champagne-Ardennes, Reims, France. (2015).
  • Conley, C.H. (Presenter), Groups and Quantization Seminar, Quantization and injective objects in O(sl(m+1), gl(m)), University of Champagne-Ardennes, Reims, France. (2015).
  • Conley, C.H. (Presenter), Colloquium, Tetrahedral molecules, University of Texas, Arlington, United States of America. (2014).
  • Conley, C.H. (Leader), Math Circle, Graphing, carefully, Texas A&M University, College Station, United States of America. (2014).
  • Conley, C.H. (Leader), Math Circle, Graphing, carefully, University of Texas, Arlington, United States of America. (2012).
  • Conley, C.H. (Presenter), Algebra, Geometry, and Number Theory Seminar, Representations of vector field Lie algebras, University of Texas, Arlington, United States of America. (2012).
  • Conley, C.H. (Presenter), MASS Colloquium, Trigonometric identities and the Weyl character formula, Pennsylvania State University, State College, United States of America. (2011).
  • Conley, C.H. (Presenter), Undergraduate Colloquium, x to the x to the x to the ..., Baylor University, Waco, United States of America. (2010).
  • Conley, C.H. (Presenter), Representation Theory Seminar, Extremal projectors, Louisiana State University, Baton Rouge, United States of America. (2009).
  • Conley, C.H. (Presenter), VIGRE Graduate Colloquium, Vector fields on the line, Louisiana State University, Baton Rouge, United States of America. (2009).
  • Conley, C.H. (Presenter), VIGRE Undergraduate Colloquium, x to the x to the x to the ..., Louisiana State University, Baton Rouge, United States of America. (2009).
  • Conley, C.H. (Presenter), Algebra Seminar, Conformal quantization for contact manifolds, University of Lyon I, United States of America. (2009).
  • Conley, C.H. (Presenter), General Seminar, Differential operator modules of vector field Lie algebras, RWTH Aachen University, Germany. (2009).
  • Conley, C.H. (Presenter), Algebra Seminar, Extensions of tensor density modules, University of California, Riverside, United States of America. (2008).
  • Conley, C.H. (Presenter), Algebra Seminar, Conformal quantization for the contact vector fields on the superline, Texas A&M University, College Station, United States of America. (2008).

Contracts, Grants, Sponsored Research

    Fellowship

  • Conley, C.H. (Principal), "Gauge supergroups," sponsored by NSF International Research Fellowship, Federal, $40628 Funded. (1998 - 1999).
  • Conley, C.H. (Principal), "Semidirect product Lie groups," sponsored by NSF Postdoctoral Fellowship, Federal, $75000 Funded. (1991 - 1994).

    • Grant - Research

  • Conley, C.H. (Principal), Shepler, A.V. (Co-Principal), "Southwest Local Algebra Meeting 2023, DMS 2302498," sponsored by National Science Foundation, Federal, $16000 Funded. (2023 - 2023).
  • Conley, C.H. (Principal), "Contact Schwarzians, extremal projectors, and infinitesimal characters," sponsored by Simons Foundation Collaboration Grant, Private, $42000 Funded. (2017 - 2022).
  • Conley, C.H. (Principal), "Lie algebra cohomology and invariant differential operators," sponsored by Simons Foundation Collaboration Grant, Private, $35000 Funded. (2011 - 2016).
  • Richter, O.K. (Principal), Conley, C.H. (Co-Principal), Shepler, A.V. (Co-Principal), "NSF grant DMS 1302770," sponsored by National Science Foundation, Federal, $12000 Funded. (2013 - 2014).
  • Richter, O.K. (Principal), Conley, C.H. (Co-Principal), Shepler, A.V. (Co-Principal), "NSF grant DMS 1132586," sponsored by National Science Foundation, Federal, $8000 Funded. (2011 - 2012).
  • Conley, C.H. (Principal), "Representations of Lie algebras," sponsored by NSA Young Investigator Award, Federal, $36000 Funded. (2003 - 2005).
  • Urbanski, M. (Principal), Schmidt, R. (Principal), "Random and Conformal Dynamical Systems," sponsored by Simons Foundation, FOND, Funded. (2018 - 2023).
  • Conley, C.H. (Principal), Schmidt, R. (Principal), "Contact Schwarzians, Extremal Projectors, and Infinitesimal Characters," sponsored by Simons Foundation, FOND, Funded. (2017 - 2022).
  • Shepler, A.V. (Principal), Schmidt, R. (Principal), "Deformations," sponsored by Simons Foundation, FOND, Funded. (2016 - 2022).
  • Richter, O.K. (Principal), Schmidt, R. (Principal), "Real-Analytic Automorphic Forms and Applications," sponsored by Simons Foundation, FOND, Funded. (2016 - 2022).
  • Conley, C.H. (Principal), Gao, S. (Principal), "Lie Algebra Cohomology and Invariant Differential Operators," sponsored by Simons Foundation, FOND, Funded. (2011 - 2017).

Service

University Service

  • Committee Member, Algebra Qualifying Exam Committee. (1997 - Present).
  • Committee Member, CAS Personel Affairs Committee. (2022 - 2025).
  • Committee Member, Combinatorics Search Committee. (November 2023 - February 2024).
  • Committee Member, CAS Computing Committee. (2021 - 2022).
  • Committee Member, Executive Committee. (2020 - 2022).
  • Co-Chair, Algebra Search Committee. (November 2021 - February 2022).
  • Committee Chair, Research Roadmap Committee. (2021).
  • Task Force Member, College of Science Task Force. (January 2017 - April 2017).
  • Faculty Advisor, Graduate Advisor. (May 2012 - January 2017).
  • Committee Member, Graduate Affairs Committee. (September 2011 - January 2017).
  • Committee Member, Graduate Curriculum Committee. (September 2014 - August 2016).
  • Committee Member, Executive Committee. (May 2013 - April 2015).
  • Member, Faculty Senate. (September 2008 - August 2014).
  • Committee Member, Executive Committee. (September 2010 - December 2011).
  • Committee Member, Strategic Planning Committee. (September 2008 - December 2011).
  • Committee Member, Executive Committee. (September 2006 - August 2008).
  • Committee Member, Executive Committee. (September 2002 - August 2004).

Professional Service

  • Reviewer, Journal Article, Mathematical Reviews/Zentralblatt Math. (2000 - Present).
  • Reviewer, Journal Article, Several Mathematics Journals. (2000 - Present).
  • Conference-Related, Southwest Local Algebra Meeting. Denton, Texas. (July 2022 - March 2023).
  • Reviewer, Grant Proposal, Funding agency. (2021).
  • Reviewer, Grant Proposal, Funding agency. (2020).
  • Conference-Related, American Mathematical Society Midwest Sectional Meeting. Denton, Texas. (September 2017).