Charles H. Conley
University of North Texas
Mathematics
(940) 565-3326
Email:

Education

PhD, University of California, Los Angeles, 1991.
Major: Mathematics
Dissertation Title: 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. (2011 – Present).
Associate Professor, University of North Texas. (2002 – 2011).
Assistant Professor, University of North Texas. (1997 – 2002).
Visiting Assistant Professor, Oklahoma State University. (1995 – 1997).
Adjunct Assistant Professor, University of California. (1994 – 1995).
C.L.E. Moore Instructor, Massachusetts Institute of Technology. (1992 – 1994).
Member, The Institute for Advanced Study. (1991 – 1992).

Professional Memberships

American Mathematical Society. (1987 – Present).

Development Activities Attended

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, 7 courses.
MATH 3510, Abstract Algebra I, 5 courses.
MATH 3740, Vector Calculus, 1 course.
MATH 4450, Introduction to the Theory of Matrices, 4 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, 5 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
Conley, C. H. (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.
Conley, C. H., Grantcharov, D. (2017). Quantization and injective submodules of differential operator modules. Advances in Mathematics. 316, 216-254.
Conley, C. H., Raum, M. (2016). Harmonic Maaß-Jacobi forms of degree 1 with higher rank indices. International Journal of Number Theory. 12(7), 1871-1897.
Conley, C. H., Ovsienko, V. (2016). Linear differential operators on contact manifolds. International Mathematics Research Notices. 2016(22), 6884-6920.
Conley, C. H., Dahal, R. (2015). Centers and characters of Jacobi group-invariant differential operator algebras. Journal of Number Theory. 148, 40-61.
Conley, C. H., Larsen, J. (2015). Equivalence classes of subquotients of pseudodifferential operator modules. Transactions of the American Mathematical Society. 367(12), 8809-8842.
Conley, C. H. (2015). Equivalence classes of subquotients of supersymmetric pseudodifferential operator modules. Algebras and Representation Theory. 18(3), 665-692.
Conley, C. H., Sepanski, M. (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.
Conley, C. H. (2009). Conformal symbols and the action of contact vector fields over the superline. Journal fur die reine und angewandte Mathematik. 633, 115-163.
Conley, C. H. (2009). Quantizations of modules of differential operators. Contemporary Mathematics. 490, 61-81.
Conley, C. H., Martin, C. (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.
Conley, C. H. (2005). Bounded subquotients of pseudodifferential operator modules. Communications in Mathematical Physics. 257(3), 641-657.
Conley, C. H., Pucci, P., Serrin, J. B. (2005). Elliptic equations and products of positive definite matrices. Mathematische Nachrichten. 278(12-13), 1490-1508.
Conley, C. H., Sepanski, M. R. (2005). Infinite commutative product formulas for relative extremal projectors. Advances in Mathematics. 196(1), 52-77.
Conley, C. H., Sepanski, M. R. (2004). Singular projective bases and the affine Bol operator. Advances in Applied Mathematics. 33(1), 158-191.
Conley, C. H., Sepanski, M. R. (2003). Relative extremal projectors. Advances in Mathematics. 174(2), 155-166.
Conley, C. H., Martin, C. (2001). A family of irreducible representations of the Witt Lie algebra with infinite dimensional weight spaces. Compositio Mathematica. 128(2), 153-175.
Conley, C. H. (2001). Bounded length 3 representations of the Virasoro Lie algebra. International Mathematics Research Notices. 2001(12), 609-628.
Conley, C. H. (1999). Super multiplicative integrals. Letters in Mathematical Physics. 47(1), 63-74.
Conley, C. H. (1998). Geometric realizations of representations of finite length II. Pacific Journal of Mathematics. 183(2), 201-211.
Conley, C. H. (1997). Geometric realizations of representations of finite length. Reviews in Mathematical Physics. 9(7), 821-851.
Conley, C. H. (1995). Little group method for smooth representations of finite length. Duke Mathematical Journal. 79(3), 619-666.
Conley, C. H. (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 and 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 1855261," Sponsored by National Science Foundation, Federal, $16000 Funded. (January 2022 – December 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).

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).