Dr. David Lyons
Professor of Mathematical Sciences

Academic Areas of Expertise:

  • Mathematics

Courses Taught at LVC

MAS 100  Concepts of Mathematics

MAS 102  Pre-Calculus

MAS 111  Analysis I

MAS 112  Analysis II

MAS 113  Introduction to Mathematical Thinking I

MAS 114  Introduction to Mathematical Thinking II

MAS 150  Finite Mathematics

MAS 161  Calculus I

MAS 162  Calculus II

MAS 170  Elementary Statistics

MAS 202  Foundations of Mathematics

MAS 222  Linear Algebra

MAS 261  Calculus III

MAS 266  Differential Equations

MAS 270  Intermediate Statistics

MAS 311  Real Analysis

MAS 322  Abstract Algebra

MAS 325  Geometry

MAS 371  Mathematical Probability

MAS 372  Mathematical Statistics

MAS 390  Special Topics

MAS 500  Independent Study

Research Topics:

  • Mathematical Physics and Quantum Information

Major Awards

  • Principal Investigator and co-Principal Investigator on four 3-Year National Science Foundation Grants.

Scholarly Work

Publications

David W. Lyons, Nathaniel P. Gibbons, Mark A. Peters, Daniel J. Upchurch, Scott N. Walck, and Ezekiel W. Wertz. Local Pauli stabilizers of symmetric hypergraph states. Journal of Physics A: Mathematical and Theoretical, 50(24):245303, 2017. arXiv:1609.01306. [ DOI | arXiv | e-print ]

David W. Lyons. Undergraduate Research in Quantum Information Science. PRIMUS, 27(4-5):508--516, 2017. [ DOI | e-print ]

David W. Lyons, Daniel J. Upchurch, Scott N. Walck, and Chase D. Yetter. Local unitary symmetries of hypergraph states. Journal of Physics A: Mathematical and Theoretical, 48(9):095301, February 2015. arXiv:1410.3904. [ journal |e-print ]

Scott N. Walck. Learn Physics by Programming in Haskell. In James Caldwell, Philip Hölzenspies, and Peter Achten, editors, Proceedings 3rd International Workshop on Trends in Functional Programming in Education, Soesterberg, The Netherlands, 25th May 2014, volume 170 of Electronic Proceedings in Theoretical Computer Science, pages 67--77. Open Publishing Association, May 2014. [ DOI ]

Curt D. Cenci, David W. Lyons, and Scott N. Walck. Local unitary group stabilizers and entanglement for multiqubit symmetric states. In Dave Bacon, Miguel Martin-Delgado, and Martin Roetteler, editors, Theory of Quantum Computation, Communication, and Cryptography, volume 6745 of Lecture Notes in Computer Science, pages 198--207. Springer, March 2014. arXiv:1011.5229v1. [ e-print ]

David W. Lyons and Scott N. Walck. Entanglement verification using local unitary stabilizers. Phys. Rev. A, 87:062321, Jun 2013. arXiv:1303.6497 [quant-ph]. [ DOI | journal | e-print ]

David W. Lyons, Abigail M. Skelton, and Scott N. Walck. Werner state structure and entanglement classification. Advances in Mathematical Physics, 2012:463610, 2012. arXiv:1109.6063v2 [quant-ph]. [ DOI | journal | e-print ]

David W. Lyons and Scott N. Walck. Entanglement classes of symmetric Werner states. Phys. Rev. A, 84:042316, October 2011. arXiv:1106.4220v2 [quant-ph]. [ DOI | journal | e-print ]

David W. Lyons and Scott N. Walck. Symmetric mixed states of n qubits: Local unitary stabilizers and entanglement classes. Phys. Rev. A, 84:042340, October 2011. arXiv:1107.1372v1 [quant-ph]. [ DOI | journal | e-print ]

Curt D. Cenci, David W. Lyons, Laura M. Snyder, and Scott N. Walck. Symmetric states: local unitary equivalence via stabilizers. Quantum Information and Computation, 10:1029--1041, November 2010. arXiv:1007.3920v1 [quant-ph]. [ journal | e-print ]

Scott N. Walck and David W. Lyons. Only n-qubit Greenberger-Horne-Zeilinger states contain n-partite information. Phys. Rev. A, 79:032326, March 2009. arXiv:0808.0859v1 [quant-ph]. [ DOI | journal | e-print ]

David W. Lyons and Scott N. Walck. Multiparty quantum states stabilized by the diagonal subgroup of the local unitary group. Phys. Rev. A, 78:042314, October 2008. arXiv:0808.2989v2 [quant-ph]. [ DOI | journal | e-print ]

David W. Lyons. Survey of Hopf fibrations and rotation conventions in mathematics and physics. arXiv:0808.3089v2 [math-ph], September 2008. [ e-print ]

David W. Lyons, Scott N. Walck, and Stephanie A. Blanda. Classification of nonproduct states with maximum stabilizer dimension. Phys. Rev. A, 77:022309, 2008. arXiv:0709.1105 [quant-ph].

Scott N. Walck and David W. Lyons. Only n-qubit Greenberger-Horne-Zeilinger states are undetermined by their reduced density matrices. Phys. Rev. Lett., 100:050501, 2008. arXiv:0707.4428 [quant-ph].

Scott N. Walck and David W. Lyons. Maximum stabilizer dimension for nonproduct states. Phys. Rev. A, 76:022303, 2007. arXiv:0706.1785 [quant-ph].

David W. Lyons and Scott N. Walck. Classification of n-qubit states with minimum orbit dimension. J. Phys. A: Math. Gen., 39:2443--2456, 2006. arXiv:quant-ph/0506241.

David W. Lyons and Scott N. Walck. Minimum orbit dimension for local unitary action on n-qubit pure states. J. Math. Phys., 46:102106, 2005. arXiv:quant-ph/0503052.

Scott N. Walck, James K. Glasbrenner, Matthew H. Lochman, and Shawn A. Hilbert. Topology of the three-qubit space of entanglement types. Phys. Rev. A, 72:052324, 2005. arXiv:quant-ph/0507208v2. [ DOI | journal | e-print ]

David W. Lyons. An elementary introduction to the Hopf fibration. Mathematics Magazine, 76(2):87--98, 2003. [ journal | e-print ]

S. N. Walck and N. C. Hansell. Characterization and visualization of the state and entanglement of two spins. Eur. J. Phys., 22:343--350, 2001. [ DOI ]

Contact Info

Email Address

lyons@lvc.edu

Location

Lynch 283-H

Phone Number

717-867-6081