Ian Anderson Ph.D.

Mathematics and Statistics

Professor


Ian M. Anderson

Contact Information

Office Location: Animal Science (ANSC) 302
Phone: (435) 797-2822
Email: Ian.Anderson@usu.edu

Educational Background

PhD, Mathematics, University of Arizona, 1976
MS, Mathematics, University of Waterloo, 1974
BS, Mathematics, University of Waterloo, 1973

Awards

Valedictorian Escort College of Science 2016, 2016

Top Professor Award, 2005

Utah State University Student Honors Program

Wynne D. Thorne Research Award, 1992

Utah State University

Wynne D. Thorne Research Award, 1992

Utah State University

Outstanding Teaching Assistantship Award, 1976

Dept. ofMathematics, Univ. of Arizona

Graduate Fellowship, 1973

Province of Ontario

National Research Council of Canada Postgraduate Scholarship, 1973

Research Assistantship, 1973

Univ. of Waterloo

Science Scholarship, 1973

National Research Council of Canada


    Publications | Book Chapters

  • Anderson, I.M, (1976). The Uniqueness of the Neutrino Energy-Momentum Tensor and the Einstein- Weyl Equations: Topics in Differential Geometry. Academic Press

An asterisk (*) at the end of a publication indicates that it has not been peer-reviewed.

Publications | Journal Articles

Academic Journal

  • Anderson, I.M, Leistner, T., Nurowski, P., Explicit Ambient Metrics and Holonomy. Journal of Differential Geometry
  • Fels, M.E, Anderson, I.M, (2015). Backlund Transformations for Darboux Integrable Systems: Examples and Applications. Journal of Geometry and Physics, 102, 1-31. doi: doi:10.1016/j.geomphys.2015.12.005
  • Anderson, I.M, Nie, Z., Nurowski, P., (2015). Non-rigid parabolic geometries of Monge type. Advances in Mathematics, 277:4, 24--55.
  • Fels, M.E, Anderson, I.M, (2014). Backlund Transformations for Darboux Integrable Differential Systems: General Theory. Selecta Mathematica, New Series
  • Anderson, I.M, Torre, C.G, (2013). GR 20 Workshop, Warsaw, July 2013.
  • Anderson, I.M, Torre, C.G, (2013). Lessons from GR 20 Workshop, Warsaw, July 2013.
  • Fels, M.E, Anderson, I.M, (2013). The Cauchy Problem for Darboux Integrable Systems and non-linear D'Alembert Formulas. Symmetry, Integrability and Geometry: Methods and Applications, 9:17, 1-22.
  • Torre, C.G, Anderson, I.M, (2012). New symbolic tools for differential geometry, gravitation, and field theory. Journal of Mathematical Physics, 53, 013511 (12 pages).
  • Torre, C.G, Anderson, I.M, (2011). New Symbolic Tools for Differential Geometry, Gravitation, and Field Theory. preprint
  • Anderson, I.M, Fels, M.E, Vassiliou, P., (2009). Superposition Formulas for Darboux Integrable Exterior Differential Systems. Advances in Mathematics, 221:6, 1910-1963.
  • Anderson, I.M, Fels, M.E, (2005). Exterior Differential Systems with Symmetry. Acta Applicandae Mathematicae, 87, 3-31.
  • Anderson, I.M, Fels, M.E, (2002). Transverse Group Actions on Bundles. Topology and its Applications, 123:3, 443-459.
  • Anderson, I.M, Fels, M., Torre, C., (2001). Group invariant solutions in mathematical physics and differential geometry. Contemporary Mathematics, 285
  • Anderson, I.M, Fels, M.E, Torre, C.G, (2000). Group invariant solutions without transversality. Comm. Math. Phys., 212:3, 653-686.
  • Anderson, I.M, Fels, M.E, Torre, C.G, (1999). Department of Mathematics Utah State University Logan, Utah 84322.
  • Anderson, I.M, Fels, M.E, Torre, C.G, (1999). Symmetry Reduction Without Transversality. arXiv preprint math-ph/9910015
  • Anderson, I.M, Juras, M., (1997). Generalized Laplace Invariants and the Method of Darboux. Duke J. Math., 89, 351-375.
  • Fels, M.E, Anderson, I.M, (1997). Symmetry reduction of variational bicomplexes and the principle of sym- metric criticality. Amer. Jour. Math., 119:3, 609-670.
  • Anderson, I.M, Kamran, N., (1997). The Variational Bicomplex for Second Order Partial Differential Equa- tions in the Plane. Duke J. Math, 87, 265-319.
  • Anderson, I.M, Torre, C., (1996). Asymptotic Conservation Laws in Classical Field Theory. Phys. Rev. Lett., 77, 4109-4133.
  • Anderson, I.M, Torre, C.G, (1996). Asymptotic conservation laws in classical field theory. Physical review letters, 77:20, 4109.
  • Anderson, I.M, Torre, C.G, (1996). Classification of local generalized symmetries for the vacuum Einstein equations. Communications in mathematical physics, 176:3, 479–539.
  • Anderson, I.M, Torre, C.G, Fredenhagen, K., Jr, M., Guhr, T., Bogomolny, E., Leyvraz, F., Schmit, C., Jakšic, V., Pillet, C., others, , (1996). Miscellaneous front pages, Comm. Math. Phys., Volume 176, Number 3 (1996).
  • Anderson, I.M, Pohjanpelto, J., (1996). Symmetries, Conservation Laws, and Variational Principles for Vector Field Theories. Proc. Camb. Phil. Soc., 120, 369-384.
  • Anderson, I.M, Torre, C., (1996). The Classification of Local Generalized Symmetries for the Einstein Equations. Comm. Math. Physics, 176, 479-539.
  • Anderson, I.M, Pohjanpelto, J., (1995). Variational Principles for Differential Equations with Symmetries and Conservation Laws II: Polynomial Equations. Mathematische Annalen, 301, 627-653.
  • Anderson, I.M, Torre, C.G, (1994). Classification of generalized symmetries for the vacuum Einstein equations. arXiv preprint gr-qc/9404030
  • Anderson, I.M, Pohjanpelto, J., (1994). Variational Principles for Differential Equations with Symmetries and Conservation Laws I: Second Order Scalar Equations. Mathematische Annalen, 299, 191-222.
  • Anderson, I.M, Kamran, N., Olver, P., (1993). Internal, External and Generalized Symmetries. Advances in Mathematics, 100, 53-100.
  • Anderson, I.M, Torre, C., (1993). Symmetries of the Einstein Equations. Physical Rev. Let- ters, 70, 3525-3529.
  • Torre, C.G, Anderson, I.M, (1993). Symmetries of the Einstein equations. arXiv preprint gr-qc/9302033
  • Anderson, I.M, Thompson, G., (1992). The Inverse Problem in the Calculus of Variations for Ordinary Differen- tial Equations. Memoirs of the AMS, 473
  • Anderson, I.M, (1988). Aspects of the Inverse Problem to the Calculus of Variations. Archivum Mathematicum (Brno), 24, 329-370.
  • Anderson, I.M, Arms, J., (1986). Perturbations of Conservation Laws in Field Theories. Annals of Physics, 167, 354-689.
  • Anderson, I.M, Bezdek, J., (1985). An Application of the c-Varieties Clustering Algorithm to Polygonal Curve Fitting. IEEE Trans SMC, 15, doi: 637-641
  • Anderson, I.M, (1985). Determinantal Ideals and the Capelli Identities. Linear Algebra and its Applications, 69, 269-277.
  • Anderson, I.M, Bezdek, J., (1984). Curvature and Tangential Deflections of Discrete Arcs. IEEE Trans. PAMI, 6, 27-40.
  • Anderson, I.M, (1984). Natural Variational Principles on Riemannian Structures. Annals ofMath- ematics, 120, 329-370.
  • Anderson, I.M, Duchamp, T., (1984). Variational Principles for Second-Order Quasi-Linear Scalar Equations. J. Diff. Equations, 51, 1-47.
  • Anderson, I.M, (1981). The Principle of Minimal Gravitational Coupling. Arch. RationalMech. Anal., 75, 349-372.
  • Anderson, I.M, Duchamp, T., (1980). On the Existence of Global Variational Principles. Amer. J. Math., 102, 781-868.
  • Anderson, I.M, (1979). On the Characterization of Energy-Momentum Tensors. General Relativ- ity and Gravitation, 10, 461-465.
  • Anderson, I.M, (1978). On the Structure of Divergence-Free Tensors. J. Math. Phys, 19, 2570-2575.
  • Anderson, I.M, (1978). Tensorial Euler-Lagrange Expressions and Conservation Laws. Aequa- tiones Mathematicae, 17, 255-291.
  • Anderson, I.M, Lovelock, D., (1976). A Characterization of the Einstein Tensor in Terms of Spinors. J. Math. Phys., 17, 1001-1003.
  • Anderson, I.M, (1974). The Neutrino Energy-Momentum Tensor and the Weyl Equations in Curved Space-Time. General Relativity and Gravitation, 6, 621-642.

In-House Journal

    Professional Journal

    • Anderson, I.M, Pohjanpelto, J., (2012). Variational principles for natural divergence-free tensors in metric field theories. Journal of Geometry and Physics , 62, 2376--2388.
    • Anderson, I.M, Kruglikov, B., (2011). Rank 2 distributions of Monge equations: Symmetries, equivalences, extensions. Advances in Mathematics, 228, 1435-1465.

    An asterisk (*) at the end of a publication indicates that it has not been peer-reviewed.

    Publications | MultiMedia

    Software

    An asterisk (*) at the end of a publication indicates that it has not been peer-reviewed.

    Publications | Technical Reports

    Research Reports

    Other Reports

      An asterisk (*) at the end of a publication indicates that it has not been peer-reviewed.

      Publications | Other

      Other

        An asterisk (*) at the end of a publication indicates that it has not been peer-reviewed.

        Teaching

        MATH 6120 - Differential Geometry, Spring 2021
        MATH 4310 - Introduction to Algebraic Structures, Spring 2021
        MATH 5810 - Topics in Mathematics, Fall 2019
        MATH 5110 - Differential Geometry, Spring 2019
        MATH 6910 - Directed Reading and Conference, Spring 2019
        MATH 5220 - Introduction to Analysis II, Spring 2019
        MATH, PHYS 5500, 5810 - Intermediate Topics in Physics (Topic), Fall 2018
        MATH 4310 - Introduction to Algebraic Structures, Fall 2018
        MATH 5210 - Introduction to Analysis I, Fall 2018
        MATH 6910 - Directed Reading and Conference, Spring 2018
        MATH 4310 - Introduction to Algebraic Structures, Spring 2018
        MATH 6350 - Multilinear Algebra and Matrix Theory, Spring 2018
        MATH 5810 - Topics in Mathematics, Spring 2018
        MATH 6810 - Topics in Mathematics (Topic), Spring 2018

        Graduate Students Mentored

        Brandon Ashley, Mathematics & Statistics, June 2017
        Ben Shaw, Mathematics & Statistics, August 2019 - July 2021
        Cody Squellati, Mathematics & Statistics, January 2018 - May 2020
        Mychelle Parker, Mathematics & Statistics, June 2016 - September 2018
        Jacob Kullberg, Mathematics & Statistics, September 2016 - March 2018
        Hannah Lewis, Mathematics & Statistics, September 2013 - October 2017
        Jesse Hicks, Mathematics & Statistics 2016
        Jordan Rozum, Mathematics & Statistics, June 2014 - October 2015
        Spencer Sitton, Mathematics & Statistics, June 2009 - June 2014
        Jesse Hicks, Mathematics & Statistics, June 2011 - December 2013
        Tom Apedaile, Mathematics & Statistics, June 2011 - December 2013
        Francesco Strazzullo, 2009
        Alan Perry, 2007
        Matt Biesecker, 2004
        Adam Bower, 2002
        Charles Miller, 1999
        Martin Juras, 1997
        Cinnamon Hillyard, 1992
        Hiroshi Nagao, 1981