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New Mexico State University
College of Arts and Sciences
Department of Mathematical Sciences

Marcus Cohen

Department of Mathematical Sciences
New Mexico State Univerisity
Las Cruces, NM 88003
Office Phone: (575) 646-1319

Employment

  • Associate Professor, Department of Mathematical Sciences, New Mexico State University. August 1984-Present
  • Assistant Professor, Department of Mathematics, University of Kentucky
    August 1980-July 1984
  • Postdoctoral Fellowship, Department of Mathematics, Stanford.
    June 1979-August 1980
  • Postdoctoral Fellowship, Department of Mathematics, University of California-Santa Cruz.
    August 1978-June 1979
  • Postdoctoral Assistantship, Department of Biology, Purdue.
    August 1977-June 1978

    Research Interests


    Current
  • Gauge Field Theory and Soliton Interactions. Particles as topological solitons in Lagrangian field theories. Dirac equations and the Maxwell-Dirac system on manifolds. Effective gauge theories of spinor soliton interactions. The first step has been accomplished: a four-spinor unification of electroweak and gravitational interactions, which recovers the Maxwell-Dirac-Einstein system for the interaction of massive, charged particles as an effective gauge theory of the far-field interactions of solitons on a curved spacetime. The next phase is now complete: the recovery of an effective SU (3) gauge theory for strong interactions from an eight-spinor Lagrangian????? What remains to be done is to "build" the families of mesons and hadrons as topological solitons of ?????


    • Previous
  • Nonlinear Optics. Coupled Mode Theory for Optical Resonators used in continuous domain optical computing, including, higher order tensorial mode couplings.
  • Nonlinear Wave Equations in Developmental and Neurobiology. Bifurcation theory of continuum embryonic and neural media. Pattern formation, selection, and recognition. Symmetries and invariant pattern recognition.

    Education
  • Ph.D. March 1977, University of Chicago, Department of Biophysics and Theoretical Biology.
  • M.Sc. May 1976, Harvard University, Population Dynamics and Ecology.
  • M.Sc. June 1975, University of Chicago, Department of Biophysics and Theoretical Biology.
  • B.A. June 1970, Harvard University, Chemistry and Physics.

    Postdoctoral Employment
  • August-1979-June 1980, Stanford University, Department of Mathematics (with Joe Keller).
  • June 1978-September 1979, University of California, Santa Cruz, Department of Mathematics (with Ralph Abraham).
  • September 1977-May 1978, Purdue University, Department of Biology (with Art Winfree)

    Predoctoral Employment
  • September 1971-May 1972, Research Assistant in Nuclear Magnetic Resonance Spectroscopy, Northwestern University, Physics Department.
  • June 1969-September 1969, Technical Writer, Harvard Observatory.
  • June 1968-September 1968, Lab Technician, Chemistry, Precision Electroplating Company, Chicago, Illinois.
  • June 1967-September 1967, Lab Technician, Electronics and EEG, University of Illinois.

    Fellowships
  • June 1976-March 1977 and September 1972-June 1975, NIH Traineeship in Theoretical Biology, University of Chicago.
  • September 1975-June 1976, Fellowship in Population Sciences, Harvard School of Public Health

    Grants
  • September 1985-September 1986, "Nonlinearities of the Brain and Their Implications for Optical Signal Processing", Air Force Office for Scientific Research (through Los Alamos National Laboratories); $19,900 (Wojciech Golic as Graduate Research Assistant on grant).
  • August 1987-July 1988, "Distributed Processing in Continuous Optical Media", "National Science Foundation, Lightwave Technology Division (through University of Colorado, Boulder); $75,000 (NMSU $32,000).
  • Fall 1987-Summer 1992, "A Multisensor Image Analysis System," Army Research Office, (with Electrical Engineering at NMSU); #2,200,000.
  • July 1988-August 1991, "Student Research Projects in the Calculus Curriculum", National Science Foundation; $228,888 (with David Pengelley, Doug Kurtz, Ed Gaughan, Art Knoebel).
  • August 1990-January 1993, "A Model Program Using Student Research Projects in Calculus and Differential Equations", National Science Foundation; $350, 874 (with David Pengelley). March 1991-April 1991, "Particles as Topological Structures in a Nonlinear Field", Arts and Sciences Minigrant, New Mexico State University.

    Patents
    A Musical Instrument with Electromechanical Feedback (U.S. Patent #138,213) 1972

    Publications
    * Publications in refereed journals
    1.* The Cyclic AMP Control System in the Development of Dictyostelium Discoideum I:Cellular Dynamics. J. Theor. Biol. 69(1977) 57-85.
    2.* The Cyclic AMP Control System in the Development of Dictyostelium Discoideum II: An Allosteric Model. J. Theor. Biol 12(1978) 231-255.
    3.* Diffusion-induced Morphogenesis in the Development of Dictyostelium. J. Theor. Biol. 93(1981) 881-908.
    4.* "Interacting Nonlinear Waves in a Neural Continuum Model: Associative Memory and Pattern Recognition," Wave Phenomena: Modern Theory and Applications (eds. Rogers and Moodie) Elsevier Science Publishers B.V. (North Holland), 1984.
    5.* Distributed Computation in Neural Networks and Their Optical Analogs. SPIE Proceedings 540 (1985) 566-580.
    6.* Self Organization, Assocation, and Categorization in a Phase Conjugating Resonator. SPIE Proceedings 625 (1986) 214-219.
    7.* Design of a New Medium for Volume Holographic Information Processing. Applied Optics (Special Issue on Optical Computing) 25 (1986) 2288-2294
    8.* Coupled Mode Theory for Neural Networks: The Processing Capabilities of Nonlinear Mode-Mode Interactions at Cubic and Higher Order. American Institute of Physics Proceedings 151 (1986) 100-109.
    9.* Neural Networks with a Hopf Bifurcation: Slowly Modulated Waves. (co-author: W. H. Julian) IEEE First International Conference on Neural Networks Proceedings (1987) II-161 to II-168.
    10. Multiple Correlations in a Holographic Resonator. SPIE Proceedings 882 (1988) 122-131.
    11.* Multistability, Chains, and Cycles in Optical Multiwave Mixing Processes. (co-author: W.H. Julian) Applied Optics 29 (1990) 5268-5280.
    12.* Multistability and Associative Memory in a Phase-Conjugating Resonator. Journal of the Optical Society of America B 8(1991) 106-113.
    13.* "Student Research Projects in the Calculus Curriculum," (co-authors: E. Gaughan, A. Knoebel, D. Kurtz, and D. Pengelley) invited chapter in Priming the Calculus Pump: Innovations and Resources. MAA Notes 17 (1990) 159-173.
    14.* Student Research Projects in Calculus, (co-authors: E. Gaughan, A. Knoebel, D. Kurtz, and D. Pengelley) MAA Spectrum Series, (1992).
    15.* "Student Perceptions of Projects in Learning Calculus," (co-authors: M. Conley, E. Gaughan, A. Knoebel, D. Kurtz, D. Pengelley and C. Stuessy) International Journal of Mathematics Educations in Science and Technology 23 (1992) 175-192
    16.* "Making Calculus Students Think with Research Projects," (co-authors: Ed Gaughan, Art Knoebel, Doug Kurtz, David Pengelley) Mathematical Thinking and Problem Solving (ed. Alan H. Schoenfeld) Erlbaum (Hillsdale, New Jersery) 1994, 193-208.
    17.* "Quantization of Helicity on a Compact Spacetime", Foundations of Physics 25 (1995) 995-1016.
    18.* Inertial Mass from Spin Nonlinearity, International Journal of Modern Physics D 7 (1998) 663-699.
    19.* "A Nonlinear Twist on Inertia, Electromagnetism, and Gravitation," Fragments of Science: Festschrift for Mendel Sachs (ed. M. Ram) World Scientific (Singapore), (1999) 135-164.
    20.* Chiral Unification of Electroweak and Gravitational Interactions, International Journal of Modern Physics D 8, 4 (1999) 417-458.
    21.* "Cosmological Determination of the Weinberg Angle", invited article in The Photon and the Poincare Group (ed. V. Dvoeglasov) World Scientific (1999).
    22. "Mass and Interaction from Eight-Spinor Nonlinearity," in Proceedings of International Workshop on Lorenz Group, CPT, and Neutrinos Zacatecas, Mexico, (1999) to appear.
    23. "Eight-Spinor Grand Unification", in Proceedings from "What Comes Beyond the Standard Model?" Bled, Slovenia, (1999) to appear.

    Submissions
    S1.*Investigations in Applied Mathematics, book prospectus submitted April 1996. Investigations will be resubmitted separately (see S2, S3, and S4) after editing to stand alone as journal articles.
    S2.* Investigations in Applied Mathematics: Gravity's Rainbow", submitted April, 1996; to be resubmitted to MAA Monthly.
    S3.* Investigations in Applied Mathematics: Suspension Bridges", submitted April, 1996; to be resubmitted to MAA Monthly.
    S4.* "Investigations in Applied Mathematics: The Kaleidoscope and the Euclidean Group", submitted April, 1996; to be resubmitted to MAA Monthly.
    S5.* "Eight-Spinor Unifications of Electroweak, Gravitational, and Strong Interactions," International Journal of Modern Physics D, submitted August, 1999; under revision in accordance with editors suggestions.
    S6.* "How Gravity Breaks Out of the Unified Field," General Relativity and Gravitation, submitted, March, 2000.

    Talks Given (May 1983-present)
    1. "The Nonlinear Optics of a Model Neural Continuum." Conference on Fronts, Interfaces, and Patterns, Center for Nonlinear Studies, Los Alamos National Laboratory. May 1983.
    2. "Parametric Interference and Resonant Scattering in a Neural Continuum Model." Department of Physics, University of Southern California. May 1983.
    3. "The Geometrical Optics of Graded Potential Waves." Conference on Waves Pheonomena, Modern Theory & Applications, Toronto. July 1983.
    4. "Nonlinear coupled Wave Equations and Some Special Solutions." Nonlinear Optics Groups, Los Alamos National Laboratory. August 1983.
    5. "Bifurcating Waves in Neural Networks: Spontaneous and Driven Behavior." Department of Mathematics, University of Kentucky. April, 1984.
    6. "Pattern Recognition by Channeled Bifurcations in Neural Network Models." New Mexico State University. April, 1984.
    7. "Wave Equations with a Memory Nonlinearity." Department of Mathematics, San Francisco State University. April, 1984.
    8. "The Geometrical Optics of Graded Potential Waves." Physics Department, California State University, Fullerton. May 1984.
    9. "Waves in Neural Networks: Memory and Pattern Recognition." Department of Biology, University of California, Santa Barbara. May, 1984.
    10. "Harmonic Analysis in the Bifurcation Theory of Partial Differential Equations." Department of Mathematical Sciences, New Mexico State University. December, 1984.
    11. "Hierarchical Serial/Parallel Processing in Neural Networks." Computing Research Laboratory, New Mexico State University. March 1985.
    12. "The Nonlinear Optics of a Neural Continuum Model." Southwest Optical Society, Albuquerque, New Mexico. March 1985.
    13. "Distributed Computation in Neural Networks and Its Implications for Optical Signal Processing." Optical Society of America, Lake Tahoe, California. March 1985.
    14. "Design of a New Medium for Volume Holographic Information Processing." Computing Research Laboratory, New Mexico State University. April 1985.
    15. "Channeled Bifurcations and Learning in Neural Network Continuum Models." American Mathematical Society, Tucson, Arizona. April 1985.
    16. "Volume Holographic Information Processing in a Phase Conjugating Resonator." Optical Society of America, Washington, D.C. October 1985.
    17. "Association, Categorization, and Abstraction." Los Angeles Conference on Optical Computing (SPIE/Optical Society of America). January 1986.
    18. "Coupled Mode Equations for a Neural Network." Neural Network Meeting, Snowbird, Utah (NSF). April 1986.
    19. "Dynamical Reconstruction of Chains of Images in a Holographic Resonator." Workshop on State of the Art Developments in Nonlinear Optics, University of Arizona, Tucson. April 1987.
    20. "Neural Networks with a Hopf Bifurcation: Slowly Modulated Waves." IEEE First International Conference on Neural Networks, San Diego, California. June 1987.
    21. "The Nonlinear Schroedinger Equation in Optics and Quantum Mechanics." Physics Department, New Mexico State University. October 1987.
    22. "Multiple Correlations in a Holographic Resonator." SPIE, Los Angeles, California. January 1988.
    23. "Nonlinear Wave Equations in Optics." Physics Department, University of Texasat El Paso. February 1988.
    24. "Coupled Mode Theory for Pattern Discrimination." AMS Regional Meeting, Las Cruces, New Mexico. April 1988.
    25. "Bifurcation and Stable Reconstruction in Optical Neural Networks." AAAS Meeting (Rocky Mountain Math Consortium Session), Corvallis, Oregon. June 1988.
    26. "Optical Multi-Wave Resonances and Generalized Volume Holography." Optoelectronic Computing Systems Center Seminar, University of Colorado, Boulder. May 1989.
    27. "Neural Networks and Pattern Recognition." Statistics Seminar, New Mexico State University. September 1989.
    28. "Asymptotic Skyrmion Interactions." Nonlinear Wave Seminar, University of Colorado, Boulder. 1990.
    29. "Calculus for All Users," invited panelist, National Science Foundation Calculus Conference, San Antonio, Texas, October 1990.
    30. "Soliton Interactions in 3 + 1 Dimensions." Department of Mathematics, University of Arizona, Tucson. April 1991.
    31. "It's All Done With Mirrors." Mathematics Education Seminar, New Mexico State University. January 1996.
    32. "Lie Groups and Relativity," The Looking-Glass World of Quaternions and the Four-Dimensional Spin of the Electron. Mathematics Seminars, New Mexico State University. Spring 1996.
    33. "The Geometry of Spin, Charge, and Mass", Colloquium, Department of Mathematical Sciences, New Mexico State University, February 1997.
    34. "What is Spin?", Friday Afternoon Seminar, Department of Mathematical Sciences, New Mexico State University, February 1997.
    35. "Spinor Unification of Electromagnetism and Gravitation," Colloquium, Department of Mathematical Sciences, New Mexico State University. April 1997.
    36. "Dirac Mass and Spin Nonlinearity," Causality and Locality in Modern Physics, Toronto. August 1997.
    37. "A Nonlinear Twist on Inertia, Electromagnetism, and Gravitation," Mendel Sachs retirement symposium, Buffalo, New York. September 1997.
    38. "Spin Geometry, Topology, and Dynamics", Colloquium, Department of Mathematics, University of Texas-Austin. April 1998.
    39. "Spinors and Spacetime Geometry", Seminar, Los Alamos National Laboratories, Los Alamos, New Mexico. Spring 1998.
    40. "Spinor Geometry of a New Unified Field Theory", Colloquium, Department of Mathematical Sciences, New Mexico State University. October 1998.
    41. "Spin Bundles and Quantization", Topology Seminar, Department of Mathematical Sciences, New Mexico State University. October 1998.
    42. "Spinors in Curved Spacetime", Physics Institute, University of Zacatecas, Zacatecas, Mexico. February 1999.
    43. "Spinor Unification of Electroweak, Gravitational, and Strong Interactions", Colloquium, Department of Physics, New Mexico State University, March 1999.
    44. "Chern Forms for Bispinor Bundles," Topology Seminar NMSU, March 1999 through April 1999 (six talks).
    45. "Mass and Interaction from Eight-Spinor Nonlinearity," International Workshop on Lorenz Group, CPT, and Neutrinos, Zacatecas, Mexico, June 1999.
    46. "Eight-Spinor Grand Unification", "What Comes Beyond the Standard Model?" : A Workshop, Bled, Slovenia, July 1999

    Workshops and Seminars Organized and Conducted (May 1983-present)

    1. New Mexico State University Calculus Projects Workshop, Las Cruces, New Mexico, January 1990.
    2. New Mexico State University Calculus Projects Workshop, Las Cruces, New Mexico, May 1990.
    3. "Student Research Projects in the Calculus Curriculum." Two-day Workshop, California Calculus Consortium, San Luis Obispo, California, July 1990.
    4. Applied Mathematics Seminar, primary speaker, New Mexico State University, Las Cruces, New Mexico, Spring 1986.
    5. Mathematical Physics Seminar, primary speaker, New Mexico State University, Las Cruces, New Mexico, Fall 1986; Fall 1992; Spring 1993; Fall 1993.
    6. Geometry Seminar, primary speaker, New Mexico State University, Las Cruces, New Mexico, Spring 1994; Fall 1994.
    7. Invited two-day workshop on the Projects Program. California Consortium of Colleges and Universities, San Luis Obispo, California, July 1993.
    8. Invited two-day workshop on "Teaching Calculus with Real-World Investigations", University of Massachusetts-Amherst. July 1998.

    Teaching Experience (August 1980-present)

    The unifying theme in my teaching is the writing and classroom testing of new "discovery" projects in each class. These projects introduce central topics via an application, and lead students to discover for themselves the utility of the theory in solving the initially presented problem. In the process, they lead the students through a step-by-step development of the theory, tied to examples at each stage that stem from the problem at hand.

    In addition to the book already published, the new projects are being compiled and selected for a new book, provisionally accepted by the Mathematical Association of America. I have taken the opportunity to "vet" them in the classroom in 1993 to the present. Students' questions and problems have led me to extensively revise and rewrite these projects.