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

Jerry Lodder

Department of Mathematical Sciences
New Mexico State University
Las Cruces, NM 88003
E-mail:jlodder@nmsu.edu
Office phone: 575 646-2835
Dept. Secretary: 575 646-3901

Education
1981-1987 Ph.D., Stanford University, Stanford, CA
June 1984 M.S., Stanford University
1977-1981 B.A. in Mathematics and German, Wabash College, Crawfordsville, IN

Professional Positions

  • Sept. 1987{1994 Assistant Professor, New Mexico State University
  • Aug. 1994{2004 Associate Professor, New Mexico State University
  • Aug. 2004{Present Professor, New Mexico State University
  • Summer 1990 Member, Mathematical Sciences Research Institute, Berkeley, CA
  • Autumn 1992 Invited Professor, Institut de Recherche Mathématique Avancée, Strasbourg, France
  • Autumn 1995 Chercheur associé, Centre National de la Recherche Scientique, Strasbourg, France
  • Spring 1996 Visiting Scholar, Massachusetts Institute of Technology
  • Autumn 1998 Research Fellow, Institut des Hautes Études Scientiques, Paris, France
  • Autumn 2000 Visiting Scholar, Stanford University, Stanford, CA
  • Aug. 2004-2005 Visiting Scholar, University of Southern California

Scholarly Interests

  • Algebraic Topology, K-Theory, Differential Geometry, Mathematics Education,
  • Use of History in Teaching Mathematics

Publications

  1. "Dihedral Homology and the Free Loop Space," Proceedings of the London Mathematical Society, 60, (1990) 201-224.
  2. "Cyclic Homology and de Rham Cohomology," Mathematische Zeitschrift, 208, (1991), 489-502.
  3. "Dihedral Homology and Homotopy Fixed Point Sets," in Contemporary Mathematics, 146, M. C. Tangora ed., (1993) 215-224.
  4. "Leibniz Homology and The James Model ," Mathematische Nachrichten, 175, (1995) 209-229.
  5. "Dihedral Homology and Hermitian K-theory," K-Theory, 10, (1996) 175-196.
  6. "Leibniz Homology and the Hilton-Milnor Theorem," Topology, 36, No. 3. (1997) 729-743.
  7. "Leibniz Cohomology for Di erentiable Manifolds," Annales de l'Institut Fourier, 48, 1, (1998) 73-95.
  8. "Rigidity of Secondary Characteristic Classes," Differential Geometry and its Applications,12, (2000) 207-218.
  9. "From Leibniz Homology to Cyclic Homology," K-Theory, 27, (2002), 359-370.
  10. "Curvature in the Calculus Curriculum," The American Mathematical Monthly, 110, 7, (2003) 593-605.
  11. "Introducing Logic via Turing Machines," accepted for the Mathematical Association of America's refereed volume Use of Recent History of Mathematics in Teaching.
  12. "Curvature and the Notion of Space," book chapter in Mathematics in the Masters' Own Words, accepted by Springer Verlag.
  13. "Leibniz Cohomology and the Calculus of Variations," Differential Geometry and its Applications, 21, (2004) 113-126.
  14. "Binary Arithmetic from the Chinese Abacus to the Electronic Digital Computer," submitted to Mathematics Magazine.
  15. "Periodicity in Leibniz Homology," submitted to K-Theory.

Web Sites Developed
www.math.nmsu.edu/hist projects

Professional Service
Referee, Topology
Referee, The American Mathematical Monthly
Referee, Communications in Algebra
Referee, K-Theory
Referee, Journal of Pure and Applied Algebra
Referee, Proceedings of the American Mathematical Society
Referee, Illinois Journal of Mathematics
Referee, Applied General Topology
Reviewer, Mathematical Reviews of the American Mathematical Society
Reviewer, Zentralblatt fur Mathematik
Member, American Mathematical Society
Member, Mathematical Association of America

Grants, Awards, Honors

  • Phi Beta Kappa, Summa cum laude
  • New Mexico State University, Arts and Sciences Minigrant, No. RC 90-051,for research activities during the summer of 1990.
  • Research Grant from the Universite Louis Pasteur to work with Prof. Lodayduring the Autumn of 1992.
  • New Mexico State University, Arts and Sciences Minigrant, No. RC 92-076,2for travel to France during 1992.
  • New Mexico State University, Joint Vice President/College Research Award, summer 1993.
  • New Mexico State University, Arts and Sciences Minigrant, No. RC 94-053,for travel to Europe during the summer of 1994.
  • Research grant from the Centre National de la Recherche Scienti que to work withProf. Loday, Autumn, 1995.
  • NSF grant, Division of Undergraduate Education, DUE-96-52872, "A Capstone Course:Learning Mathematics Through Original Sources," June, 1997 - May, 1999, Principal Investigator.
  • New Mexico State University, Department of Mathematical Sciences Summer ResearchAward, summer 1997.
  • NSF grant, Division of Mathematical Sciences, DMS-97-04891, "Leibniz Cohomology,Differential Geometry and Foliations," August, 1997 - July, 1999, Principal Investigator.
  • New Mexico State University, Department of Mathematical Sciences Summer ResearchAward, summer 2002.
  • NSF grant, Division of Undergraduate Education, DUE-02-31113, "Teaching DiscreteMathematics via Original Historical Sources," June, 2003 - June, 2006, Principal Investigator.

Graduate Student Committees
W. Gallegos Master's Committee Member, Mathematics, March, 1991
M. Rollins Ph.D. Committee Member, EE, October, 1991
D. Stull Master's Committee, Dean's Representative, CEP, March, 1992
M. Srikant Master's Committee Member, Mathematics, June 1993
A. Robinson Master's Committee, Dean's Representative, IE, April, 1994
D. Risinger Master's Committee Member, Mathematics, April, 1995
E. Quinonez-Rico Ph.D. Committee Member, Mathematics, September, 1997
N. Romero Master's Committee, Dean's Representative, Business, April, 1998
K. Jorgenson Ph.D. Committee Member, Mathematics, April, 1999
J.-Y. Oh Ph.D. Committee Chair, IE, November, 2001
Y. Chuca Master's Committee Member, Mathematics, April, 2002
C. Trenado Master's Committee Member, Mathematics, November, 2002
K. Bataineh Ph.D. Committee Member, Mathematics, March, 2003
L. Hanna Master's Committee Member, Mathematics, April, 2003
J.-Y. Oh Ph.D. Final Defense, Dean's Representative, IE, June, 2003

Teaching Experience
1982 - June 1987 Taught ten courses in Calculus at Stanford University.
Sept. 1987 - Present New Mexico State University
Autumn 1987: Math 125, Math 291; Spring 1988: Math 192, Math 291
Summer 1988: Math 279
Autumn 1988: Math 392, Math 480; Spring 1989: Math 291, Math 279
Autumn 1989: Math 230, Stat 251; Spring 1990: Math 191, Math 482
Autumn 1990: Math 291P, Math 481; Spring 1991: Math 192, Math 482
Autumn 1991: Math 291, Math 459; Spring 1992: Math 279, Math 643
Autumn 1992: academic leave; Spring 1993: Math 192, Math 480
Autumn 1993: Math 279, Math 291; Spring 1994: Math 192, Math 480
Autumn 1994: Math 332, Math 451; Spring 1995: Math 411G, Math 643
Autumn 1995: sabbatical leave; Spring 1996: sabbatical leave
Autumn 1996: Math 280, Math 541; Spring 1997: Math 411G, Math 542
Autumn 1997: Math 655; Spring 1998: Math 411G
Autumn 1998: academic leave; Spring 1999: Math 279, Math 411G
Autumn 1999: Math 279, Math 591; Spring 2000: academic leave
Autumn 2000: academic leave; Spring 2001: Math 280, Math 291
Autumn 2001: Math 391, Math 480; Spring 2002: Math 279, Math 561
Autumn 2002: Math 279G, Math 643; Spring 2003: Math 330, Math 555
Autumn 2003: Math 279; Spring 2004: Math 210, Math 561
Aug. 2004-2005: sabbatical leave

Service to the University

  • 1990-1991 Member, Dept. of Mathematical Sciences, Holiday Symposium Committee
  • Member, Dept. of Mathematical Sciences, Student Honors AssemblyCommittee
  • Spring 1991 Course Coordinator, Math 192
  • 1991-1992 Member, Dept. of Mathematical Sciences, Pi Mu Epsilon Committee
  • Member, Dept. of Mathematical Sciences, High School Contest Committee
  • Fall 1991 Course Coordinator, Math 291
  • Spring 1992 Course Coordinator, Math 279
  • Spring 1993 Member, Dept. of Mathematical Sciences, Student Honors Assembly
  • 1993-1994 Member, Dept. of Mathematical Sciences, Teaching Committee
  • 1993-1994 Member, Dept. of Mathematical Sciences, High School Contest Committee
  • 1993-1994 Member, Dept. of Mathematical Sciences, Student Honors Assembly
  • Spring 1994 Course Coordinator, Math 192
  • 1994-1995 Member, Dept. of Mathematical Sciences, Teaching Committee
  • 1994-1995 Member, Dept. of Mathematical Sciences, Student Honors Assembly
  • 1994-1995 Member, Dept. of Mathematical Sciences, Holiday Symposium Committee
  • 1995-1996 sabbatical leave
  • Autumn 1996 Course Coordinator, Math 280
  • 1996-1997 Chair, Dept. of Mathematical Sciences, Curriculum Committee
  • 1997-1998 Member, Dept. of Mathematical Sciences, Tenure and Promotion Committee
  • 1997-1999 Member, Dept. of Mathematical Sciences, Graduate Studies Committee
  • 1998-1999 Member, College of Arts and Sciences, Research A airs Committee
  • 2000-2001 Member, Dept. of Mathematical Sciences, Hiring Committee
  • 2001-2002 Member, College of Arts and Sciences, Research A airs Committee
  • 2001 Departmental Liaison, Rocky Mountain Consortium of Mathematics
  • Spring 2001 Course Coordinator, Math 291
  • 2001-2002 Member, Dept. of Mathematical Sciences, Display Case Committee
  • 2001-2002 Chair, College of Arts and Sciences, Research A airs Committee
  • 2001-2002 Member, College of Arts and Sciences, College Council
  • 2002-2003 Chair, Dept. of Mathematical Sciences, Hiring Committee
  • 2002-2003 Member, Dept. of Mathematical Sciences, Tenure and Promotion Committee
  • 2002-2003 Member, Dept. of Mathematical Sciences, Majors and Minors Committee
  • 2002-2004 Departmental Liaison, Rocky Mountain Consortium of Mathematics
  • 2002-2004 Member, College of Arts and Sciences, Research A airs Committee
  • 2003 Member, Dept. of Mathematical Sciences, Advisory Committee
  • 2003-2004 Member, Dept. of Mathematical Sciences, Tenure and Promotion Committee
  • 2003-2004 Member, Dept. of Mathematical Sciences, Teaching Committee

Conference Addresses and Selected Seminar Lectures

  • "Dihedral Homology and the Free Loop Space," conference address, regional meeting of the American Mathematical Society, Las Cruces, NM, April 8, 1988.
  • "Cyclic Homology of Polynomial Algebras," conference address, conference on Geometry and Topology, Lehigh University, Bethlehem, PA, May 27, 1989.
  • "Cyclic Homology and K-theory," colloquium address, Southwest Missouri State University,Springfield, MO, April 10, 1989.
  • "Dihedral Homology and Hermitian K-theory," seminar lecture, joint UNM-NMSU Geometry and Topology Seminar, Las Cruces, NM, Feb. 29, 1992.
  • "Dihedral Homology and Hermitian K-theory," conference address, International Conference on K-theory, Strasbourg, France, July 2, 1992.
  • "On Dihedral Homology," seminar lecture, Universität Osnabürck, Osnabrück, Germany Oct. 28, 1992.
  • "Dihedral Homology and Homotopy Fixed Point Sets," seminar lecture, Institut de Recherche Mathématique Avancée, Strasbourg, France, Nov. 10, 1992.
  • "Leibniz Homology and multi-simplicial Sets," seminar lecture, Institut de Recherche Mathématique Avancée, Strasbourg, France, Dec. 1, 1992.
  • "Leibniz Homology and the James Model," colloquium address, Washington University, St. Louis, MO, March 4, 1993.
  • "Leibniz Homology and the James Model," plenary address, conference on Homologie des Algebres non commutatives, Luminy, France, June 14, 1993.
  • "Leibniz Homology and the James Model," joint seminar lecture, UNM-NMSU Geometry and Topology Seminar, Albuquerque, NM, Oct. 23, 1993.
  • "A Noncommutative Framework for Lie Algebra Homology," conference address, Algebraic K-theory and Arithmetic, Waterloo, Canada, March 2, 1994.
  • "Projects as Alternative Teaching Strategies," invited address, New Experiences in Teaching, Minneapolis, MN, August 12-14, 1994.
  • "L'homologie de Leibniz pour les variétés différentiables," seminar lecture, Institut de Recherche Mathématique Avancée, Strasbourg, France, Dec. 7, 1995.
  • "On Leibniz Homology," colloquium address, Washington University, Saint Louis, MO, Feb. 22, 1996.
  • "Leibniz Homology and Geometry," seminar lecture, Massachusetts Institute of Technology, Cambridge, MA, March 18, 1996.
  • "Leibniz Homology and the Godbillon-Vey invariant," conference address, Conference on Higher Homotopy Structures in Topology and Mathematical Physics, Vassar College, Poughkeepsie, NY, June 14, 1996.
  • "Leibniz Cohomology and Foliations," invited plenary address, Méthodes homologiques et répresentations de groupes, Luminy France, July 4, 1997.
  • "The Leibniz Invariant for Di erentiable Manifolds," invited address, American Mathematical Society Summer Research Conference on Algebraic K-theory, Seattle, July 24, 1997.
  • "Leibniz Cohomology and Foliations," conference lecture, Special Session on Geometry and Analysis of Foliations, Regional Meeting of the AMS, Albuquerque, Nov. 8, 1997.
  • "Leibniz Cohomology and Foliations," International Congress of Mathematicians,Berlin Germany, Aug. 18-27, 1998, invited short communication.
  • "Non-commutative Gelfand-Fuks Cohomology and Foliations," Joint Mathematics Meeting, San Antonio, Jan. 13-16, 1999, invited special session speaker.
  • "Finding Motivation for Upper Division Mathematics through Original Historical Sources," Joint Mathematics Meeting, San Antonio, Jan. 13-16, 1999, Mathematical Association of America minicourse leader, (joint with Professor Pengelley).
  • "A Structure Theorem for Leibniz Cohomology and Applications," invited plenary address,Colloque: Up to Homotopy, Luminy France, June 22, 2000.
  • "Rigidity of Secondary Characteristic Classes," Stanford University, Oct. 18, 2000, seminar lecture.
  • "Researches on the Curvature of Surfaces," Joint Mathematics Meeting, New Orleans, Jan. 10-13, 2001, invited special session speaker.
  • "Leibniz Homology, Characteristic Classes, K-theory and Binary Decision Trees," New Mexico State University, Oct. 10, 17, 24, 2001, topology seminar lectures.
  • "Dialgebra Homology and Binary Planar Trees," New Mexico State University, Jan. 23, 2002, topology seminar lecture.
  • "Curvature in the Calculus Curriculum," Joint Mathematics Meeting, San Diego, Jan. 7-9, 2002, invited special session speaker.
  • "New Manifold Invariants," New Mexico State University, Oct. 17, 2002, colloquium lecture.
  • "Introducing Logic via Turing Machines," Joint Mathematics Meeting, Baltimore, Jan. 15-18, 2003, invited special session speaker.
  • "The Leibniz Coboundary of the Riemann Curvature Tensor," New Mexico State University Oct. 29, 2003, topology seminar lecture.
  • "Teaching Discrete Mathematics via Primary Historical Sources," Joint Mathematics Meeting, Phoenix, Jan. 7-10, 2004, invited special session speaker.
  • "On Leibniz Homology," University of Southern California, Nov. 22, 2004,algebra seminar lecture.
  • "Learning Induction from Pascal's Arithmetical Triangle," Joint Mathematics Meeting, Atlanta, Jan. 4-8, 2005, National Science Foundation funded display.
  • "New Manifold Invariants," University of Southern California, Jan. 31, 2005, geometry seminar lecture.

Languages
French, German