Faculty
Jerry M. LodderMy scholarly activities are characterized by both breadth and depth, ranging from traditional research topics in algebraic topology to applications in differential geometry to groundbreaking publications in mathematics pedagogy. My work has found external funding in three separate grants from the National Science Foundation, additional funding as a research fellow at the Institut de Recherche Mathématique Avancée in Strasbourg, the Institut des Hautes Etudes Scientifiques near Paris, as well as a further research grant from the Centre National de la Recherche Scientifique (CNRS). Outside of New Mexico State University, I have delivered numerous seminar lectures, conference addresses, colloquia, workshops, and special session presentations, in a variety of venues, ranging from regional meetings of the American Mathematical Society to national meetings to international conferences, including the quadrennial International Congress of Mathematicians.
As an area of specialization, I have pioneered Leibniz cohomology as a tool for the study of the algebraic structure and geometric space, capturing classical ideas of curvature as cochains in the Leibniz complex, while detecting modern invariants of Ktheory and characteristic classes, both primary and exotic, as nontrivial Leibniz cohomology classes. When applied to differentiable manifolds, Leibniz cohomology offers new geometric information with the potential to be a complete diffeomorphism invariant. Born as a collaboration with Distinguished Research Professor JeanLouis Loday of Strasbourg, my work significantly enlarges the scope of the Leibniz theory, with students of the Loday school (Frabetti and Wagemann) writing papers that directly build on my results. The subject will endure for the foreseeable future.

Ted StanfordMy areas of interest are “knot theory and topological dynamics” or maybe “lowdimensional topology and topological dynamics.”
My research is mostly concerned with knots and links in S3. I have done some work with finitetype invariants (also called Vassiliev invariants), and some of their generalizations. I have worked on other topics related to knots and links, such as braids and knotted graphs. I am also doing some work on knot and link groups and some of their representations into a finite group or into finitedimensional algebras. Current and recent collaborators in knot theory include Jacob Mostovoy, Jim Conant, and Swatee Naik. Along other lines, I have a research project with Erik Bollt and others to understand the symbol dynamics arising from a nongenerating partition of a topological dynamical system.
