Research Focus:
Topology of three- and four- dimensional space
Topology, the study of space and continuity, interacts with almost all areas of mathematics. It is often referred to as “rubber sheet geometry,” with perhaps the best-known topological object being the Moebius strip, whose one-sided nature is vividly illustrated in a famous print by M.C. Escher.
Most of the current research group focuses on the topology of three- and four-dimensional space, which is close to the popular image of the subject. In the last 20 years, deep and surprising connections between this “geometric” topology and physical theories such as quantum gravity have emerged, and LSU is actively involved in exploring these connections.
Pat Gilmer works on topological quantum field theory, and Oliver Dasbach and Neal Stoltzfus are part of a National Science Foundation Focused Research Group searching for a direct link between hyperbolic structure in low dimensions and physical notions like quantum groups and path integrals.
The topology group has received strong support from federal agencies. Currently, Professors Scott Balridge, Tara Brendle, Dasbach, Gilmer, and Stoltzfus are supported by the NSF, while Cohen is supported by the National Security Agency.
Department of Mathematics
LSU’s Department of Mathematics has an active faculty that has been successful in making new mathematical discoveries, as well as engaging in work that contributes to developments in Algebra, Analysis, Topology, Probability, and Applied Mathematics. The department also makes strong contributions to mathematics education in Louisiana through partnerships with the Cain Center for Math and Science Literacy.
Among the many faculty members involved in such research is Robert Lipton, who leads an internationally respected group in applied mathematics that focuses on the mathematical problems associated with the design of new composites and superconductivity.
Peter Wolenski and other LSU mathematicians are investigating control theory problems motivated by questions in engineering. Gestur Olfasson and Boris Rubin lead LSU’s prominent research group in harmonic analysis. They are world renowned for contributions to integral and convex geometry, Radon transforms, wavelet transforms, and harmonic analysis on symmetric spaces. Their work has been featured in the Annals of Mathematics and Inventiones Mathematica.
Probabilists Hui Hsiung Kuo, Ambar Sungupta, and Padmanabhan Sundar study stochastic analysis. They have written problems in white noise analysis, mathematical physics, and mathematical finance.
In addition, the LSU research group in graph and matroid theory, led by James Oxley, has made such substantial mathematical advances and contributions that it is now one of the most prolific and highly regarded centers for the subject in the nation.
But what are faculty achievements without students? The Department of Mathematics has outstanding opportunities for undergraduates including the Research Experiences for Undergraduates Program, which provides able college sophomores and juniors the opportunity to engage in research on the topic of recognized mathematical significance. Also, the Mathematics Consultation Clinic helps prepare students for dynamic positions in industry and academics.
