Contact: Maridith Geuder
With assistance from a regional research consortium, a Mississippi State mathematician is proposing a new approach to prove a famous mathematical conjecture.
Assistant professor Kevin P. Knudson of the university's department of mathematics and statistics is among two dozen individuals from 15 states receiving the Oak Ridge Associated Universities' 2003 Ralph E. Powe Junior Faculty Enhancement Award. Named for the late MSU research vice president, the $5,000 awards were established by the Tennessee-based organization to provide "seed money" for faculty members in the early stages of their careers.
Knudson, who taught at Wayne State University before joining the MSU faculty last year, has focused his study on the homology theory of groups of matrices. The plural of matrix, matrices are rectangular arrays of numbers, algebraic symbols or mathematical functions that may be added and multiplied according to certain rules.
"Roughly speaking, homology measures the number of 'holes' of various dimensions in a geometrical object," he explained.
According to Knudson, a widely debated conjecture advanced by Eric Friedlander of Northwestern University asserts that the homology of the two different spaces is the same. Friedlander long has worked to find relationships and applications across various mathematical fields.
Knudson, who holds a doctorate from Duke University, said his new approach to Friedlander's conjecture will be boosted with the Powe award. If successful, "proof [of the conjecture] would have far-reaching consequences in the fields of algebraic geometry, equivariant topology, and algebraic K-theory," he added.
Department head Bruce R. Ebanks said that Knudson's research has "resulted in a steady stream of publications in excellent journals, numerous invited presentations at conferences and several research grants and fellowships. He's also a very fine teacher."