LEXINGTON, Ky. (Aug. 21, 2017) ― University of Kentucky mathematics professor Bert Guillou recently received funding from the National Science Foundation (NSF) for his research in homotopy theory. The $139,765 grant over three years will further understanding of all of the ways that a sphere can be mapped onto a sphere of a different dimension.
“This project will attempt to classify mappings in two related contexts,” Guillou said. “The first is a rigid world of algebraic geometry, where all objects can be described by polynomial equations. The other is the equivariant setting, where symmetries of the spheres are taken into account.”
Guillou will use recently developed techniques to tighten the connection between these two arenas and extend the range of dimensions in which these mappings can be classified.
“The calculation of the set of mappings of spheres has bearing on the classification of manifolds and to gauge theories in physics,” Guillou said.
Guillou joined the College of Arts and Sciences Department of Mathematics in 2012. He graduated with his doctorate in mathematics from the University of Chicago and received his undergraduate degrees in mathematics and philosophy from the University of Michigan.