In collaboration with
James Lepowsky and
Arne Meurman, he constructed the
monster vertex algebra, a vertex algebra which provides a representation of the
monster group. Around 1990, as a member of the School of Mathematics at the
Institute for Advanced Study, Frenkel worked on the mathematical
theory of knots, hoping to develop a theory in which the knot would be seen as a physical object. He continued to develop the idea with his student
Mikhail Khovanov, and their collaboration ultimately led to the discovery of
Khovanov homology, a refinement of the
Jones polynomial, in 2002. A detailed description of Igor Frenkel's research over the years can be found in ==References==