String Topology of Finite Groups of Lie Type

Explore the intriguing connections between finite groups of Lie type and string topology in this comprehensive lecture. Delve into the cohomology calculations of groups like SL_n(F_q) and Sp_n(F_q), examining their significance in various mathematical fields such as K-theory and stratification results. Investigate the observed agreement between mod ell cohomology of these groups and that of LBG(C), the free loop space on the classifying space of corresponding complex algebraic groups. Gain insights into recent research combining ell-compact groups with string topology, as presented by Jesper Grodal in collaboration with Anssi Lahtinen. Discover the underlying reasons for this apparent "coincidence" and broaden your understanding of this fascinating area of mathematics.