Chromatic homotopy theory is a branch of algebraic topology which has seen an explosion of new activity in recent years. In particular, in the summer of 2023 Burklund, Hahn, Levy and Schlank announced the negative resolution of Ravenel's Telescope Conjecture, which had been open since 1984. That conjecture said that two categories are the same; now we know that they are different, and we expect to find a rich and intricate structure in the gap between them.
In this talk I will attempt to survey, for a general pure mathematical audience, the main ideas of chromatic homotopy theory and some highlights of recent progress.
Neil Strickland is Professor of Algebraic Topology at the University of Sheffield. He was previously a C.L.E. Moore Instructor at the Massachusetts Institute of Technology and then a research fellow at Trinity College Cambridge before moving to Sheffield in 1998.