I will give a brief overview of the development of motivic cohomology, its parallels with singular cohomology and its place in motivic stable homotopy theory. I will then describe some of the recent off-shoots of motivic cohomology: cycles with modulus, Chow-Witt theory, and motivic filtrations on p-adic K-theory, and conclude with some speculations on future developments.
https://icm2022.abstractserver.com/program/#/details/sessions/211 [4]
Links:
[1] https://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/de/node/3444
[3] https://www.mpim-bonn.mpg.de/de/node/11392
[4] https://icm2022.abstractserver.com/program/#/details/sessions/211