Recordings can be found here:

https://huji.cloud.panopto.eu/Panopto/Pages/Sessions/List.aspx?folderID=b9e88c65-aaa3-4df5-90ff-af090084e964

Lecture notes can be found here:

https://sites.google.com/view/lioryanovskishomepage/home

Lior Yanovski "Descent in algebraic K-theory" (80885 in shnaton)

Abstract: Algebraic K-theory is a fundamental invariant of rings and
categories with applications to various fields of mathematics
including number theory, topology, and algebraic geometry.
It is however very hard to compute. This is largely due to the lack of
good descent properties of algebraic K-theory (i.e., it does not
satisfy a good "local-to-global principle").

From a modern perspective, the algebraic K-theory groups are viewed as
the homotopy groups of the algebraic K-theory spectrum, which is
roughly speaking a space endowed with a
homotopy-coherent commutative group structure. Using techniques of
stable homotopy theory, one can study a spectrum by decomposing it
into more accessible "monochromatic" pieces
(and hopefully also gluing them back together).

In this seminar, after a gentle introduction to algebraic K-theory and
stable homotopy theory, we shall focus on the recent ground-breaking
results of Land-Mathew-Meier-Tamme and
Clausen-Mathew-Naumann-Noel on purity and descent in chromatically
localized algebraic K-theory.

If time permits, we shall also discuss the results of Ben
Moshe-Carmeli-Schlank and myself on higher descent and/or those of
Clausen-Mathew on hyperdescent.