$
\newcommand\A{\mathrm{A}}
\newcommand\E{\mathrm{E}}
\newcommand\G{\mathrm{G}}
\newcommand\H{\mathrm{H}}
\newcommand\K{\mathrm{K}}
\newcommand\L{\mathrm{L}}
\newcommand\M{\mathrm{M}}
\newcommand\Ascr{\mathcal{A}}
\newcommand\Cscr{\mathcal{C}}
\newcommand\Dscr{\mathcal{D}}
\newcommand\Escr{\mathcal{E}}
\newcommand\Kscr{\mathcal{K}}
\newcommand\Perfscr{\mathcal{P}\mathrm{erf}}
\newcommand\Acscr{\mathcal{A}\mathrm{c}}
\newcommand\heart{\heartsuit}
\newcommand\cn{\mathrm{cn}}
\newcommand\op{\mathrm{op}}
\newcommand\Ho{\mathrm{Ho}}
\newcommand\dR{\mathrm{dR}}
\newcommand\HH{\mathrm{HH}}
\newcommand\TC{\mathrm{TC}}
\newcommand\ku{\mathrm{ku}}
\newcommand{\bMap}{\mathbf{Map}}
\newcommand{\End}{\mathrm{End}}
\newcommand{\Mod}{\mathrm{Mod}}
\newcommand\bE{\mathbf{E}}
\newcommand\bZ{\mathbf{Z}}
\newcommand\bAM{\mathbf{AM}}
\newcommand\bLM{\mathbf{LM}}
\newcommand\Spec{\mathrm{Spec}}
\newcommand\we{\simeq}
\newcommand\qc{\mathrm{qc}}
$
I have posted two Oberwolfach Reports ([1] and [2]) from this year, one on the even filtration of
Hahn–Raksit–Wilson [3] and one on forthcoming work of my own on filtered derived commutative rings.
The first report serves as my arXiv review of Hahn–Raksit–Wilson, although I wrote it before it appeared on the
arXiv and I do not discuss their application of the even filtration to $\TC$ of the Adams summand of
$\ku$. Basically, the even filtration is a big deal.
References
[1] Antieau, The even filtration after Hahn, Raksit, and Wilson, Oberwolfach Report
24/2022.
[2] Antieau, What is de Rham cohomology?, Oberwolfach Report
35/2022.
[3] Hahn, Raksit, and Wilson, A motivic filtration on the topological cyclic homology of
commutative ring spectra, arXiv:2206.11208.