Stuff I'm interested in lately, easy for me to find:
- Actions on injective spaces/the coarsely Helly property as a "nonpositive curvature" property for groups, e.g. this paper by Urs Lang, this paper by Dominic Descombes and Urs Lang, and this paper by Thomas Haettel, Nima Hoda, and Harry Petyt.
- "Spaces of cubulations", e.g. this paper by Jonas Beyrer and Elia Fioravanti and this paper by Ruth Charney, Karen Vogtmann, and Corey Bregman.
- Some recent developments involving the Bestvina-Bromberg-Fujiwara construction: this paper by Matt Durham, Yair Minsky, and Alex Sisto and this paper by Mladen Bestvina, Ken Bromberg, and Koji Fujiwara.
- Coarse median spaces and their asymptotic cones: this and this paper by Brian Bowditch, this one by Rudolf Zeidler, and this one by Jason Behrstock, Cornelia Drutu, and Mark Sapir.
- Some cool recent stuff involving cube complexes: Michelle Chu's effective virtual specialness results, Marissa Miller's result on hierarchical hyperbolicity of the genus-2 handlebody group, Kasia Jankiewicz's lower bounds on cubical dimension, work of Devin Murray, Yulan Qing, and Abdul Zalloum on sublinearly contracting rays.