Our former student Giles Gardam (did honours with Anne Thomas) just announced his new exciting result that Kaplansky’s unit conjecture is false. See the blog post by Gil Kalai: https://gilkalai.wordpress.com/2021/02/25/to-cheer-you-up-in-difficult-times-21-giles-gardam-lecture-and-new-result-on-kaplanskys-conjectures/ Congratulations Giles!