the tale of three triangles

the tale of three triangles is a long-form video created using manim. you can watch it on youtube, or on bilibili, where it has been subtitled in mandarin and reposted with permission. the comments are more interesting on the second.¹

the video was also featured by content creator 3blue1brown as an honorable mention in the first summer of math exposition (some1), which had over 1000 entrants. you can watch 3blue1brown's video on youtube, and here is a playlist of entries, including my contribution.

repetitions of pak-stanley labels²

the pak-stanley algorithm is a correspondence between superstable configurations on a graph G and the regions of the G-shi hyperplane arrangement. if G is complete, this correspondence is bijective. it remains an open problem to characterize the failure of bijectivity for arbitrary G. in this paper, we make significant progress towards resolving this open problem by solving it for trees and graphs with a single cycle, as well as indicating the next steps for further analysis.