Click the title above to play a fun computer game called PathForms. Its goal is to visualize what is called Nielsen's algorithm in geometric group theory. In its classic definition, Nielsen's algorithm is stated in an unrevealing algebraic form. We created a visual, geometric way of describing and running Nielsen's algorithm: the player draws several paths in a tree and then transforms the paths by inverting them and concatenating.
For level 1 of the game, the goal is to keep shortening the paths to eventually bring them to the two shortest paths: a and b. We expect to eventually implement several other levels of this game, with different goals, so please come again and play again.
In Spring 2025 (as an IML project):
Professor: Igor Mineyev.
Graduate mentor: Jihong Cai.
Undergraduate students: Haochen Ding, Maxwell Liu, Diya Mathew, Ruoqi Wang.
In Summer 2025 (we met informally and had summer fun improving the game):
Professor: Igor Mineyev.
Graduate mentor: Jihong Cai.
Undergraduate students: Maxwell Liu.
The link to this and other games is available from Igor Mineyev's Math Page.