A Three-Regime Theorem for Flow-Firing

Date

Apr 16, 2026

Time

3:00 PM - 4:00 PM

Speaker

Selvi Kara

Affiliation

Bryn Mawr College

Language

en

Main Topic

Biologie

Host

Local Organisers: Nikola Sadovek, Maximilian Wiesmann, Giulio Zucal

Description

Flow-firing, introduced by Felzenszwalb-Klivans, is a 2D analogue of chip-firing: an integer flow on the edges of a cell complex evolves by repeatedly applying local rerouting moves around faces. In their original work, the only proven confluent family on the grid stabilized (independent of firing choices) into an Aztec diamond, a centered diamond-shaped patch of unit squares. In this talk I will explain how far this phenomenon extends. For a natural family of conservative “pulse” initial conditions, we prove a three-regime theorem: there is a small-support regime with unique stabilization to the Aztec diamond, an intermediate regime where stabilization occurs but the terminal state is not unique (though the Aztec diamond can still occur), and a large-support regime where confluence fails, including a range where the Aztec-diamond outcome is impossible.

Last modified: Mar 10, 2026, 7:37:54 AM