A Tropical Proof of the Brill-Noether Theorem

This is a continuation of my talk from last week. Recall that we observed how the degeneration technique provides limits of line bundles on the stable curve, but these limits are not unique, which prevents us from classifying them effectively. This week, we will see that this “obstacle” also presents an opportunity to explore the twisting of the limit line bundles through the chip-firing game, ultimately leading to a proof of the Brill-Noether non-existence theorem.