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math.AG2026
A Tropical Viewpoint on the Nagata--Biran--Szemberg Conjecture
Juliette Bruce
We give a tropical perspective on the recent arguments announced by OpenAI for Nagata's conjecture and the Nagata--Biran--Szemberg conjecture. By degenerating to both the normal co…
math.AG2026
Level structures on tropical abelian varieties
Eran Assaf, Madeline Brandt, Juliette Bruce +2
We introduce level structures on tropical abelian varieties and give a modular interpretation of , the tropicalization of the moduli space $\mathcal{A}_g[m]…
math.AG2025
Tropicalizations of locally symmetric varieties
Eran Assaf, Madeline Brandt, Juliette Bruce +2
This paper provides a rigorous study of tropicalizations of locally symmetric varieties. We give applications beyond tropical geometry, to the cohomology of moduli spaces as well a…