Philip Tosteson

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20242026

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math.AG2026

Stable homology of strata of abelian differentials

Philip Tosteson

We show that the homology of strata of abelian differentials stabilizes in a range where the number of simple zeros is large relative to the homological degree. In this range, we s…

math.AG2025

Representation stability for moduli spaces of admissible covers

Megan Chang-Lee, Siddarth Kannan, Philip Tosteson

We prove a representation stability result for the sequence of spaces $M_{g, n}^{A}$ of pointed admissible $A$ -covers of stable $n$ -pointed genus- $g$ curves, for an abelian…

math.AG2025

Homological stability and Manin's conjecture for rational curves on quartic del Pezzo surfaces

Ronno Das, Brian Lehmann, Sho Tanimoto +1

We prove a version of Manin's conjecture (over $F_{q}$ for $q$ large) and the Cohen--Jones--Segal conjecture (over $C$ ) for maps from rational curves to split qua…