Counting self-intersecting multi curves – Viveca Erlandsson (Aalto University)

Venue

Sala Seminari (Dip. Matematica).

Abstract

I will describe some joint work in progress with Juan Souto studying the asymptotic growth on the number $n_k^S(L)$ of multicurves with $k$ self-intersections of length at most $L$ on a hyperbolic surface $S$. More concretely, I will show that for small $k$, $\frac{n_k^S(L)}{L^{6g-6}}$ has a limit as $L\to\infty$. Moreover, when $S$ is the punctured torus, this limit exists for any fixed $k$.

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