We are excited to announce "Curve counting: what's next?" to be held at the Hamilton Mathematics Institute, in Dublin, Ireland. A five-day workshop featuring invited talks by leading experts, selected talks by early-career researchers, and ample time for informal discussions and collaboration.
Dates: May 25–29, 2026
Venue: Hamilton Mathematics Institute (HMI), Trinity College Dublin
Speakers:
Viveka Erlandsson
Hugo Parlier
Ser Peow Tan
Dragomir Saric
Jean-Marc Schlenker
Juan Souto
Jing Tao
Dylan Thurston
Organisers:
Ara Basmajian
Tom Cremaschi
Didac Martinez-Granado
Schedule:
HMI Curve Counting - Schedule (v 4_19_2026)Talks
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Monday 25
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Time: 10-11
Speaker: Hugo Parlier
Title: TBA
Abstract: TBA
Time: 11.30-12.30
Speaker: Viveka Erlandsson
Title: TBA
Abstract: TBA
Time: 14-15
Speaker: Juan Souto
Title: "Can you hear the shape of a hyperbolic surface? Now for real."
Abstract: We associate a musical instrument, a {\em hyperbolic marimba}, to every pair $(X,\Gamma)$ where $X$ is a hyperbolic surface and $\Gamma\subset X$ a simple multicurve labeled with musical keys. It works as follows: take a geodesic and every time it hits $\Gamma$, play the corresponding note. We investigate to which extent do the so-produced melodies characterize $(X,\Gamma)$ up to isometry. This is joint work with Ludovico Battista.
Time: 16-16.30
Speaker: Sophie Wright
Title: TBA
Abstract: TBA
Time: 16.30-17
Speaker: David Fisac
Title: TBA
Abstract: TBA
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Tuesday 26
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Time: 10-11
Speaker: Dylan Thurston
Title: TBA
Abstract: TBA
Time: 11.30-12
Speaker: Meenakshy Jyothis
Title: TBA
Abstract: TBA
Time: 12-12.30
Speaker: Sayantika Mondal
Title: TBA
Abstract: TBA
Time: 14-15
Speaker: Jing Tao
Title: TBA
Abstract: TBA
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Wednesday 27
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Time: 10-11
Speaker: Dragomir Saric
Title: Quadratic differentials and random walks on the dual graph of a pants decomposition
Abstract: Let X be an infinite Riemann surface with an upper-bounded geodesic pants decomposition. Using horizontal foliations of quadratic differentials, we prove that the geodesic flow on X is ergodic if and only if the random walk on the weighted dual graph of the pants decomposition of X is recurrent. We provide concrete and new families of Riemann surfaces with an explicit understanding of the phase transitions from ergodic to non-ergodic geodesic flows. In addition, we show that rough isometry of surfaces does not preserve the ergodicity of the geodesic flow, while rough isometry of their dual graphs does. This is a joint work with C. Bordenave and X. Dong.
Time: 11.30-12
Speaker: Marie Trin
Title: Large genus asymptotic for frequency of non-simple curves
Abstract: As an application of her counting results Mirzakhani proved that in genus 2 there is 48 times more non-separating than separating simple closed curves. This result has been extended to large genus genus by Delecroix-Goujard-Zograf-Zorich: they prove that in large genus almost every simple closed curves is non-separating. In this talk we will explain what happens if we get interested in curves with self-intersections. What is their frequency? How does it behave asymptotically? Which type of curves are more likely? This a joint work with M.Liu, K.Rafi and J.Souto
Time: 12-12.30
Speaker: Milo Banarse
Title: TBA
Abstract: TBA
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Thursday 28
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Time: 10-11
Speaker: TBA
Title: TBA
Abstract: TBA
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Friday 29
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Time: 10-11
Speaker: Jean-Marc Schlenker
Title: Parameterizing quasifuchsian manifolds by measured laminations and foliations
Abstract:
Let $M$ be a quasifuchsian, or more generally convex co-compact hyperbolic 3-manifold.
We will recall why the ideal boundary of $M$ is equipped with a conformal structure $c$, but also with a measured foliation $f$. At the same time, the boundary of the convex core of $M$ is equipped with a hyperbolic metric $m$ and a measured bending lamination $l$.
We will then explain how $M$ is uniquely determined by $l$ (joint with Bruno Dular), and why, near the Fuchsian locus, $M$ is uniquely determined by $f$ (a recent result of Choudhury--Markovic).
We are grateful for the following funding:
