3 papers
math.GT2026
Exact curve counting of given word length on the once-punctured torus
Filippo Baroni, David Fisac, Mingkun Liu
On the once-punctured torus, we give an exact formula for the number of curves in any given mapping class group orbit of given word length. This settles a conjecture of Chas in [Ch…
math.GT2026
Isospectrality and isometry groups for infinite-type hyperbolic surfaces with discrete length spectrum
Federica Fanoni, David Fisac
We study infinite-type hyperbolic surfaces with discrete length spectrum. In this setup, we show that Sunada's method can only produce finite isospectral families, but that there i…
math.GT2025
Markov's Conjecture on integral necklaces
David Fisac
We use the geometric reformulation of Markov's uniqueness conjecture in terms of the simple length spectrum on the modular torus to rewrite the conjecture in combinatorial terms by…