9 citations · 22 across the 8 of their papers we have counts for
6 papers · 1 filter
Counting Tripods on the Torus
Jayadev S. Athreya, David Aulicino, Harry Richman
Motivated by the problem of counting finite BPS webs, we count certain immersed metric graphs, tripods, on the flat torus. Classical Euclidean geometry turns this into a lattice po…
A New Approach to the Automorphism Group of a Platonic Surface
David Aulicino
We borrow a classical construction from the study of rational billiards in dynamical systems known as the "unfolding construction" and show that it can be used to study the automor…
Platonic solids and high genus covers of lattice surfaces
Jayadev S. Athreya, David Aulicino, W. Patrick Hooper
We study the translation surfaces obtained by considering the unfoldings of the surfaces of Platonic solids. We show that they are all lattice surfaces and we compute the topology…
Rank 2 Affine Manifolds in Genus 3
David Aulicino, Duc-Manh Nguyen
We complete the classification of rank two affine manifolds in the moduli space of translation surfaces in genus three. Combined with a recent result of Mirzakhani and Wright, this…
The Cantor-Bendixson Rank of Certain Bridgeland-Smith Stability Conditions
David Aulicino
We provide a novel proof that the set of directions that admit a saddle connection on a meromorphic quadratic differential with at least one pole of order at least two is closed, w…
Rank two affine submanifolds in and
David Aulicino, Duc-Manh Nguyen
We classify all rank two affine manifolds in strata in genus three with two zeros. This confirms a conjecture of Maryam Mirzakhani in these cases. Several technical results are pro…