9 citations · 22 across the 8 of their papers we have counts for
14 papers
Algebraically primitive invariant subvarieties with quadratic field of definition
Paul Apisa, David Aulicino
We show that the only algebraically primitive invariant subvarieties of strata of translation surfaces with quadratic field of definition are the decagon, Weierstrass curves, and e…
A Zero Lyapunov Exponent in Genus Implies the Eierlegende Wollmilchsau
David Aulicino, Frederik Benirschke, Chaya Norton
We prove that the closed orbit of the Eierlegende Wollmilchsau is the only -orbit closure in genus three with a zero Lyapunov exponent in its Kontsevich-Zo…
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…
Shimura-Teichmüller Curves in Genus 5
David Aulicino, Chaya Norton
We prove that there are no Shimura-Teichmüller curves generated by genus five translation surfaces, thereby completing the classification of Shimura-Teichmüller curves in general.…
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…
A Trajectory from a Vertex to Itself on the Dodecahedron
Jayadev S. Athreya, David Aulicino
We prove that there exists a geodesic trajectory on the dodecahedron from a vertex to itself that does not pass through any other vertex.
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…
Affine Manifolds and Zero Lyapunov Exponents in Genus 3
David Aulicino
In previous work, the author fully classified orbit closures in genus three with maximally many (four) zero Lyapunov exponents of the Kontsevich-Zorich cocycle. In this paper, we p…
Classification of higher rank orbit closures in H^{odd}(4)
David Aulicino, Duc-Manh Nguyen, Alex Wright
The moduli space of genus 3 translation surfaces with a single zero has two connected components. We show that in the odd connected component H^{odd}(4) the only GL^+(2,R) orbit cl…
Affine Invariant Submanifolds with Completely Degenerate Kontsevich-Zorich Spectrum
David Aulicino
We prove that if the Lyapunov spectrum of the Kontsevich-Zorich cocycle over an affine SL-invariant submanifold is completely degenerate, i.e. $λ_2 = \cdots = λ_g =…
Teichmüller Discs with Completely Degenerate Kontsevich-Zorich Spectrum
David Aulicino
We reduce a question of Eskin-Kontsevich-Zorich and Forni-Matheus-Zorich, which asks for a classification of all -invariant ergodic probability measures wi…