31 citations · 100 across the 28 of their papers we have counts for
37 papers
The grounded spirituality of mathematics
Tarik Aougab
We propose that mathematics is done largely as a means of both coping with and celebrating our physicality in the natural world. Inspired by David Abram's "Becoming Animal", we sug…
Navigating the AI crisis: a humble guide for students
Tarik Aougab
We present some basic recommendations for (mostly graduate) students when it comes to choosing to use, or avoid, AI in their mathematical research and education. These include: mai…
Quasi-isometric rigidity of the integers: an elementary primer
Tarik Aougab, Hikaru Jitsukawa, Kim Ruane
Chatawate (Flame) Ruethaimetapat was a passionate, enthusiastic, and wonderful person who passed away in August of 2024. At the time of their passing they were working towards thei…
Pseudo-Anosovs from the perspective of their mapping tori
Tarik Aougab
In this chapter, we outline some of the many combinatorial tools developed over the past three decades for studying a pseudo-Anosov diffeomorphism of a surface by analyzing the geo…
On fixed points of pseudo-Anosov maps
Tarik Aougab, David Futer, Samuel J. Taylor
We give a formula to estimate the number of fixed points of a pseudo-Anosov homeomorphism of a surface. When the homeomorphism satisfies a mild property called strong irreducibilit…
The arc complex is not quasi-isometric to the sphere complex
Tarik Aougab, Marissa Loving
We show that the arc complex is not quasi-isometric to the sphere complex associated to the double of a genus handlebody. Along the wa…
From arcs to curves: quadratic growth of 1-systems
Tarik Aougab, Jonah Gaster
We show that a collection of simple closed curves pairwise intersecting at most once on an orientable surface of Euler characteristic has at most curves. Up…
Subgraph Entropy
Tarik Aougab, Matt Clay, Tawfiq Hamed
Given , we prove that there exists depending only on so that if is a metric graph of rank with metric entropy , then there exists a proper subgraph $…
On the monodromy and spin parity of single-cylinder origamis in the minimal stratum
Tarik Aougab, Adam Friedman-Brown, Luke Jeffreys +1
In a paper with Menasco-Nieland, the first author constructed factorially many origamis in the minimal stratum of the moduli space of translation surfaces having simultaneously a s…
Constructing reducibly geometrically finite subgroups of the mapping class group
Tarik Aougab, Harrison Bray, Spencer Dowdall +3
In this article, we consider qualified notions of geometric finiteness in mapping class groups called parabolically geometrically finite (PGF) and reducibly geometrically finite (R…
Currents with corners and counting weighted triangulations
Tarik Aougab, Jayadev Athreya
Let be a closed orientable hyperbolic surface. We introduce the notion of a \textit{geodesic current with corners} on , which behaves like a geodesic current away from certa…
A note on an effective characterization of covers with an application to higher rank representations
Tarik Aougab, Max Lahn, Marissa Loving +1
In this note we prove an effective characterization of when two finite-degree covers of a connected, orientable surface of negative Euler characteristic are isomorphic in terms of…
Unmarked simple length spectral rigidity for covers
Tarik Aougab, Max Lahn, Marissa Loving +1
We prove that every closed orientable surface S of negative Euler characteristic admits a pair of finite-degree covers which are length isospectral over S but generically not simpl…
Combinatorially random curves on surfaces
Tarik Aougab, Jonah Gaster
We study topological properties of random closed curves on an orientable surface of negative Euler characteristic. Letting denote the conjugacy class of the st…
Origamis associated to minimally intersecting filling pairs
Tarik Aougab, William Menasco, Mark Nieland
Let denote the closed orientable surface of genus . In joint work with Huang, the first author constructed exponentially-many (in ) mapping class group orbits of pair…
Thermodynamic metrics on outer space
Tarik Aougab, Matt Clay, Yo'av Rieck
In this paper we consider two piecewise Riemannian metrics defined on the Culler-Vogtmann outer space which we call the entropy metric and the pressure metric. As a result of work…
Curves on the torus intersecting at most k times
Tarik Aougab, Jonah Gaster
We show that any set of distinct homotopy classes of simple closed curves on the torus that pairwise intersect at most times has size . Prior to this wo…
Isometry groups of infinite-genus hyperbolic surfaces
Tarik Aougab, Priyam Patel, Nicholas G. Vlamis
Given a 2-manifold, a fundamental question to ask is which groups can be realized as the isometry group of a Riemannan metric of constant curvature on the manifold. In this paper,…
Characterizing covers via simple closed curves
Tarik Aougab, Max Lahn, Marissa Loving +1
Given two finite covers and of a connected, oriented, closed surface of genus at least , we attempt to characterize the equivalence of and …
Automorphisms of the k-curve graph
Shuchi Agrawal, Tarik Aougab, Yassin Chandran +4
Given a natural number k and an orientable surface S of finite type, define the k-curve graph to be the graph with vertices corresponding to isotopy classes of essential simple clo…
Covers of surfaces, Kleinian groups, and the curve complex
Tarik Aougab, Priyam Patel, Samuel J. Taylor
We prove an effective version of a theorem relating curve complex distance to electric distance in hyperbolic 3-manifolds, up to errors that are polynomial in the complexity of the…
Determining the finite subgraphs of curve graphs
Tarik Aougab, Ian Biringer, Jonah Gaster
We prove that there is an algorithm to determine if a given finite graph is an induced subgraph of a given curve graph.
Packing curves on surfaces with few intersections
Tarik Aougab, Ian Biringer, Jonah Gaster
Przytycki has shown that the size of a maximal collection of simple closed curves that pairwise intersect at most times on a topological surface grows…
Pulling back stability with applications to Out() and relatively hyperbolic groups
Tarik Aougab, Matthew Gentry Durham, Samuel J. Taylor
We prove that stability -- a strong quasiconvexity property -- pulls back under proper actions on proper metric spaces. This result has several applications, including that convex…