Person: McMullen, Curtis
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McMullen
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Curtis
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McMullen, Curtis
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Publication Cascades in the Dynamics of Measured Foliations(Elsevier Masson, 2014-03-14) McMullen, CurtisPublication Knots which Behave Like the Prime Numbers(Oxford University Press (OUP), 2013) McMullen, CurtisThis paper establishes a version of the Chebotarev density theorem in which number fields are replaced by 3-manifolds.Publication Moduli Spaces in Genus Zero and Inversion of Power Series(Swets & Zeitlinger, 2014-03-11) McMullen, CurtisPublication Moduli Spaces of Isoperiodic Forms on Riemann Surfaces(2014-03-11) McMullen, CurtisThis paper describes the intrinsic geometry of a leaf \(\mathcal{A}(L)\) of the absolute period foliation of the Hodge bundle \(\Omega \bar{M}_g\): its singular Euclidean structure, its natural foliations and its discretized Teichmuller dynamics. We establish metric completeness of \(\mathcal{A}(L)\) for general g, and then turn to a study of the case g = 2. In this case the Euclidean structure comes from a canonical meromorphic quadratic differential on \(\mathcal{A}(L) \cong \mathbb{H}\), whose zeros, poles and exotic trajectories are analyzed in detail.Publication Cubic curves and totally geodesic subvarieties of moduli space(Annals of Mathematics, Princeton U, 2017) McMullen, Curtis; Mukamel, Ronen; Wright, AlexIn this paper we present the first example of a primitive, totally geodesic subvariety F⊂g,nF⊂Mg,n with dim(F)>1dim(F)>1. The variety we consider is a surface F⊂1,3F⊂M1,3 defined using the projective geometry of plane cubic curves. We also obtain a new series of Teichmüller curves in 4M4, and new SL2(ℝ)SL2(R)-invariant varieties in the moduli spaces of quadratic differentials and holomorphic 1-forms.Publication Horocycles in hyperbolic 3-manifolds(2015) McMullen, Curtis; Mohammadi, Amir; Oh, HeePublication Geodesic planes in hyperbolic 3-manifolds(2015) McMullen, Curtis; Mohammadi, Amir; Oh, HeePublication The work of Maryam Mirzakhani(2014) McMullen, CurtisMaryam Mirzakhani has been awarded the Fields Medal for her outstanding work on the dynamics and geometry of Riemann surfaces and their moduli spaces.Publication Entropy and the clique polynomial(Oxford University Press (OUP), 2014) McMullen, CurtisThis paper gives a sharp lower bound on the spectral radius ρ(A) of a reciprocal Perron–Frobenius matrix A ∈ M2g(Z), and shows in particular that ρ(A) g ≥ (3 + √ 5)/2. This bound supports conjectures on the minimal entropy of pseudo-Anosov maps. The proof is based on a study of the curve complex of a directed graph.Publication The Gauss–Bonnet theorem for cone manifolds and volumes of moduli spaces(2013) McMullen, CurtisThis paper generalizes the Gauss–Bonnet formula to a class of stratified spaces called Riemannian cone manifolds. As an application, we compute the volumes of the moduli spaces M0,n with respect to the complex hyperbolic metrics introduced by Picard, Deligne–Mostow and Thurston.