Search
Now showing items 71-78 of 78
Dynamics on K3 Surfaces: Salem Numbers and Siegel Disks
(Walter de Gruyter, 2002)
This paper presents the first examples of K3 surface automorphisms \(f : X \rightarrow X\) with Siegel disks (domains on which f acts by an irrational rotation). The set of such examples is countable, and the surface \(X\) ...
Cubic curves and totally geodesic subvarieties of moduli space
(Annals of Mathematics, Princeton U, 2017)
In 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 ...
Automorphisms of projective K3 surfaces with minimum entropy
(Springer Science + Business Media, 2015)
The work of Maryam Mirzakhani
(2014)
Maryam Mirzakhani has been awarded the Fields Medal for her outstanding work on the dynamics and geometry of Riemann surfaces and their moduli spaces.
Entropy and the clique polynomial
(Oxford University Press (OUP), 2014)
This 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 ...
The Gauss–Bonnet theorem for cone manifolds and volumes of moduli spaces
(2013)
This 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 ...