Now showing items 21-35 of 35

• #### The second rational homology group of the moduli space of curves with level structures ﻿

(2012)
Let Γ be a finite-index subgroup of the mapping class group of a closed genus g surface that contains the Torelli group. For instance, Γ can be the level L subgroup or the spin mapping class group. We show that H2(Γ;Q) ∼= Q ...

(2012)
• #### The Picard group of the moduli space of curves with level structures ﻿

(2012)
For 4 - L and g large, we calculate the integral Picard groups of the moduli spaces of curves and principally polarized abelian varieties with level L structures. In particular, we determine the divisibility properties of ...
• #### Opening gaps in the spectrum of strictly ergodic Schrodinger operators ﻿

(2012)
We consider Schrodinger operators with dynamically defined potentials arising from continuous sampling along orbits of strictly ergodic transformations. The Gap Labeling Theorem states that the possible gaps in the spectrum ...
• #### The Density of States Measure of the Weakly Coupled Fibonacci Hamiltonian ﻿

(2012)
We consider the density of states measure of the Fibonacci Hamiltonian and show that, for small values of the coupling constant V , this measure is exact-dimensional and the almost everywhere value dV of the local ...
• #### A Birman exact sequence for Aut(Fn) ﻿

(2012)
The Birman exact sequence describes the effect on the mapping class group of a surface with boundary of gluing discs to the boundary components. We construct an analogous exact sequence for the automorphism group of a free ...
• #### The Weil-Peterson Hessian of Length on Teichmuller Space ﻿

(2012)
We present a brief but nearly self-contained proof of a formula for the Weil-Petersson Hessian of the geodesic length of a closed curve (either simple or not simple) on a hyperbolic surface. The formula is the sum of the ...
• #### Small generating sets for the Torelli group ﻿

(2012)
Proving a conjecture of Dennis Johnson, we show that the Torelli subgroup Ig of the genus g mapping class group has a finite generating set whose size grows cubically with respect to g. Our main tool is a new space called ...

(2012)
• #### Ergodic properties of compositions of interval exchange maps and rotations ﻿

(2012)
We study the ergodic properties of compositions of interval exchange transformations (IETs) and rotations. We show that for any IET T, there is a full measure set of α ∈ [0, 1) so that T  Rα is uniquely ergodic, where Rα is ...
• #### Handle Addition for Doubly-Periodic Scherk Surfaces ﻿

(2012)
We prove the existence of a family of embedded doubly periodic minimal surfaces of (quotient) genus g with orthogonal ends that generalizes the classical doubly periodic surface of Scherk and the genus-one Scherk surface ...

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