Now showing items 22-30 of 30

• #### New Anomalous Lieb-Robinson Bounds in Quasiperiodic XY Chains ﻿

(2014)
We announce and sketch the rigorous proof of a new kind of anomalous (or sub-ballistic) Lieb-Robinson (LR) bound for an isotropic XY chain in a quasiperiodic transversal magnetic field. Instead of the usual effective light ...
• #### On the existence and uniqueness of global solutions for the KdV equation with quasi-periodic initial data ﻿

(2015)
We consider the KdV equation ∂tu+∂3xu+u∂xu=0 with quasi-periodic initial data whose Fourier coefficients decay exponentially and prove existence and uniqueness, in the class of functions which have an expansion with ...
• #### 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 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 ...

(2012)
• #### 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 ...
• #### 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 ...

(1989)
• #### 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 ...