Browsing Mathematics Department by Title
Now showing items 3744 of 44

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 ... 
Positive Lyapunov exponents and a Large Deviation Theorem for continuum Anderson models, briefly
(2019)In this short note, we prove positivity of the Lyapunov exponent for 1D continuum Anderson models by leveraging some classical tools from inverse spectral theory. The argument is much simpler than the existing proof due ... 
The second rational homology group of the moduli space of curves with level structures
(2012)Let Γ be a finiteindex 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 ... 
The WeilPeterson Hessian of Length on Teichmuller Space
(2012)We present a brief but nearly selfcontained proof of a formula for the WeilPetersson 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 ... 
Wignervon Neumann type perturbations of periodic Schrödinger operators
(2015)Schrödinger operators on the half line. More precisely, the perturbations we consider satisfy a generalized bounded variation condition at infinity and an LP decay condition. We show that the absolutely continuous spectrum ...