Now showing items 11-20 of 45
The Picard group of the moduli space of curves with level structures
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 ...
Generators for the hyperelliptic Torelli group and the kernel of the Burau representation at t=−1
We prove that the hyperelliptic Torelli group is generated by Dehn twists about separating curves that are preserved by the hyperelliptic involution. This verifies a conjecture of Hain. The hyperelliptic Torelli group can ...
Dichotomy for arithmetic progressions in subsets of reals
(American Mathematical Society, 2016)
Let H stand for the set of homeomorphisms φ:[0, 1] → [0, 1]. We prove the following dichotomy for Borel subsets A ⊂ [0, 1]: • either there exists a homeomorphism φ ∈ Hsuch that the image φ(A) contains no 3-term arithmetic ...
Fundamental domains and generators for lattice Veech groups
(European Mathematical Society Publishing House, 2017)
The moduli space QMg of non-zero genus g quadratic differentials has a natural action of G=GL+2(R) / ⟨±(1001) ⟩. The Veech group PSL(X,q) is the stabilizer of (X,q)∈QMg in G. We describe a new algorithm for finding elements ...
On the unirationality of del Pezzo surfaces of degree two
(London Mathematical Society, 2014)
Among geometrically rational surfaces, del Pezzo surfaces of degree 2 over a field k containing at least one point are arguably the simplest that are not known to be unirational over k. Looking for k-rational curves on ...
Higher-dimensional analogs of Chatelet surfaces
(London Mathematical Society, 2012)
We discuss the geometry and arithmetic of higher-dimensional analogs of Chatelet surfaces; namely, we describe the structure of their Brauer and Picard groups and show that they can violate the Hasse principle. In addition, ...
Generating the Johnson filtration
(Mathematical Sciences Publishers, 2015)
For k≥1, let J1g(k) be the k th term in the Johnson filtration of the mapping class group of a genus g surface with one boundary component. We prove that for all k≥1, there exists some Gk≥0 such that J1g(k) is generated ...
Opening gaps in the spectrum of strictly ergodic Schrodinger operators
(European Mathematical Society, 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 ...
Lecture notes in mathematics: rudiments of Riemann surfaces
(Rice University, 1971)
On the existence and uniqueness of global solutions for the KdV equation with quasi-periodic initial data
(American Mathematical Society, 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 ...