Browsing Mathematics Faculty Publications by Title
Now showing items 1231 of 39

Failure of the Hasse Principle on General K3 Surfaces
(2013)We show that transcendental elements of the Brauer group of an algebraic surface can obstruct the Hasse principle. We construct a general K3 surface X of degree 2 over Q, together with a twotorsion Brauer class that is ... 
Filtering smooth concordance classes of topologically slice knots
(2013)We propose and analyze a structure with which to organize the difference between a knot in S3 bounding a topologically embedded 2–disk in B4 and it bounding a smoothly embedded disk. The n–solvable filtration of the ... 
Fundamental domains and generators for lattice Veech groups
(2017)The moduli space QMg of nonzero 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 ... 
Generating the Johnson filtration
(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 ... 
Generators for the hyperelliptic Torelli group and the kernel of the Burau representation at t=−1
(2015)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 ... 
Handle Addition for DoublyPeriodic 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 genusone Scherk surface ... 
Higherdimensional analogs of Chatelet surfaces
(2012)We discuss the geometry and arithmetic of higherdimensional 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, ... 
Homology cobordism and Seifert fibered 3manifolds
(2014)It is known that every closed oriented 3manifold is homology cobordant to a hyperbolic 3manifold. By contrast we show that many homology cobordism classes contain no Seifert fibered 3manifold. This is accomplished by ... 
Knot Concordance and Homology Cobordism
(201306)We consider the question: “If the zeroframed surgeries on two oriented knots in S3 are Zhomology cobordant, preserving the homology class of the positive meridians, are the knots themselves concordant?” We show that this ... 
Level structures on Abelian varieties, Kodaira dimensions, and Lang's conjecture
(2018)Assuming Lang's conjecture, we prove that for a prime p, number field K, and positive integer g, there is an integer r such that no principally polarized abelian variety A/K has full levelpr structure. To this end, we use ... 
Log minimal model program for the moduli space of stable curves: the first flip
(2013)We give a geometric invariant theory (GIT) construction of the log canonical model M¯g(α) of the pairs (M¯g,αδ) for α∈(7/10–ϵ,7/10] for small ϵ∈Q+. We show that M¯g(7/10) is isomorphic to the GIT quotient of the Chow variety ... 
New Anomalous LiebRobinson Bounds in Quasiperiodic XY Chains
(2014)We announce and sketch the rigorous proof of a new kind of anomalous (or subballistic) LiebRobinson (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 quasiperiodic initial data
(2015)We consider the KdV equation ∂tu+∂3xu+u∂xu=0 with quasiperiodic initial data whose Fourier coefficients decay exponentially and prove existence and uniqueness, in the class of functions which have an expansion with ... 
On the unirationality of del Pezzo surfaces of degree two
(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 krational curves on ... 
Open Problems and Conjectures Related to the Theory of Mathematical Quasicrystals
(2016)This list of problems arose as a collaborative effort among the participants of the Arbeitsgemeinschaft on Mathematical Quasicrystals, which was held at the Mathematisches Forschungsinstitut Oberwolfach in October 2015. ...