Browsing Mathematics Faculty Publications by Issue Date
Now showing items 120 of 30

On the existence and uniqueness of global solutions for the KdV equation with quasiperiodic initial data
(20150629)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 ... 
Cubic fourfolds containing a plane and a quantic del Pezzo surface
(2014)We isolate a class of smooth rational cubic fourfolds X containing a plane whose associated quadric surface bundle does not have a rational section. This is equivalent to the nontriviality of the Brauer class β of the even ... 
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 ... 
Abelian quotients of subgroups of the mapping class group and higher Prym representations
(201308)A wellknown conjecture asserts that the mapping class group of a surface (possibly with punctures/boundary) does not virtually surject onto Z if the genus of the surface is large. We prove that if this conjecture holds ... 
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 ... 
Ergodic properties of compositions of interval exchange maps and rotations
(2013)We study the ergodic properties of compositions of interval exchange transforma tions and rotations. We show that for any interval exchange transformation T, there is a full measure set of 2 [0; 1) so that T R is ... 
The complex of partial bases for Fn and nite generation of the Torelli subgroup of Aut(Fn)
(2013)We study the complex of partial bases of a free group, which is an analogue for Aut(Fn) of the curve complex for the mapping class group. We prove that it is connected and simply connected, and we also prove that its ... 
Effective Computation of Picard Groups and BrauerManin Obstructions of Degree Two K3 Surfaces Over Number Fields
(2013)Using the KugaSatake correspondence we provide an effective algorithm for the computation of the Picard and Brauer groups of K3 surfaces of degree 2 over number fields. 
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 ... 
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 ... 
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 ... 
BorelCantelli Sequences
(201206) 
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 ... 
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 ... 
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 ... 
Higherdimensional analogs of Chatelet surfaces
(2012)We discuss the geometry and arithmetic of higherdimensional analogs of Chˆatelet surfaces; namely, we describe the structure of their Brauer and Picard groups and show that they can violate the Hasse principle. In ...