Now showing items 31-39 of 39
Filtering smooth concordance classes of topologically slice knots
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 ...
Knot Concordance and Homology Cobordism
(American Mathematical Society, 2013-06)
We consider the question: “If the zero-framed surgeries on two oriented knots in S3 are Z-homology cobordant, preserving the homology class of the positive meridians, are the knots themselves concordant?” We show that this ...
Abelian quotients of subgroups of the mapping class group and higher Prym representations
(London Mathematical Society, 2013-08)
A well-known 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 ...
Open Problems and Conjectures Related to the Theory of Mathematical Quasicrystals
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. ...
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 ...
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 ...
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, ...
Ergodic properties of compositions of interval exchange maps and rotations
(IOP Publishing, 2012)
We study the ergodic properties of compositions of interval exchange transformations (IETs) and rotations. We show that for any IET T, there is a full measure set of α ∈ [0, 1) so that T Rα is uniquely ergodic, where Rα is ...