Browsing Mathematics Department by Issue Date
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Generic spectral results for CMV matrices with dynamically defined Verblunsky coefficients
(2020)We consider CMV matrices with dynamically defined Verblunsky coefficients. These coefficients are obtained by continuous sampling along the orbits of an ergodic transformation. We investigate whether certain spectral ... 
Anderson localization for quasiperiodic CMV matrices and quantum walks
(2019)We consider CMV matrices, both standard and extended, with analytic quasiperiodic Verblunsky coefficients and prove Anderson localization in the regime of positive Lyapunov exponents. This establishes the CMV analog of a ... 
Anderson localization for radial tree graphs with random branching numbers
(2019)We prove Anderson localization for the discrete Laplace operator on radial tree graphs with random branching numbers. Our method relies on the representation of the Laplace operator as the direct sum of halflineﾠJacobi ... 
Multidimensional AlmostPeriodic Schrödinger Operators with Cantor Spectrum
(2019)We construct multidimensional almostperiodic Schrödinger operators whose spectrum has zero lower boxcounting dimension. In particular, the spectrum in these cases is a generalized Cantor set of zero Lebesgue measure. 
Limitperiodic Schrödinger operators with Lipschitz continuous IDS
(2019)We show that there exist limitperiodic Schrödinger operators such that the associated integrated density of states is Lipschitz continuous. These operators arise in the inverse spectral theoretic KAM approach of Pöschel. 
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 ... 
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 ... 
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 ... 
Dichotomy for arithmetic progressions in subsets of reals
(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 3term arithmetic ... 
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. ... 
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 ... 
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 ... 
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 ... 
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 ... 
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 ... 
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 ... 
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 ... 
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 ...