Mathematics Faculty Publications
http://hdl.handle.net/1911/17014
2019-05-24T06:49:58ZLevel structures on Abelian varieties, Kodaira dimensions, and Lang's conjecture
http://hdl.handle.net/1911/102314
Level structures on Abelian varieties, Kodaira dimensions, and Lang's conjecture
Abramovich, Dan; Várilly-Alvarado, Anthony
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 level-pr structure. To this end, we use a result of Zuo to prove that for each closed subvariety X in the moduli space Ag of principally polarized abelian varieties of dimension g, there exists a level mX such that the irreducible components of the preimage of X in Ag[m] are of general type for m>mX.
2018-01-01T00:00:00ZOpen Problems and Conjectures Related to the Theory of Mathematical Quasicrystals
http://hdl.handle.net/1911/98893
Open Problems and Conjectures Related to the Theory of Mathematical Quasicrystals
Adiceam, Faustin; Damanik, David; Gähler, Franz; Grimm, Uwe; Haynes, Alan; Julien, Antoine; Navas, Andrés; Sadun, Lorenzo; Weiss, Barak
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. The purpose of our meeting was to bring together researchers from a variety of disciplines, with a common goal of understanding different viewpoints and approaches surrounding the theory of mathematical quasicrystals. The problems below reflect this goal and this diversity and we hope that they will motivate further cross-disciplinary research and lead to new advances in our overall vision of this rapidly developing field.
2016-01-01T00:00:00ZWigner-von Neumann type perturbations of periodic Schrödinger operators
http://hdl.handle.net/1911/94850
Wigner-von Neumann type perturbations of periodic Schrödinger operators
Lukic, Milivoje; Ong, Darren C.
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 is preserved, and give bounds on the Hausdorff dimension of the singular part of the resulting perturbed measure. Under additional assumptions, we instead show that the singular part embedded in the essential spectrum is contained in an explicit countable set. Finally, we demonstrate that this explicit countable set is optimal. That is, for every point in this set there is an open and dense class of periodic Schrödinger operators for which an appropriate perturbation will result in the spectrum having an embedded eigenvalue at that point.
2015-01-01T00:00:00ZHomology cobordism and Seifert fibered 3-manifolds
http://hdl.handle.net/1911/94828
Homology cobordism and Seifert fibered 3-manifolds
Cochran, Tim D.; Tanner, Daniel
It is known that every closed oriented 3-manifold is homology cobordant to a hyperbolic 3-manifold. By contrast we show that many homology cobordism classes contain no Seifert fibered 3-manifold. This is accomplished by determining the isomorphism type of the rational cohomology ring of all Seifert fibered 3-manifolds with no 2-torsion in their first homology. Then we exhibit families of examples of 3-manifolds (obtained by surgery on links), with fixed linking form and cohomology ring, that are not homology cobordant to any Seifert fibered space (as shown by their rational cohomology rings). These examples are shown to represent distinct homology cobordism classes using higher Massey products and Milnor's µ-invariants for links.
2014-01-01T00:00:00Z