Research
Research in the Mathematical Sciences 2016 3:32
Published on: 5 December 2016
Research
Research in the Mathematical Sciences 2016 3:32
Published on: 5 December 2016
Research
In this paper, we provide an explicit construction of weight 0 meromorphic modular forms. Following work of Petersson, we build these via Poincaré series. There are two main aspects of our investigation which ...
Research in the Mathematical Sciences 2016 3:24
Published on: 1 December 2016
Research
Research in the Mathematical Sciences 2016 3:41
Published on: 14 November 2016
Research
Research in the Mathematical Sciences 2016 3:40
Published on: 14 November 2016
Research
We consider the coherent cohomology of toroidal compactifications of locally symmetric varieties (such as Shimura varieties) with coefficients in the canonical and subcanonical extensions of automorphic vector...
Research in the Mathematical Sciences 2016 3:39
Published on: 10 November 2016
Research
Kirwan identified a condition on a smooth function under which the usual techniques of Morse–Bott theory can be applied to this function. We prove that if a function satisfies this condition locally then it al...
Research in the Mathematical Sciences 2016 3:25
Published on: 7 November 2016
Research
We establish asymptotic formulae for the first and second moments of quadratic Dirichlet L-functions, at the center of the critical strip, associated to the real quadratic function field ...
Research in the Mathematical Sciences 2016 3:38
Published on: 2 November 2016
Research
Dynamical degrees and spectra can serve to distinguish birational automorphism groups of varieties in quantitative, as opposed to only qualitative, ways. We introduce and discuss some properties of those degre...
Research in the Mathematical Sciences 2016 3:23
Published on: 1 November 2016
Research
We construct the compatible system of l-adic representations associated to a regular algebraic cuspidal automorphic representation of
Research in the Mathematical Sciences 2016 3:37
Published on: 26 October 2016
Research
We show that the Euler system associated with Rankin–Selberg convolutions of modular forms, introduced in our earlier works with Lei and Kings, varies analytically as the modular forms vary in p-adic Coleman fami...
Research in the Mathematical Sciences 2016 3:29
Published on: 1 October 2016
Research
Research in the Mathematical Sciences 2016 3:21
Published on: 1 October 2016
Research
Research in the Mathematical Sciences 2016 3:20
Published on: 1 October 2016
Research
We construct adic, compactified eigenvarieties parameterizing adic overconvergent Hilbert modular eigenforms of finite slope by constructing integral families of modular sheaves on the relevant formal Shimura ...
Research in the Mathematical Sciences 2016 3:34
Published on: 8 September 2016
Research
Research in the Mathematical Sciences 2016 3:28
Published on: 1 September 2016
Research
It is well known that time-dependent Hamilton–Jacobi–Isaacs partial differential equations (HJ PDEs) play an important role in analyzing continuous dynamic games and control theory problems. An important tool ...
Research in the Mathematical Sciences 2016 3:19
Published on: 1 September 2016
Research
We show that an effective version of Siegel’s theorem on finiteness of integer solutions for a specific algebraic curve and an application of elementary Galois theory are key ingredients in a complexity classi...
Research in the Mathematical Sciences 2016 3:18
Published on: 1 September 2016
Research
Heegner points play an outstanding role in the study of the Birch and Swinnerton-Dyer conjecture, providing canonical Mordell–Weil generators whose heights encode first derivatives of the associated Hasse–Weil L-...
Research in the Mathematical Sciences 2016 3:27
Published on: 24 August 2016
Research
We give a unified, and somewhat simplified, account of the regulator formulas appearing in papers of Bertolini, Darmon and Rotger, describing the syntomic regulator on the first, second and third self-products...
Research in the Mathematical Sciences 2016 3:26
Published on: 22 August 2016
RESEARCH
The adèles of a scheme have local components—these are topological higher local fields. The topology plays a large role since Yekutieli showed in 1992 that there can be an abundance of inequivalent topologies ...
Research in the Mathematical Sciences 2016 3:22
Published on: 15 August 2016
Research
We use quilted Floer theory to generalize Seidel’s long exact sequence in symplectic Floer theory to fibered Dehn twists. We then apply the sequence to construct versions of the Floer and Khovanov–Rozansky exa...
Research in the Mathematical Sciences 2016 3:17
Published on: 15 August 2016
Research
We explore relations between Higgs bundles that result from isogenies between low-dimensional Lie groups, with special attention to the spectral data for the Higgs bundles. We focus on isogenies onto
Research in the Mathematical Sciences 2016 3:14
Published on: 1 August 2016
Research
Research in the Mathematical Sciences 2016 3:16
Published on: 1 July 2016
Research
Research in the Mathematical Sciences 2016 3:7
Published on: 1 July 2016
Review
The purpose of the present paper is to expose, in substantial detail, certain remarkable similarities between inter-universal Teichmüller theory and the theory surrounding Bogomolov’s proof of the geometric versi...
Research in the Mathematical Sciences 2016 3:6
Published on: 5 June 2016
Research
A complex variety, degenerating over a punctured disk, carries a limit mixed Hodge structure on its cohomology, encoding the action of monodromy. The associated limit mixed Hodge–Deligne polynomial can be expr...
Research in the Mathematical Sciences 2016 3:10
Published on: 5 June 2016