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...
Authors: Kai-Wen Lan
Citation:Research in the Mathematical Sciences
2016
3:39
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...
Authors: Tara Holm and Yael Karshon
Citation:Research in the Mathematical Sciences
2016
3:25
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
...
Authors: Julio C. Andrade, Sunghan Bae and Hwanyup Jung
Citation:Research in the Mathematical Sciences
2016
3:38
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...
Authors: Christian Böhning, Hans-Christian Graf von Bothmer and Pawel Sosna
Citation:Research in the Mathematical Sciences
2016
3:23
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...
Authors: David Loeffler and Sarah Livia Zerbes
Citation:Research in the Mathematical Sciences
2016
3:29
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 ...
Authors: Fabrizio Andreatta, Adrian Iovita and Vincent Pilloni
Citation:Research in the Mathematical Sciences
2016
3:34
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 ...
Authors: Jérôme Darbon and Stanley Osher
Citation:Research in the Mathematical Sciences
2016
3:19
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...
Authors: Jin-Yi Cai, Heng Guo and Tyson Williams
Citation:Research in the Mathematical Sciences
2016
3:18
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-...
Authors: Henri Darmon and Victor Rotger
Citation:Research in the Mathematical Sciences
2016
3:27
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...
Authors: Amnon Besser
Citation:Research in the Mathematical Sciences
2016
3:26
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 ...
Authors: O. Braunling, M. Groechenig and J. Wolfson
Citation:Research in the Mathematical Sciences
2016
3:22
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...
Authors: Katrin Wehrheim and Chris T. Woodward
Citation:Research in the Mathematical Sciences
2016
3:17
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
Authors: Steven B. Bradlow and Laura P. Schaposnik
Citation:Research in the Mathematical Sciences
2016
3:14
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...
Authors: Shinichi Mochizuki
Citation:Research in the Mathematical Sciences
2016
3:6
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...
Authors: Eric Katz and Alan Stapledon
Citation:Research in the Mathematical Sciences
2016
3:10
In this paper, we deal with the low Mach number limit for the system of quantum hydrodynamics, far from the vortex nucleation regime. More precisely, in the framework of a periodic domain and ill-prepared init...
Authors: Donatella Donatelli and Pierangelo Marcati
Citation:Research in the Mathematical Sciences
2016
3:13
This research report outlines work, partially joint with Jeremy Kahn and Kevin Pilgrim, which gives parallel theories of elastic graphs and conformal surfaces with boundary. On one hand, this lets us tell when...
Authors: Dylan P. Thurston
Citation:Research in the Mathematical Sciences
2016
3:15
Bloch–Okounkov studied certain functions on partitions f called shifted symmetric polynomials. They showed that certain q-series arising from these functions (the so-called q-brackets
...
Authors: Michael J. Griffin, Marie Jameson and Sarah Trebat-Leder
Citation:Research in the Mathematical Sciences
2016
3:11
In this paper, we consider the Fourier coefficients of meromorphic Jacobi forms of negative index. This extends recent work of Creutzig and the first two authors for the special case of Kac–Wakimoto characters...
Authors: Kathrin Bringmann, Larry Rolen and Sander Zwegers
Citation:Research in the Mathematical Sciences
2016
3:5
We propose a new formulation for integrating over smooth curves and surfaces that are described by their closest point mappings. Our method is designed for curves and surfaces that are not defined by any expli...
Authors: Catherine Kublik and Richard Tsai
Citation:Research in the Mathematical Sciences
2016
3:3
The aim of this paper is to find and prove generalizations of some of the beautiful integral parametrizations in Bhargava’s theory of higher composition laws to the case where the base ring
...
Authors: Evan M. O’Dorney
Citation:Research in the Mathematical Sciences
2016
3:8
We completely characterize sections of the cones of nonnegative polynomials, convex polynomials and sums of squares with polynomials supported on circuits, a genuine class of sparse polynomials. In particular,...
Authors: Sadik Iliman and Timo de Wolff
Citation:Research in the Mathematical Sciences
2016
3:9
This paper proposes a mathematical model and formalism to study coded exposure (flutter shutter) cameras. The model includes the Poisson photon (shot) noise as well as any additive (readout) noise of finite va...
Authors: Yohann Tendero and Stanley Osher
Citation:Research in the Mathematical Sciences
2016
3:4
We study mixed versions of the classical quotient functor from Chow motives to numerical motives. We compare two natural definitions, which turn out to be very different. We investigate fullness, conservativit...
Authors: Giuseppe Ancona
Citation:Research in the Mathematical Sciences
2016
3:12
This paper studies algebraic and analytic structures associated with the Lerch zeta function, complex variables viewpoint taken in part II. The Lerch transcendent
...
Authors: Jeffrey C. Lagarias and Wen-Ching Winnie Li
Citation:Research in the Mathematical Sciences
2016
3:2
We use the unique canonically twisted module over a certain distinguished super vertex operator algebra—the moonshine module for Conway’s group—to attach a weak Jacobi form of weight zero and index one to any ...
Authors: John F. R. Duncan and Sander Mack-Crane
Citation:Research in the Mathematical Sciences
2016
3:1
The Umbral Moonshine Conjectures assert that there are infinite-dimensional graded modules, for prescribed finite groups, whose McKay–Thompson series are certain distinguished mock modular forms. Gannon has pr...
Authors: John F. R. Duncan, Michael J. Griffin and Ken Ono
Citation:Research in the Mathematical Sciences
2015
2:26
We compute explicit rational models for some Hilbert modular surfaces corresponding to square discriminants, by connecting them to moduli spaces of elliptic K3 surfaces. Since they parametrize decomposable pri...
Authors: Abhinav Kumar
Citation:Research in the Mathematical Sciences
2015
2:24
Tropical geometry gives a bound on the ranks of divisors on curves in terms of the combinatorics of the dual graph of a degeneration. We show that for a family of examples, curves realizing this bound might on...
Authors: Dustin Cartwright
Citation:Research in the Mathematical Sciences
2015
2:23
We provide new proofs of two key results of p-adic Hodge theory: the Fontaine-Wintenberger isomorphism between Galois groups in characteristic 0 and characteristic p, and the Cherbonnier–Colmez theorem on decompl...
Authors: Kiran S Kedlaya
Citation:Research in the Mathematical Sciences
2015
2:20
Published on: 16 October 2015
The
Erratum to this article has been published in
Research in the Mathematical Sciences
2015
2:25
Inspired by the original definition of mock theta functions by Ramanujan, a number of authors have considered the question of explicitly determining their behavior at the cusps. Moreover, these examples have b...
Authors: Kathrin Bringmann and Larry Rolen
Citation:Research in the Mathematical Sciences
2015
2:17
Let E/F be an everywhere unramified extension of number fields with Gal(E/F) simple and nonabelian. In a recent paper, the first named author suggested an approach to nonsolvable base change and descent of automo...
Authors: Jayce Robert Getz and Paul Edward Herman
Citation:Research in the Mathematical Sciences
2015
2:14
We construct super vertex operator algebras which lead to modules for moonshine relations connecting the four smaller sporadic simple Mathieu groups with distinguished mock modular forms. Starting with an orbi...
Authors: Miranda C N Cheng, Xi Dong, John F R Duncan, Sarah Harrison, Shamit Kachru and Timm Wrase
Citation:Research in the Mathematical Sciences
2015
2:13
We introduce a new class of symmetric space orbital integrals important for applications in certain relative trace formula appearing in the theory of automorphic representations. We verify a fundamental lemma for...
Authors: Jason KC Polák
Citation:Research in the Mathematical Sciences
2015
2:9