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  1. Research

    On the rigid cohomology of certain Shimura varieties

    We construct the compatible system of l-adic representations associated to a regular algebraic cuspidal automorphic representation of http://static-content.springer.com/image/art%3A10.1186%2Fs40687-016-0078-5/40687_2016_78_Article_IEq1.gif

    Michael Harris, Kai-Wen Lan, Richard Taylor and Jack Thorne

    Research in the Mathematical Sciences 2016 3:37

    Published on: 26 October 2016

  2. Research

    Rankin–Eisenstein classes in Coleman families

    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...

    David Loeffler and Sarah Livia Zerbes

    Research in the Mathematical Sciences 2016 3:29

    Published on: 1 October 2016

  3. Research

    The adic, cuspidal, Hilbert eigenvarieties

    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 ...

    Fabrizio Andreatta, Adrian Iovita and Vincent Pilloni

    Research in the Mathematical Sciences 2016 3:34

    Published on: 8 September 2016

  4. Research

    Elliptic curves of rank two and generalised Kato classes

    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-...

    Henri Darmon and Victor Rotger

    Research in the Mathematical Sciences 2016 3:27

    Published on: 24 August 2016

  5. Research

    On the regulator formulas of Bertolini, Darmon and Rotger

    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...

    Amnon Besser

    Research in the Mathematical Sciences 2016 3:26

    Published on: 22 August 2016

  6. Research

    Exact triangle for fibered Dehn twists

    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...

    Katrin Wehrheim and Chris T. Woodward

    Research in the Mathematical Sciences 2016 3:17

    Published on: 15 August 2016

  7. RESEARCH

    Geometric and analytic structures on the higher adèles

    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 ...

    O. Braunling, M. Groechenig and J. Wolfson

    Research in the Mathematical Sciences 2016 3:22

    Published on: 15 August 2016

  8. Research

    Higgs bundles and exceptional isogenies

    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

    Steven B. Bradlow and Laura P. Schaposnik

    Research in the Mathematical Sciences 2016 3:14

    Published on: 1 August 2016

  9. Short Report

    From rubber bands to rational maps: a research report

    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...

    Dylan P. Thurston

    Research in the Mathematical Sciences 2016 3:15

    Published on: 15 May 2016

  10. RESEARCH

    Low Mach number limit for the quantum hydrodynamics system

    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...

    Donatella Donatelli and Pierangelo Marcati

    Research in the Mathematical Sciences 2016 3:13

    Published on: 15 May 2016

  11. Research

    On the Fourier coefficients of negative index meromorphic Jacobi forms

    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...

    Kathrin Bringmann, Larry Rolen and Sander Zwegers

    Research in the Mathematical Sciences 2016 3:5

    Published on: 10 May 2016

  12. Research

    On p-adic modular forms and the Bloch–Okounkov theorem

    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 ...

    Michael J. Griffin, Marie Jameson and Sarah Trebat-Leder

    Research in the Mathematical Sciences 2016 3:11

    Published on: 10 May 2016

  13. Research

    Rings of small rank over a Dedekind domain and their ideals

    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 ...

    Evan M. O’Dorney

    Research in the Mathematical Sciences 2016 3:8

    Published on: 14 April 2016

  14. Research

    Numerical functors on Voevodsky’s motives

    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...

    Giuseppe Ancona

    Research in the Mathematical Sciences 2016 3:12

    Published on: 20 March 2016

  15. RESEARCH

    On a mathematical theory of coded exposure

    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...

    Yohann Tendero and Stanley Osher

    Research in the Mathematical Sciences 2016 3:4

    Published on: 20 March 2016

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