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  1. Content type: 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...

    Authors: Kai-Wen Lan

    Citation: Research in the Mathematical Sciences 2016 3:39

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  2. Content type: 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...

    Authors: Tara Holm and Yael Karshon

    Citation: Research in the Mathematical Sciences 2016 3:25

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  3. Content type: 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...

    Authors: Christian Böhning, Hans-Christian Graf von Bothmer and Pawel Sosna

    Citation: Research in the Mathematical Sciences 2016 3:23

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  4. Content type: Research

    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

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

    Citation: Research in the Mathematical Sciences 2016 3:37

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  5. Content type: 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...

    Authors: David Loeffler and Sarah Livia Zerbes

    Citation: Research in the Mathematical Sciences 2016 3:29

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  6. Content type: 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 ...

    Authors: Fabrizio Andreatta, Adrian Iovita and Vincent Pilloni

    Citation: Research in the Mathematical Sciences 2016 3:34

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  7. Content type: 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 ...

    Authors: Jérôme Darbon and Stanley Osher

    Citation: Research in the Mathematical Sciences 2016 3:19

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  8. Content type: 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-...

    Authors: Henri Darmon and Victor Rotger

    Citation: Research in the Mathematical Sciences 2016 3:27

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  9. Content type: 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...

    Authors: Amnon Besser

    Citation: Research in the Mathematical Sciences 2016 3:26

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  10. Content type: 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 ...

    Authors: O. Braunling, M. Groechenig and J. Wolfson

    Citation: Research in the Mathematical Sciences 2016 3:22

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  11. Content type: 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...

    Authors: Katrin Wehrheim and Chris T. Woodward

    Citation: Research in the Mathematical Sciences 2016 3:17

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  12. Content type: 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

    Authors: Steven B. Bradlow and Laura P. Schaposnik

    Citation: Research in the Mathematical Sciences 2016 3:14

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  13. Content type: 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...

    Authors: Shinichi Mochizuki

    Citation: Research in the Mathematical Sciences 2016 3:6

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  14. Content type: RESEARCH

    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

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  15. Content type: Short 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...

    Authors: Dylan P. Thurston

    Citation: Research in the Mathematical Sciences 2016 3:15

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  16. Content type: Research

    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

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  17. Content type: RESEARCH

    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

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  18. Content type: Research

    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

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  19. Content type: Research

    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

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  20. Content type: Research

    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

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  21. Content type: Research

    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

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  22. Content type: Research

    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

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    The Erratum to this article has been published in Research in the Mathematical Sciences 2015 2:25

  23. Content type: Research

    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

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  24. Content type: Research

    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

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  25. Content type: Research

    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

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  26. Content type: Research

    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

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