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  1. Content type: Research

    The present paper introduces a novel notion of ‘(effective) computability,’ called viability, of strategies in game semantics in an intrinsic (i.e., without recourse to the standard ChurchTuring computability),

    Authors: Norihiro Yamada

    Citation: Research in the Mathematical Sciences 2018 6:3

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  2. Content type: Research

    We study the general properties of certain rank 4 rigid local systems considered by Goursat. We analyze when they are irreducible, give an explicit integral description as well as the invariant Hermitian form H w...

    Authors: Danylo Radchenko and Fernando Rodriguez Villegas

    Citation: Research in the Mathematical Sciences 2018 5:38

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  3. Content type: Research

    In this paper, we address the following two closely related questions. First, we complete the classification of finite symmetry groups of type IIA string theory on http://static-content.springer.com/image/art%3A10.1007%2Fs40687-018-0150-4/40687_2018_150_Article_IEq1.gif ...

    Authors: Miranda C. N. Cheng, Sarah M. Harrison, Roberto Volpato and Max Zimet

    Citation: Research in the Mathematical Sciences 2018 5:32

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  4. Content type: Research

    Given a tensor f in a Euclidean tensor space, we are interested in the critical points of the distance function from f to the set of tensors of rank at most k, which we call the critical rank-at-most-k tensors fo...

    Authors: Jan Draisma, Giorgio Ottaviani and Alicia Tocino

    Citation: Research in the Mathematical Sciences 2018 5:27

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  5. Content type: Research

    This introductory paper studies a class of real analytic functions on the upper half plane satisfying a certain modular transformation property. They are not eigenfunctions of the Laplacian and are quite disti...

    Authors: Francis Brown

    Citation: Research in the Mathematical Sciences 2018 5:7

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  6. Content type: Research

    This is a slightly expanded version of my lecture at the conference Modular forms are everywhere at Bonn, May 2017, taking into account remarks by Don Zagier and Shaul Zemel, and suggestions of the referees.

    Authors: Roelof Bruggeman

    Citation: Research in the Mathematical Sciences 2018 5:5

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  7. Content type: Research

    We prove that certain degenerate abelian varieties that include compactified Jacobians, namely stable semiabelic varieties, satisfy autoduality. We establish this result by proving a comparison theorem that re...

    Authors: Jesse Leo Kass

    Citation: Research in the Mathematical Sciences 2017 4:27

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  8. Content type: Research

    A fourientation of a graph is a choice for each edge of the graph whether to orient that edge in either direction, leave it unoriented, or biorient it. Fixing a total order on the edges and a reference orienta...

    Authors: Spencer Backman and Sam Hopkins

    Citation: Research in the Mathematical Sciences 2017 4:18

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  9. Content type: Research

    In this paper we study the stochastic Galerkin approximation for the linear transport equation with random inputs and diffusive scaling. We first establish uniform (in the Knudsen number) stability results in ...

    Authors: Shi Jin, Jian-Guo Liu and Zheng Ma

    Citation: Research in the Mathematical Sciences 2017 4:15

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  10. Content type: Research

    A polynomial with integer coefficients yields a family of dynamical systems indexed by primes as follows: For any prime p, reduce its coefficients mod p and consider its action on the field ...

    Authors: Andrew Bridy and Derek Garton

    Citation: Research in the Mathematical Sciences 2017 4:13

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  11. Content type: Research

    What is the probability that the smallest part of a random integer partition of N is odd? What is the expected value of the smallest part of a random integer partition of N? It is straightforward to see that the ...

    Authors: Hieu T. Ngo and Robert C. Rhoades

    Citation: Research in the Mathematical Sciences 2017 4:17

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  12. Content type: Research

    The hierarchical interpolative factorization (HIF) offers an efficient way for solving or preconditioning elliptic partial differential equations. By exploiting locality and low-rank properties of the operator...

    Authors: Yingzhou Li and Lexing Ying

    Citation: Research in the Mathematical Sciences 2017 4:12

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  13. Content type: Research

    We implement new techniques involving Artin fans to study the realizability of tropical stable maps in superabundant combinatorial types. Our approach is to understand the skeleton of a fundamental object in l...

    Authors: Dhruv Ranganathan

    Citation: Research in the Mathematical Sciences 2017 4:11

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  14. Content type: Research

    We present a ray-based finite element method for the high-frequency Helmholtz equation in smooth media, whose basis is learned adaptively from the medium and source. The method requires a fixed number of grid ...

    Authors: Jun Fang, Jianliang Qian, Leonardo Zepeda-Núñez and Hongkai Zhao

    Citation: Research in the Mathematical Sciences 2017 4:9

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  15. Content type: Research

    Given a family X of complex varieties degenerating over a punctured disk, one is interested in computing related invariants called the motivic nearby fiber and the refined limit mixed Hodge numbers, both of which...

    Authors: Alan Stapledon

    Citation: Research in the Mathematical Sciences 2017 4:8

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  16. Content type: Research

    We present a spectrally accurate method for the rapid evaluation of free-space Stokes potentials, i.e., sums involving a large number of free space Green’s functions. We consider sums involving stokeslets, str...

    Authors: Ludvig af Klinteberg, Davoud Saffar Shamshirgar and Anna-Karin Tornberg

    Citation: Research in the Mathematical Sciences 2017 4:1

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  17. Content type: Research

    We study the qualitative homogenization of second-order Hamilton–Jacobi equations in space-time stationary ergodic random environments. Assuming that the Hamiltonian is convex and superquadratic in the momentu...

    Authors: Wenjia Jing, Panagiotis E. Souganidis and Hung V. Tran

    Citation: Research in the Mathematical Sciences 2017 4:6

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  18. Content type: Research

    In this paper, we prove the existence of an infinite-dimensional graded supermodule for the finite sporadic Thompson group Th whose McKay–Thompson series are weakly holomorphic modular forms of weight

    Authors: Michael J. Griffin and Michael H. Mertens

    Citation: Research in the Mathematical Sciences 2016 3:36

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  19. Content type: Research

    This paper studies algebraic and analytic structures associated with the Lerch zeta function. It defines a family of two-variable Hecke operators http://static-content.springer.com/image/art%3A10.1186%2Fs40687-016-0082-9/40687_2016_82_Article_IEq1.gif

    Authors: Jeffrey C. Lagarias and Wen-Ching Winnie Li

    Citation: Research in the Mathematical Sciences 2016 3:33

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  20. Content type: Research

    We investigate Poincaré series, where we average products of terms of Fourier series of real-analytic Siegel modular forms. There are some (trivial) special cases for which the products of terms of Fourier ser...

    Authors: Kathrin Bringmann, Olav K. Richter and Martin Westerholt-Raum

    Citation: Research in the Mathematical Sciences 2016 3:30

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  21. Content type: 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 ...

    Authors: Kathrin Bringmann and Ben Kane

    Citation: Research in the Mathematical Sciences 2016 3:24

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