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  1. Research

    Autoduality holds for a degenerating abelian variety

    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...

    Jesse Leo Kass

    Research in the Mathematical Sciences 2017 4:27

    Published on: 6 December 2017

  2. Research

    Fourientations and the Tutte polynomial

    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...

    Spencer Backman and Sam Hopkins

    Research in the Mathematical Sciences 2017 4:18

    Published on: 12 September 2017

  3. Research

    Uniform spectral convergence of the stochastic Galerkin method for the linear transport equations with random inputs in diffusive regime and a micro–macro decomposition-based asymptotic-preserving method

    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 ...

    Shi Jin, Jian-Guo Liu and Zheng Ma

    Research in the Mathematical Sciences 2017 4:15

    Published on: 7 August 2017

  4. Research

    Dynamically distinguishing polynomials

    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 ...

    Andrew Bridy and Derek Garton

    Research in the Mathematical Sciences 2017 4:13

    Published on: 10 July 2017

  5. Research

    Integer partitions, probabilities and quantum modular forms

    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 ...

    Hieu T. Ngo and Robert C. Rhoades

    Research in the Mathematical Sciences 2017 4:17

    Published on: 3 July 2017

  6. Research

    Distributed-memory hierarchical interpolative factorization

    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...

    Yingzhou Li and Lexing Ying

    Research in the Mathematical Sciences 2017 4:12

    Published on: 5 June 2017

  7. Research

    Skeletons of stable maps II: superabundant geometries

    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...

    Dhruv Ranganathan

    Research in the Mathematical Sciences 2017 4:11

    Published on: 1 June 2017

  8. Research

    Formulas for monodromy

    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...

    Alan Stapledon

    Research in the Mathematical Sciences 2017 4:8

    Published on: 10 April 2017

  9. Research

    A geometric perspective on p-adic properties of mock modular forms

    Bringmann et al. (Trans Am Math Soc 364(5):2393–2410, 2012) showed how to ‘regularize’ mock modular forms by a certain linear combination of the Eichler integral of their shadows in order to obtain p-adic modular...

    Luca Candelori and Francesc Castella

    Research in the Mathematical Sciences 2017 4:5

    Published on: 3 March 2017

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