Abstract:
We produce Brill-Noether general graphs in every genus, confirming a conjecture of Baker and giving a new proof of the Brill-Noether Theorem, due to Griffiths and Harris, over any algebraically closed field.

Abstract:
In this article, we will prove that the set of 4-dissimilarity vectors of n-trees is contained in the tropical Grassmannian G_{4,n}. We will also propose three equivalent conjectures related to the set of m-dissimilarity vectors of n-trees for the case m > 4. Using a computer algebra system, we can prove these conjectures for m = 5.

Abstract:
Analogously as in classical algebraic geometry, linear pencils of tropical plane curves are parameterized by tropical lines in a coefficient space. A special example of such a linear pencil is the set of tropical plane curves with an n-element support set through a general configuration of n points in the tropical plane. In [RGST], it is proved that these linear pencils are compatible with their support set. In this article, we give a characterization of points lying in the fixed locus of a tropical linear pencil and show that each compatible linear pencil comes from a general configuration.

Abstract:
Although manga constitute a massive transcultural flow, they are extremely diverse as far as genre and content are concerned. This article attempts to bridge these differences by highlighting phenomenological patterns within popular manga: by bracketing content, the author focuses on the experience of reading manga, thereby considering the medial aspect of these works. By examining a diverse corpus of contemporary popular series (Bleach, Death Note, Fruits Basket, and Kitchen Princess), the article pays attention to elements such as reading rhythm, contrast, fragmentation, and page tabularity, in order to pave the way for future study of manga’s place in the contemporary medial ethos.

Abstract:
This paper improves the convergence and robustness of a multigrid-based solver for the cross sections of the driven Schroedinger equation. Adding an Coupled Channel Correction Step (CCCS) after each multigrid (MG) V-cycle efficiently removes the errors that remain after the V-cycle sweep. The combined iterative solution scheme (MG-CCCS) is shown to feature significantly improved convergence rates over the classical MG method at energies where bound states dominate the solution, resulting in a fast and scalable solution method for the complex-valued Schroedinger break-up problem for any energy regime. The proposed solver displays optimal scaling; a solution is found in a time that is linear in the number of unknowns. The method is validated on a 2D Temkin-Poet model problem, and convergence results both as a solver and preconditioner are provided to support the O(N) scalability of the method. This paper extends the applicability of the complex contour approach for far field map computation [S. Cools, B. Reps, W. Vanroose, An Efficient Multigrid Calculation of the Far Field Map for Helmholtz and Schroedinger Equations, SIAM J. Sci. Comp. 36(3) B367--B395, 2014].

Abstract:
A degeneration of curves gives rise to an interesting relation between linear systems on curves and on graphs. In this paper, we consider the case of linear pencils and as an application, we obtain some results on pencils on real curves.

Abstract:
A point P on a smooth hypersurface X of degree d in an N-dimensional projective space is called a star point if and only if the intersection of X with the embedded tangent space T_P(X) is a cone with vertex P. This notion is a generalization of total inflection points on plane curves and Eckardt points on smooth cubic surfaces in three-dimensional projective space. We generalize results on the configuration space of total inflection points on plane curves to star points. We give a detailed description of the configuration space for hypersurfaces with two or three star points. We investigate collinear star points and we prove that the number of star points on a smooth hypersurface is finite.

Abstract:
A sufficiently generic bivariate Laurent polynomial with given Newton polygon Delta defines an algebraic curve C, many of whose numerical invariants are encoded in the combinatorics of Delta. These include the genus (classical), the gonality, the Clifford index and the Clifford dimension (an enhancement of recent results by Kawaguchi), the scrollar invariants and, for sufficiently nice instances of Delta, certain secondary scrollar invariants that were introduced by Schreyer (new observation). After discussing these invariants, we study to what extent they allow one to reconstruct Delta from the abstract geometry of C.