2 citations · 9 across the 12 of their papers we have counts for
16 papers
The virtual Euler characteristic for binary matroids
Madeline Brandt, Juliette Bruce, Daniel Corey
Inspired by Kontsevich's graphic orbifold Euler characteristic we define a virtual Euler characteristic for any finite set of isomorphism classes of matroids of rank . Our main…
Towards tropically counting binodal surfaces
Madeline Brandt, Alheydis Geiger
Tropical counting tools are useful for many enumerative questions. We count tropical multinodal surfaces using floor plans, looking at the case when two nodes are tropically close…
Classification of Quadratic Packing Polynomials on Sectors of
Madeline Brandt, Kåre Schou Gjaldbæk
We study quadratic polynomials giving bijections from the integer lattice points of sectors of onto , called packing polynomials. We determine all qua…
On the Top-Weight Rational Cohomology of
Madeline Brandt, Juliette Bruce, Melody Chan +3
We compute the top-weight rational cohomology of for , , and , and we give some vanishing results for the top-weight rational cohomology of and $ A_{10…
Tropical flag varieties
Madeline Brandt, Christopher Eur, Leon Zhang
Flag matroids are combinatorial abstractions of flags of linear subspaces, just as matroids are of linear subspaces. We introduce the flag Dressian as a tropical analogue of the pa…
A Tropical Count of Binodal Cubic Surfaces
Madeline Brandt, Alheydis Geiger
There are 280 binodal cubic surfaces passing through 17 general points. For the typically used tropical point conditions, we show that 214 of these give tropicalizations such that…
Divisorial motivic zeta functions for marked stable curves
Madeline Brandt, Martin Ulirsch
We define a divisorial motivic zeta function for stable curves with marked points which agrees with Kapranov's motivic zeta function when the curve is smooth and unmarked. We show…
Voronoi Cells in Metric Algebraic Geometry of Plane Curves
Madeline Brandt, Madeleine Weinstein
Voronoi cells of varieties encode many features of their metric geometry. We prove that each Voronoi or Delaunay cell of a plane curve appears as the limit of a sequence of cells o…
Matroids and their Dressians
Madeline Brandt, David E Speyer
We study Dressians of matroids using the initial matroids of Dress and Wenzel. These correspond to cells in regular matroid subdivisions of matroid polytopes. An efficient algorith…
Symmetric powers of algebraic and tropical curves: a non-Archimedean perspective
Madeline Brandt, Martin Ulirsch
We show that the non-Archimedean skeleton of the -th symmetric power of a smooth projective algebraic curve is naturally isomorphic to the -th symmetric power of the trop…
The slack realization space of a matroid
Madeline Brandt, Amy Wiebe
We introduce a new model for the realization space of a matroid, which is obtained from a variety defined by a saturated determinantal ideal, called the slack ideal, coming from th…
Tropical superelliptic curves
Madeline Brandt, Paul Alexander Helminck
We present an algorithm for computing the Berkovich skeleton of a superelliptic curve over a valued field. After defining superelliptic weighted metric graphs, we show t…
Optimal Packings of Two to Four Equal Circles on Any Flat Torus
Madeline Brandt, William Dickinson, AnnaVictoria Ellsworth +2
We find explicit formulas for the radii and locations of the circles in all the optimally dense packings of two, three or four equal circles on any flat torus, defined to be the qu…
The degree of
Madeline Brandt, DJ Bruce, Taylor Brysiewicz +2
We provide a closed formula for the degree of over an algebraically closed field of characteristic zero. In addition, we describe symbolic and numerical techniques w…
From Curves to Tropical Jacobians and Back
Barbara Bolognese, Madeline Brandt, Lynn Chua
Given a curve defined over an algebraically closed field which is complete with respect to a nontrivial valuation, we study its tropical Jacobian. This is done by first tropicalizi…
Quadratic Packing Polynomials on Sectors of
Madeline Brandt
A polynomial on a region in the plane is called a packing polynomial if the restriction of to yields a bijection to . In this…