9 citations · 28 across the 19 of their papers we have counts for
26 papers
Combinatorial geometry of the 2D Toda lattice and Davey Stewartson equation
Rodrigo Navarro Betancourt, Marvin Anas Hahn, Vera Posch +1
The KP equation is a prototypical -dimensional integrable PDE. Its soliton solutions are famously parametrized by the Sato Grassmannian. In seminal work, Kodama and Williams…
Failing to keep the balance: explicit formulae and topological recursion for leaky Hurwitz numbers
Marvin Anas Hahn, Reinier Kramer
Recently a new family of enumerative invariants called leaky Hurwitz numbers was introduced by Cavalieri-Markwig-Ranganathan in the context of logarithmic intersection theory. They…
Tropicalising hypergeometric -functions
Marvin Anas Hahn, Brian O'Callaghan, Jonas Wahl
Weighted Hurwitz numbers arise as coefficients in the power sum expansion of deformed hypergeometric --functions. They specialise to essentially all known cases of Hurwitz numbe…
A refined twist on Hurwitz numbers
Raphaël Fesler, Marvin Anas Hahn, Maksim Karev +1
We introduce a two-parameter refinement of the Jucys-Murphy theory, that we call the CJT-refinement, unifying Schur, zonal, and, conjecturally, Jack actions of the ring of symmetri…
Universal piecewise polynomiality for counting curves in toric surfaces
Marvin Anas Hahn, Vincenzo Reda
Inspired by piecewise polynomiality results of double Hurwitz numbers, Ardila and Brugallé introduced an enumerative problem which they call double Gromov--Witten invariants of Hir…
Order-One Rolling Shutter Cameras
Marvin Anas Hahn, Kathlén Kohn, Orlando Marigliano +1
Rolling shutter (RS) cameras dominate consumer and smartphone markets. Several methods for computing the absolute pose of RS cameras have appeared in the last 20 years, but the rel…
Tropical twisted Hurwitz numbers for elliptic curves
Marvin Anas Hahn, Hannah Markwig
Hurwitz numbers enumerate branched morphisms between Riemann surfaces. For a fixed elliptic target, Hurwitz numbers are intimately related to mirror symmetry following work of Dijk…
Combinatorics of pruned Hurwitz numbers
Sean Gearoid Fitzgerald, Marvin Anas Hahn, Síofra Kelly
Hurwitz numbers enumerate branched morphisms between Riemannn surfaces with fixed numerical data. They represent important objects in enumerative geometry that are accessible by co…
Twisted Hurwitz numbers: Tropical and polynomial structures
Marvin Anas Hahn, Hannah Markwig
Hurwitz numbers count covers of curves satisfying fixed ramification data. Via monodromy representation, this counting problem can be transformed to a problem of counting factoriza…
Subspaces Fixed by a Nilpotent Matrix
Marvin Anas Hahn, Gabriele Nebe, Mima Stanojkovski +1
The linear spaces that are fixed by a given nilpotent matrix form a subvariety of the Grassmannian. We classify these varieties for small . Mutiah, Weekes and Yacob…
Orders and Polytropes: Matrix Algebras from Valuations
Yassine El Maazouz, Marvin Anas Hahn, Gabriele Nebe +2
We apply tropical geometry to study matrix algebras over a field with valuation. Using the shapes of min-max convexity, known as polytropes, we revisit the graduated orders introdu…
Intersection numbers on tropical Hassett spaces
Marvin Anas Hahn, Shiyue Li
We study the intersection of tropical psi-classes on tropical heavy/light Hassett spaces, generalising a result of Kerber--Markwig for tropical moduli spaces of rational stable cur…
Valued rank-metric codes
Yassine El Maazouz, Marvin Anas Hahn, Alessandro Neri +1
In this paper, we study linear spaces of matrices defined over discretely valued fields and discuss their dimension and minimal rank drops over the associated residue fields. To th…
One-parameter families of multiview varieties via quotient lattices
Marvin Anas Hahn
We develop a novel theory of one-parameter families of multi-view varieties. These families are induced by quotient lattices over discrete valuation rings and generalise the notion…
Mustafin models of projective varieties and vector bundles
Marvin Anas Hahn
Mustafin varieties are well-studied degenerations of projective spaces induced by a choice of integral points in a Bruhat--Tits building. In recent work, Annette Werner and the aut…
A short note on Cayley-Salmon equations
Marvin Anas Hahn, Sara Lamboglia, Alejandro Vargas
A Cayley-Salmon equation for a smooth cubic surface in is an expression of the form such that the zero set is and , are…
Strongly semistable reduction of syzygy bundles on plane curves
Marvin Anas Hahn, Annette Werner
We investigate degenerations of syzygy bundles on plane curves over -adic fields. We use Mustafin varieties which are degenerations of projective spaces to find a large family o…
Wall-crossing and recursion formulae for tropical Jucys covers
Marvin Anas Hahn, Danilo Lewanski
In recent work, the authors derived a tropical interpretation of monotone and strictly monotone double Hurwitz numbers. In this paper, we apply the technique of tropical flows to t…
Triply mixed coverings of arbitrary base curves: Quasimodularity, quantum curves and a mysterious topological recursions
Marvin Anas Hahn, Jan-Willem M. van Ittersum, Felix Leid
Simple Hurwitz numbers enumerate branched morphisms between Riemann surfaces with fixed ramification data. In recent years, several variants of this notion for genus base curve…
Bi-pruned Hurwitz numbers
Marvin Anas Hahn
Hurwitz numbers enumerate ramified coverings of the Riemann sphere with fixed ramification data. Certain kinds of ramification data are of particular interest, such as double Hurwi…
Tropical Jucys Covers
Marvin Anas Hahn, Danilo Lewanski
We study monotone and strictly monotone Hurwitz numbers from a bosonic Fock space perspective. This yields to an interpretation in terms of tropical geometry involving local multip…
Tropicalized quartics and canonical embeddings for tropical curves of genus 3
Marvin Anas Hahn, Hannah Markwig, Yue Ren +1
Brodsky, Joswig, Morrison and Sturmfels showed that not all abstract tropical curves of genus can be realized as a tropicalization of a quartic in the euclidean plane. In this…
Wall-crossing formulae and strong piecewise polynomiality for mixed Grothendieck dessins d'enfant, monotone, and simple double Hurwitz numbers
Marvin Anas Hahn, Reinier Kramer, Danilo Lewanski
We derive explicit formulae for the generating series of mixed Grothendieck dessins d'enfant/monotone/simple Hurwitz numbers, via the semi-infinite wedge formalism. This reveals th…
Mustafin varieties, moduli spaces and tropical geometry
Marvin Anas Hahn, Binglin Li
Mustafin varieties are flat degenerations of projective spaces, induced by a choice of an tuple of lattices in a vector space over a non-archimedean field. They were introduced…