14 citations · 47 across the 16 of their papers we have counts for
9 papers · 1 filter
Asymptotic Brill-Noether Existence at the Half-Canonical Degree: Energy Pairing, Cheeger Inequality and Covering Radii
Madhusudan Manjunath
We study asymptotic versions of the Brill-Noether existence conjecture on graphs via techniques inspired by the geometry of numbers. We confirm an asymptotic version of the conject…
Poincaré Series of Divisors on Graphs and Chains of Loops
Madhusudan Manjunath
We study Poincaré series associated to a finite collection of divisors on i. a finite graph and ii. a certain family of metric graphs called chain of loops. Our main results are pr…
Brill-Noether Existence on Graphs via -Divisors, Polytopes and Lattices
Madhusudan Manjunath
We study Brill-Noether existence on a finite graph using methods from polyhedral geometry and lattices. We start by formulating analogues of the Brill-Noether conjectures (both the…
Syzygies over the Polytope Semiring
Madhusudan Manjunath
Tropical geometry and its applications indicate a "theory of syzygies" over polytope semirings. Taking cue from this indication, we study a notion of syzygies over the polytope sem…
Embeddings and immersions of tropical curves
Dustin Cartwright, Andrew Dudzik, Madhusudan Manjunath +1
We construct immersions of trivalent abstract tropical curves in the Euclidean plane and embeddings of all abstract tropical curves in higher dimensional Euclidean space. Since not…
Explicit Deformation of Lattice Ideals via Chip Firing Games on Directed Graphs
Spencer Backman, Madhusudan Manjunath
For a finite index sublattice of the root lattice , we construct a deterministic algorithm to deform the lattice ideal to a nearby generic lattice ideal, answering…
The rank of a divisor on a finite graph: geometry and computation
Madhusudan Manjunath
We study the problem of computing the rank of a divisor on a finite graph, a quantity that arises in the Riemann-Roch theory on a finite graph developed by Baker and Norine (Advanc…
The Laplacian lattice of a graph under a simplicial distance function
Madhusudan Manjunath
We provide a complete description of important geometric invariants of the Laplacian lattice of a multigraph under the distance function induced by a regular simplex, namely Vorono…
Riemann-Roch for Sub-Lattices of the Root Lattice
Omid Amini, Madhusudan Manjunath
Recently, Baker and Norine {Advances in Mathematics, 215(2): 766-788, 2007} found new analogies between graphs and Riemann surfaces by developing a Riemann-Roch machinery on a fini…