14 citations · 47 across the 16 of their papers we have counts for
18 papers
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…
Equations over Polyhedral Semirings
Madhusudan Manjunath
We study the theory of equations in one variable over polyhedral semirings. The article revolves around a notion of solution to a polynomial equation over a polyhedral semiring. Ou…
A Tropical Geometric Approach To Exceptional Points
Ayan Banerjee, Rimika Jaiswal, Madhusudan Manjunath +1
Non-Hermitian systems have been widely explored in platforms ranging from photonics to electric circuits. A defining feature of non-Hermitian systems is exceptional points (EPs), w…
Rational Normal Curves, Chip Firing and Free Resolutions
Rahul Karki, Madhusudan Manjunath
We study rational normal curves via a connection to the chip firing game. A key technique, introduced in this article, is to interpret the defining ideal of the rational normal cur…
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…
Tutte Short Exact Sequences of Graphs
Madhusudan Manjunath
We associate two modules, the -parking critical module and the toppling critical module, to an undirected connected graph . The -parking critical module and the toppling c…
Commutative Algebra of Generalised Frobenius Numbers
Madhusudan Manjunath, Ben Smith
We study commutative algebra arising from generalised Frobenius numbers. The -th (generalised) Frobenius number of natural numbers is the largest natural numbe…
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…
Tropical Graph Curves
Madhusudan Manjunath
We study tropical line arrangements associated to a three-regular graph that we refer to as \emph{tropical graph curves}. Roughly speaking, the tropical graph curve associated…
Smoothing of Limit Linear Series of Rank One on Saturated Metrized Complexes of Algebraic Curves
Ye Luo, Madhusudan Manjunath
We investigate the smoothing problem of limit linear series of rank one on an enrichment of the notions of nodal curves and metrized complexes called saturated metrized complexes.…
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…
Minimal Free Resolutions of the -parking Function Ideal and the Toppling Ideal
Madhusudan Manjunath, Frank-Olaf Schreyer, John Wilmes
The -parking function ideal of a directed multigraph is a monomial ideal which encodes some of the combinatorial information of . It is an initial ideal of the topp…
Monomials, Binomials, and Riemann-Roch
Madhusudan Manjunath, Bernd Sturmfels
The Riemann-Roch theorem on a graph G is related to Alexander duality in combinatorial commutive algebra. We study the lattice ideal given by chip firing on G and the initial ideal…
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…