11 citations · 31 across the 23 of their papers we have counts for
6 papers · 1 filter
Vector bundles on tropical schemes
Jaiung Jun, Kalina Mincheva, Jeffrey Tolliver
We define vector bundles for tropical schemes, and explore their properties. The paper largely consists of three parts; (1) we study free modules over zero-sum free semirings, whic…
Gluing of graphs and their Jacobians
Alessandro Chilelli, Jaiung Jun
The Jacobian of a graph is a discrete analogue of the Jacobian of a Riemann surface. In this paper, we explore how Jacobians of graphs change when we glue two graphs along a common…
On quiver representations over
Jaiung Jun, Alex Sistko
We study the category of representations of a quiver over "the field with one element", denoted by , and the Hall algebra of $\text…
Hall Lie algebras of toric monoid schemes
Jaiung Jun, Matt Szczesny
We associate to a projective -dimensional toric variety a pair of co-commutative (but generally non-commutative) Hopf algebras . These arise as Hall algebr…
Homology of systemic modules
Jaiung Jun, Kalina Mincheva, Louis Rowen
We develop the rudiments of a tropical homology theory, based on "triples" and "systems." Results include a version of Schanuel's lemma, projective dimension, the homology semi-mod…
Lattices, Spectral Spaces, and Closure Operations on Idempotent Semirings
Jaiung Jun, Samarpita Ray, Jeffrey Tolliver
Spectral spaces, introduced by Hochster, are topological spaces homeomorphic to the prime spectra of commutative rings. In this paper we study spectral spaces in perspective of ide…