62 citations · 157 across the 19 of their papers we have counts for
24 papers
The phylogenetic rank of a graph
Franklin Ashworth, Oliver Clarke, Jeffrey Giansiracusa +3
The Pachter-Sturmfels phylogenetic rank of a graph G is the minimal number of metric trees needed to embed G isometrically. Here, all edges of G are of length one and the product o…
Projective hypersurfaces in tropical scheme theory I: the Macaulay ideal
Alex Fink, Jeffrey Giansiracusa, Noah Giansiracusa +1
A "tropical ideal" is an ideal in the idempotent semiring of tropical polynomials that is also, degree by degree, a tropical linear space. We introduce a construction based on tran…
Ladder Decomposition for Morphisms of Persistence Modules
Živa Urbančič, Jeffrey Giansiracusa
The output of persistent homology is an algebraic object called a persistence module. This object admits a decomposition into a direct sum of interval persistence modules described…
An structure on the matroid grassmannian
Jeffrey Giansiracusa
In analogy with the origin of the additive structure of -theory, we construct an structure on the matroid Grassmannian (the space of oriented matroids) for which the…
Persistent homology as a probe for center vortices and deconfinement in SU(2) lattice gauge theory
Nicholas Sale, Biagio Lucini, Jeffrey Giansiracusa
Topological Data Analysis (TDA) is a field that leverages tools and ideas from algebraic topology to provide robust methods for analysing geometric and topological aspects of data.…
Probing center vortices and deconfinement in lattice gauge theory with persistent homology
Nicholas Sale, Biagio Lucini, Jeffrey Giansiracusa
We investigate the use of persistent homology, a tool from topological data analysis, as a means to detect and quantitatively describe center vortices in lattice g…
A general framework for tropical differential equations
Jeffrey Giansiracusa, Stefano Mereta
We construct a general framework for tropical differential equations based on idempotent semirings and an idempotent version of differential algebra. Over a differential ring equip…
Quantitative analysis of phase transitions in two-dimensional XY models using persistent homology
Nicholas Sale, Jeffrey Giansiracusa, Biagio Lucini
We use persistent homology and persistence images as an observable of three different variants of the two-dimensional XY model in order to identify and study their phase transition…
Characteristic classes of bundles of K3 manifolds and the Nielsen realization problem
Jeffrey Giansiracusa, Alexander Kupers, Bena Tshishiku
Let be the K3 manifold. In this note, we discuss two methods to prove that certain generalized Miller--Morita--Mumford classes for smooth bundles with fiber are non-zero. A…
The circle transfer and cobordism categories
Jeffrey Giansiracusa
The circle transfer has appeared in several contexts in topology. In this note we observe that this map admits a geometric re-interpretation as a morphi…
On the relation between hyperrings and fuzzy rings
Jeffrey Giansiracusa, Jaiung Jun, Oliver Lorscheid
We construct a full embedding of the category of hyperfields into Dress's category of fuzzy rings and explicitly characterize the essential image --- it fails to be essentially sur…
A Grassmann algebra for matroids
Jeffrey Giansiracusa, Noah Giansiracusa
We introduce an idempotent analogue of the exterior algebra for which the theory of tropical linear spaces (and valuated matroids) can be seen in close analogy with the classical G…
On the Hochschild homology of involutive algebras
Ramses Fernandez-Valencia, Jeffrey Giansiracusa
We study the homological algebra of bimodules over involutive associative algebras. We show that Braun's definition of involutive Hochschild cohomology in terms of the complex of i…
The universal tropicalization and the Berkovich analytification
Jeffrey Giansiracusa, Noah Giansiracusa
Given an integral scheme X over a non-archimedean valued field k , we construct acuniversal closed embedding of X into a k-scheme equipped with a model over the field with one elem…
Equations of tropical varieties
Jeffrey Giansiracusa, Noah Giansiracusa
We introduce a scheme-theoretic enrichment of the principal objects of tropical geometry. Using a category of semiring schemes, we construct tropical hypersurfaces as schemes over…
Invariance properties of Miller-Morita-Mumford characteristic numbers of fibre bundles
Thomas Church, Martin Crossley, Jeffrey Giansiracusa
Characteristic classes of fibre bundles in the category of closed oriented manifolds give rise to characteristic numbers by integrating the classes over the base.…
The framed little 2-discs operad and diffeomorphisms of handlebodies
Jeffrey Giansiracusa
The framed little 2-discs operad is homotopy equivalent to a cyclic operad. We show that the derived modular envelope of this cyclic operad (i.e., the modular operad freely generat…
Cyclic operad formality for compactified moduli spaces of genus zero surfaces
Jeffrey Giansiracusa, Paolo Salvatore
The framed little 2-discs operad is homotopy equivalent to the Kimura-Stasheff-Voronov cyclic operad of moduli spaces of genus zero stable curves with tangent rays at the marked po…
Formality of the framed little 2-discs operad and semidirect products
Jeffrey Giansiracusa, Paolo Salvatore
We prove that the operad of framed little 2-discs is formal. Tamarkin and Kontsevich each proved that the unframed 2-discs operad is formal. The unframed 2-discs is an operad in th…
Vanishing of universal characteristic classes for handlebody groups and boundary bundles
Jeffrey Giansiracusa, Ulrike Tillmann
Using certain Thom spectra appearing in the study of cobordism categories, we show that the odd half of the Miller-Morita-Mumford classes on the mappping class group of a surface w…
On the homotopy type of the Deligne-Mumford compactification
Johannes Ebert, Jeffrey Giansiracusa
An old theorem of Charney and Lee says that the classifying space of the category of stable nodal topological surfaces and isotopy classes of degenerations has the same rational ho…
Pontrjagin-Thom maps and the homology of the moduli stack of stable curves
Johannes Ebert, Jeffrey Giansiracusa
We study the singular homology (with field coefficients) of the moduli stack of stable n-pointed complex curves of genus g (the Deligne-Mumford compactification). Each of its irred…
The diffeomorphism group of a K3 surface and Nielsen realization
Jeffrey Giansiracusa
The Nielsen Realization problem asks when the group homomorphism from Diff(M) to pi_0 Diff(M) admits a section. For M a closed surface, Kerckhoff proved that a section exists over…
The stable mapping class group of simply connected 4-manifolds
Jeffrey Giansiracusa
We consider mapping class groups Γ(M) = pi_0 Diff(M fix \partial M) of smooth compact simply connected oriented 4-manifolds M bounded by a collection of 3-spheres. We show that if…