23 citations · 101 across the 22 of their papers we have counts for
25 papers
Corrigendum to "Asymptotic homology of graph braid groups"
Byung Hee An, Gabriel C. Drummond-Cole, Ben Knudsen
We correct an error in the paper referred to in the title. Part of the argument is organized as a general method for establishing when (derived) functors factor through a fixed Ser…
Homotopy theory of curved operads and curved algebras
Joan Bellier-Millès, Gabriel C. Drummond-Cole
Curved algebras are algebras endowed with a predifferential, which is an endomorphism of degree -1 whose square is not necessarily 0. This makes the usual definition of quasi-isomo…
Asymptotic homology of graph braid groups
Byung Hee An, Gabriel C. Drummond-Cole, Ben Knudsen
We give explicit formulas for the asymptotic Betti numbers of the unordered configuration spaces of an arbitrary finite graph over an arbitrary field.
Endomorphism operads of functors
Gabriel C. Drummond-Cole, Joseph Hirsh, Damien Lejay
We consider the endomorphism operad of a functor, which is roughly the object of natural transformations from (monoidal) powers of that functor to itself. There are many examples f…
Coextension of scalars in operad theory
Gabriel C. Drummond-Cole, Philip Hackney
The functor between operadic algebras given by restriction along an operad map generally has a left adjoint. We give a necessary and sufficient condition for the restriction functo…
Homotopy transfer and formality
Gabriel C. Drummond-Cole, Geoffroy Horel
In a recent paper, the second author and Joana Cirici proved a theorem that says that given appropriate hypotheses, -formality of a differential graded algebraic structure is eq…
Betti numbers of unordered configuration spaces of small graphs
Gabriel C. Drummond-Cole
The purpose of this document is to provide data about known Betti numbers of unordered configuration spaces of small graphs in order to guide research and avoid duplicated effort.…
An action of the Polishchuk differential operator via punctured surfaces
Gabriel C. Drummond-Cole, Mehdi Tavakol
For a family of Jacobians of smooth pointed curves there is a notion of tautological algebra. There is an action of on this algebra. We define and study a lifting…
Representations are adjoint to endomorphisms
Gabriel C. Drummond-Cole, Joseph Hirsh, Damien Lejay
The functor that takes a ring to its category of modules has an adjoint if one remembers the forgetful functor to abelian groups: the endomorphism ring of linear natural transforma…
Dwyer--Kan homotopy theory for cyclic operads
Gabriel C. Drummond-Cole, Philip Hackney
We introduce a general definition for colored cyclic operads over a symmetric monoidal ground category, which has several appealing features. The forgetful functor from colored cyc…
Edge stabilization in the homology of graph braid groups
Byung Hee An, Gabriel C. Drummond-Cole, Ben Knudsen
We introduce a novel type of stabilization map on the configuration spaces of a graph, which increases the number of particles occupying an edge. There is an induced action on homo…
Subdivisional spaces and graph braid groups
Byung Hee An, Gabriel C. Drummond-Cole, Ben Knudsen
We study the problem of computing the homology of the configuration spaces of a finite cell complex . We proceed by viewing , together with its subdivisions, as a subdivision…
Betti numbers of configuration spaces of surfaces
Gabriel C. Drummond-Cole, Ben Knudsen
We give explicit formulas for the Betti numbers, both stable and unstable, of the unordered configuration spaces of an arbitrary surface of finite type.
Homotopy probability theory on a Riemannian manifold and the Euler equation
Gabriel C. Drummond-Cole, John Terilla
Homotopy probability theory is a version of probability theory in which the vector space of random variables is replaced with a chain complex. A natural example extends ordinary pr…
An operadic approach to operator-valued free cumulants
Gabriel C. Drummond-Cole
An operadic framework is developed to explain the inversion formula relating moments and cumulants in operator-valued free probability theory.
A non-crossing word cooperad for free homotopy probability theory
Gabriel C. Drummond-Cole
We construct a cooperad which extends the framework of homotopy probability theory to free probability theory. The cooperad constructed, which seems related to the sequence and cac…
Chain-Level String Topology Operations
Gabriel C. Drummond-Cole, Kate Poirier, Nathaniel Rounds
We construct a space of string diagrams, which are a type of fatgraph with some additional data, and show that there are string topology operations on the chains of the free loop s…
Cones in homotopy probability theory
Gabriel C. Drummond-Cole, John Terilla
This note defines cones in homotopy probability theory and demonstrates that a cone over a space is a reasonable replacement for the space. The homotopy Gaussian distribution in on…
Model structures for coalgebras
Gabriel C. Drummond-Cole, Joseph Hirsh
Classically, there are two model category structures on coalgebras in the category of chain complexes over a field. In one, the weak equivalences are maps which induce an isomorphi…
An update on domineering on rectangular boards
Gabriel C. Drummond-Cole
Domineering is a combinatorial game played on a subset of a rectangular grid between two players. Each board position can be put into one of four outcome classes based on who the w…
Homotopy Probability Theory II
Gabriel C. Drummond-Cole, Jae-Suk Park, John Terilla
This is the second of two papers that introduce a deformation theoretic framework to explain and broaden a link between homotopy algebra and probability theory. This paper outlines…
Homotopy Probability Theory I
Gabriel C. Drummond-Cole, Jae-Suk Park, John Terilla
This is the first of two papers that introduce a deformation theoretic framework to explain and broaden a link between homotopy algebra and probability theory. In this paper, cumul…
Formal formality of the hypercommutative algebras of low dimensional Calabi-Yau varieties
Gabriel C. Drummond-Cole
There is a homotopy hypercommutative algebra structure on the cohomology of a Calabi-Yau variety. The truncation of this homotopy hypercommutative algebra to a strict hypercommutat…
The minimal model for the Batalin-Vilkovisky operad
Gabriel C. Drummond-Cole, Bruno Vallette
The purpose of this paper is to explain and to generalize, in a homotopical way, the result of Barannikov-Kontsevich and Manin which states that the underlying homology groups of s…