Marcy Robertson

A topological characterisation of the Kashiwara–Vergne groups

Zsuzsanna Dancso, Iva Halacheva, Marcy Robertson

Journal article  |  2023  |  Transactions of the American Mathematical Society

In [Math. Ann. 367 (2017), pp. 1517–1586] Bar-Natan and the first author show that solutions to the Kashiwara–Vergne equations are..

An infinity operad of normalized cacti

L Basualdo Bonatto, S Chettih, A Linton, S Raynor, M Robertson, N Wahl

Journal article  |  2022  |  Topology and its Applications

We endow the normalized cacti with the structure of an ∞-operad by showing that its existing composition laws are associative up t..

Circuit algebras are wheeled props

Zsuzsanna Dancso, Iva Halacheva, Marcy Robertson

Journal article  |  2021  |  JOURNAL OF PURE AND APPLIED ALGEBRA

Circuit algebras, introduced by Bar-Natan and the first author, are a generalization of Jones's planar algebras, in which one drop..

Modular operads and the nerve theorem

Philip Hackney, Marcy Robertson, Donald Yau

Journal article  |  2020  |  ADVANCES IN MATHEMATICS

We describe a category of undirected graphs which comes equipped with a faithful functor into the category of (colored) modular op..

A graphical category for higher modular operads

Philip Hackney, Marcy Robertson, Donald Yau

Journal article  |  2020  |  ADVANCES IN MATHEMATICS

We present a homotopy theory for a weak version of modular operads whose compositions and contractions are only defined up to homo..

Operads of genus zero curves and the Grothendieck-Teichmuller group

Pedro Boavida de Brito, Geoffroy Horel, Marcy Robertson

Journal article  |  2019  |  GEOMETRY & TOPOLOGY

Higher cyclic operads

Philip Hackney, Marcy Robertson, Donald Yau

Journal article  |  2019  |  ALGEBRAIC AND GEOMETRIC TOPOLOGY

We introduce a convenient definition for weak cyclic operads, which is based on unrooted trees and Segal conditions. More specific..

ON FACTORIZATIONS OF GRAPHICAL MAPS

Philip Hackney, Marcy Robertson, Donald Yau

Journal article  |  2018  |  HOMOLOGY HOMOTOPY AND APPLICATIONS

We study the categories governing infinity (wheeled) properads. The graphical category, which was already known to be generalized ..

Lecture Notes on Infinity-Properads

Philip Hackney, Marcy Robertson

Book Chapter  |  2018

THE HOMOTOPY THEORY OF SIMPLICIAL PROPS

Philip Hackney, Marcy Robertson

Journal article  |  2017  |  ISRAEL JOURNAL OF MATHEMATICS

The category of (colored) props is an enhancement of the category of colored operads, and thus of the category of small categories..