Publications

Cover of the book Infinity Properads and Infinity Wheeled Properads

Infinity Properads and Infinity Wheeled Properads
with Marcy Robertson and Donald Yau
Lecture Notes in Mathematics 2147
arxiv:1410.6716 [math.AT]

Preprints

Operadic categories and 2-Segal sets (preprint)
arxiv:2312.00756 [math.CT]

Partial groups as symmetric simplicial sets (preprint)
with Justin Lynd
arxiv:2310.01513 [math.GR]

Free decomposition spaces (preprint)
with Joachim Kock
arxiv:2210.11192 [math.CT]

Culf maps and edgewise subdivision (preprint)
with Joachim Kock; appendix also with Jan Steinebrunner
arxiv:2210.11191 [math.AT]

Accepted / In Press

Pushouts of Dwyer maps are (∞,1)-categorical (preprint)
with Viktoriya Ozornova, Emily Riehl, and Martina Rovelli
(to appear in Algebraic & Geometric Topology)
arxiv:2205.02353 [math.AT]

Segal conditions for generalized operads (preprint)
(to appear in the volume “Higher Structures in Geometry, Topology and Physics” of Contemporary Mathematics, AMS)
arxiv:2208.13852 [math.CT]

Published

Categories of graphs for operadic structures
(in Mathematical Proceedings)
arxiv:2109.06231 [math.CT]

Labelled cospan categories and properads
with Jonathan Beardsley
(in Journal of Pure and Applied Algebra)
arxiv:2206.00698 [math.CT]

An (∞,2)-categorical pasting theorem
with Viktoriya Ozornova, Emily Riehl, and Martina Rovelli
(in Transactions of the American Mathematical Society)
arxiv:2106.03660 [math.AT]

On pasting in (∞,2)-categories (extended abstract)
(in Oberwolfach Reports)
doi:10.14760/OWR-2021-46

Induced model structures for higher categories
with Martina Rovelli
(in Proceedings of the American Mathematical Society)
arxiv:2102.01104 [math.CT]

On rectification and enrichment of infinity properads
with Hongyi Chu
(in Journal of the London Mathematical Society)
arxiv:2007.00634 [math.AT]

Coextension of scalars in operad theory
with Gabriel C. Drummond-Cole
(in Mathematische Zeitschrift)
arxiv:1906.12275 [math.CT]

Dwyer–Kan homotopy theory for cyclic operads
with Gabriel C. Drummond-Cole
(in Proceedings of the Edinburgh Mathematical Society)
arxiv:1809.06322 [math.AT]

Modular operads and the nerve theorem
with Marcy Robertson and Donald Yau
(in Advances in Mathematics)
arxiv:1906.01144 [math.CT]

A graphical category for higher modular operads
with Marcy Robertson and Donald Yau
(in Advances in Mathematics)
arxiv:1906.01143 [math.AT]

Higher cyclic operads
with Marcy Robertson and Donald Yau
(in Algebraic & Geometric Topology)
arxiv:1611.02591 [math.AT]

A criterion for existence of right-induced model structures
with Gabriel C. Drummond-Cole
(in Bulletin of the London Mathematical Society)
arxiv:1712.07787 [math.CT]

Configuration spaces form a Segal semi-dendroidal space
(in Higher Structures)
arxiv:1707.05027 [math.AT]

On factorizations of graphical maps
with Marcy Robertson and Donald Yau
(in Homology, Homotopy and Applications)
arxiv:1705.08546 [math.AT]

Lectures on infinity-properads
with Marcy Robertson
(in the 2016 MATRIX Annals)
arxiv:1610.00486 [math.AT]

A simplicial model for infinity properads
with Marcy Robertson and Donald Yau
(in Higher Structures)
arxiv:1502.06522 [math.AT]

The homotopy theory of simplicial props
with Marcy Robertson
(in Israel Journal of Mathematics)
arxiv:1209.1087 [math.AT]

Diagrams encoding group actions on Γ-spaces
with Julie Bergner
(in Manifolds and K-theory, Contemporary Mathematics 682)
arxiv:1212.4542 [math.AT]

Shrinkability, relative left properness, and derived base change
with Marcy Robertson and Donald Yau
(in New York Journal of Mathematics)
arxiv:1510.01341 [math.AT]

Relative left properness of colored operads
with Marcy Robertson and Donald Yau
(in Algebraic & Geometric Topology)
arxiv:1411.4668 [math.AT]

Reedy categories which encode the notion of category actions
with Julie Bergner
(in Fundamenta Mathematicae)
arxiv:1207.3467 [math.AT]

Group actions on Segal operads
with Julie Bergner
(in Israel Journal of Mathematics)
arxiv:1207.3465 [math.AT]

On the category of props
with Marcy Robertson
(in Applied Categorical Structures)
arxiv:1207.2773 [math.CT]

Operations & spectral sequences

Homology operations and cosimplicial iterated loop spaces
(in Homology, Homotopy and Applications)
arxiv:1102.0020 [math.AT]

Spectral sequence operations converge to Araki-Kudo operations
(in Journal of Pure and Applied Algebra)
arxiv:1101.5395 [math.AT]

Operations in the homology spectral sequence of a cosimplicial infinite loop space
(in Journal of Pure and Applied Algebra)
arxiv:1101.3798 [math.AT]

phd thesis Homology operations in the spectral sequence of a cosimplicial space

Ranks of graphs

On the minimum semi-definite rank of a simple graph
with Matthew Booth, Benjamin Harris, Charles R. Johnson, Margaret Lay, Terry D. Lenker, Lon H. Mitchell, Sivaram K. Narayan, Amanda Pascoe, and Brian D. Sutton
(in Linear and Multilinear Algebra)

Linearly independent vertices and minimum semidefinite rank
with Benjamin Harris, Margaret Lay, Lon H. Mitchell, Sivaram K. Narayan, and Amanda Pascoe
(in Linear Algebra and its Applications)

On the minimum rank among positive semidefinite matrices with a given graph
with Matthew Booth, Benjamin Harris, Charles R. Johnson, Margaret Lay, Lon H. Mitchell, Sivaram K. Narayan, Amanda Pascoe, Kelly Steinmetz, Brian D. Sutton, and Wendy Wang
(in SIAM Journal on Matrix Analysis and Applications)

Knots

k-alternating knots
with Leonard Van Wyk and Nathan Walters
(in Topology and its Applications)