Infinity Properads and Infinity Wheeled Properads

with Marcy Robertson and Donald Yau

Lecture Notes in Mathematics 2147

arxiv:1410.6716 [math.AT]

## Preprints

The decomposition space perspective (preprint)

arxiv:2409.19061 [math.AT]

Dimension and partial groups (preprint)

with Rémi Molinier

arxiv:2406.19854 [math.GR], hal-04630052

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]

Culf maps and edgewise subdivision (preprint)

with Joachim Kock; appendix also with Jan Steinebrunner

arxiv:2210.11191 [math.AT]

## In Press

Higher Segal spaces and partial groups (extended abstract)

(to appear in Oberwolfach Reports)

## Published

Free decomposition spaces

with Joachim Kock

(in Collectanea Mathematica)

arxiv:2210.11192 [math.CT]

Pushouts of Dwyer maps are (∞,1)-categorical

with Viktoriya Ozornova, Emily Riehl, and Martina Rovelli

(in Algebraic & Geometric Topology)

arxiv:2205.02353 [math.AT]

Segal conditions for generalized operads

(in Higher Structures in Topology, Geometry, and Physics, Contemporary Mathematics 802)

arxiv:2208.13852 [math.CT]

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)