Publications
Infinity Properads and Infinity Wheeled Properads
with Marcy Robertson and Donald Yau
Lecture Notes in Mathematics 2147
arxiv:1410.6716 [math.AT]
Preprints
Coskeletality and the higher Segal conditions (preprint)
arxiv:2607.24476 [math.AT]
On partial groups of small order (preprint)
arxiv:2605.26199 [math.GR], dataset, code
Embeddable partial groups (preprint)
with Justin Lynd and Edoardo Salati
arxiv:2601.19772 [math.GR]
Higher Segal spaces and partial groups (preprint)
with Justin Lynd
arxiv:2507.05437 [math.GR]
Models for cyclic infinity operads (preprint)
with Brandon Doherty
arxiv:2506.15622 [math.AT]
Operadic categories and 2-Segal sets (preprint)
arxiv:2312.00756 [math.CT]
Accepted / In Press
Binary partial groups (preprint)
with Justin Lynd and Edoardo Salati
(to appear in Archiv der Mathematik)
arxiv:2603.03167 [math.GR]
Published
The decomposition space perspective
(in Higher Segal Spaces and Applications, Contemporary Mathematics 838)
arxiv:2409.19061 [math.AT]
Culf maps and edgewise subdivision
with Joachim Kock; appendix also with Jan Steinebrunner
(in Transactions of the American Mathematical Society)
arxiv:2210.11191 [math.AT]
Dimension and partial groups
with Rémi Molinier
(in Proceedings of the American Mathematical Society)
arxiv:2406.19854 [math.GR], hal-04630052
Higher Segal spaces and partial groups (extended abstract)
(in Oberwolfach Reports)
doi:10.14760/OWR-2024-39
Partial groups as symmetric simplicial sets
with Justin Lynd
(in Journal of Pure and Applied Algebra)
arxiv:2310.01513 [math.GR]
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)
Conferences
Organized
- Future Directions in Higher Structures, August 2026 at the University of Melbourne and MATRIX. Organized with Marcy Robertson.
- International Category Theory Conference CT2026, July 2026 at Johns Hopkins University. Member of organizing committee, along with Nick Gurski, Angélica Osorno, Emily Riehl, and Maru Sarazola.
- Special Session on Homotopy Theory and Category Theory in Interaction, AMS Spring Southeastern Sectional Meeting at Florida State University, March 2024. Organized with Ettore Aldrovandi and Brandon Doherty.
- Lloyd Roeling Conference in Algebraic Topology at UL Lafayette, March 2024. Organized with Daniel Davis and Robin Koytcheff.
- Operad Pop-Up, August 2020. Organized with Geoffroy Horel and Marcy Robertson.
- Topology in Australia and South Korea, April 2018 Pohang. Organized with Gabriel C. Drummond-Cole and Marcy Robertson.
- Special session on Category Theory, Algebraic Topology, K-Theory at the 61st Annual Meeting of the Australian Mathematical Society December 2017.
- Topology in Australia and South Korea May 2017 Melbourne. Organized with Vigleik Angeltveit, Gabriel C. Drummond-Cole, and Marcy Robertson.
- Higher structures in geometry and physics June 2016 at MATRIX. Organized with Marcy Robertson.
- Special Session on Homotopy Theory and Commutative Algebra At the Joint Math Meetings in January 2013, San Diego. Organized with Julie Bergner and Inês Henriques.
- Co-organized several talks on Bousfield Localization at the West Coast Algebraic Topology Summer School August 2011 at the University of Washington, Seattle. (With Robert Hank, Donald Larson, Viraj Navkal, Luke Wolcott, and Enxin Wu)
Presented
- International Category Theory Conference CT2025 July 2025, Masaryk University, Brno
- The South Central Topology Conference IV March 2025, Texas A&M
- The Fourth International Conference on Operad Theory and Related Topics November 2024, Chern Institute of Mathematics, Nankai University
- Homotopical Algebra and Higher Structures August 2024, Oberwolfach
- Higher Segal Spaces and their Applications to Algebraic K-Theory, Hall Algebras, and Combinatorics January 2024, Banff International Research Station
- International Category Theory Conference CT2023 July 2023, UCLouvain, Louvain-la-Neuve
- Special Session on Higher Structures and Homotopical Algebra October 2022, AMS Fall Eastern Sectional Meeting, University of Massachusetts-Amherst
- Higher Structures in Prague September 2022, Institute of Mathematics of the Czech Academy of Sciences
- Special Session on Higher Structures in Topology, Geometry and Physics March 2022, AMS Spring Central Sectional Meeting, Purdue University (Online)
- Homotopical Algebra and Higher Structures, September 2021, Oberwolfach
- 64th Annual Meeting of the Australian Mathematical Society, December 2020, University of New England / Online
- The 3rd Conference on Operad Theory and Related Topics, September 2020, Jilin University / Online
Workshop on ∞-categories and their applications August 2020, Max Planck Institute for Mathematics, BonnSpecial Session on Higher Structures in Topology, Geometry and Physics April 2020, AMS Spring Central Sectional Meeting, Purdue University (Cancelled due to pandemic)- Special Session on Applied Category Theory November 2019, AMS Fall Sectional Meeting, University of California, Riverside
- Category Theory 2019, July 2019, Edinburgh, Scotland
- Workshop on Functor Calculus, March 2019, Ohio State University
- Special Session on Structured Homotopy Theory October 2018, AMS Central Sectional Meeting, University of Michigan
- Higher Structures Lisbon July 2017
- Infinity-Operads and Applications July 2017
- Interactions between operads and motives September 2016 Hausdorff Research Institute for Mathematics, Bonn
- Workshop: Higher structures June 2016
- Barcelona Topology Workshop November 2015
- ICM 2014 Satellite Conference on Algebraic Topology 2014/08/09 - 2014/08/12 Dalian Nationalities University, Dalian, China
- West Coast Algebraic Topology Summer School July 2016 at Stanford. I presented a sketch of the proof of Waldhausen’s splitting theorem.
- CMS Summer Meeting 2012/06/02 - 2012/06/04 Regina, Saskatchewan
- Special Session on Homotopy Theory and K-Theory 2010/10/09 - 2010/10/10 AMS Western Section Meeting, UCLA
- AMS-MAA-SIAM Special Session on Research in Mathematics by Undergraduates Joint Mathematics Meetings 2004/01/08 - 2004/01/09 Phoenix, Arizona
- Michigan Undergraduate Mathematics Conference October 2003
- Big Sky Discrete Mathematics Conference 2003/09/11 - 2003/09/13 University of Montana-Missoula
All conferences
Below is a mostly complete list of conferences, special sessions, and workshops that I’ve attended. It might be useful if you think you remember me from somewhere!
International Category Theory Conference CT2025 2025/07/13 – 2025/07/19 Masaryk University, Brno
The South Central Topology Conference IV 2025/03/08 – 2025/03/09 Texas A&M
The Fourth International Conference on Operad Theory and Related Topics 2024/11/03 – 2024/11/08 Chern Institute of Mathematics, Nankai University
Homotopical Algebra and Higher Structures 2024/08/25 - 2024/08/30 Oberwolfach
Topology of moduli spaces 2024/08/19 – 2024/08/23 University of Copenhagen
Gulf States Math Alliance 2024 Conference 2024/02/23 – 2024/02/25 Stephen F. Austin State University
Higher Segal Spaces and their Applications to Algebraic K-Theory, Hall Algebras, and Combinatorics 2024/01/21 – 2024/01/26 Banff International Research Station
International Category Theory Conference CT2023 2023/07/02 – 2023/07/08 UCLouvain
Special Session on Higher Structures and Homotopical Algebra 2022/10/01 - 2022/10/02 AMS Fall Eastern Sectional Meeting, University of Massachusetts-Amherst
Higher Structures in Prague 2022/09/12 - 2022/09/16 Institute of Mathematics of the Czech Academy of Sciences
Applied Category Theory 2022 2022/07/18 - 2022/07/22 University of Strathclyde / Online
Special Session on Higher Structures in Topology, Geometry and Physics 2022/03/26 - 2019/03/27 AMS Spring Central Sectional Meeting, Purdue University
paraDIGMS 2021 Fall Conference 2021/10/28 - 2021/10/31 IMSI / Online
Homotopical Algebra and Higher Structures 2021/09/19 - 2021/09/25 Oberwolfach
Applied Category Theory 2021 2021/07/12 - 2021/07/16 Cambridge / Online
paraDIGMS 2021 Spring Conference 2021/04/23 - 2021/04/26 IMSI / Online
Workshop on Polynomial Functors 2021/03/15 - 2021/03/19 Topos Institute / Online
Higher Homotopical Structures: Opening Workshop 2021/02/01 - 2021/02/12 Centre de Recerca Mathemàtica, Barcelona / Online
64th Annual Meeting of the Australian Mathematical Society 2020/12/08 - 2020/12/11 University of New England / Online
Workshop: Monoidal and 2-categories in representation theory and categorification 2020/11/30 - 2020/12/04 Hausdorff Center for Mathematics / Online
Virtual Workshop on Higher Topos Theory 2020/11/20 - 2020/11/21 Online
The 3rd Conference on Operad Theory and Related Topics 2020/09/18 - 2020/09/20 Jilin University / Online
Workshop on ∞-categories and their applications 2020/08/17 - 2020/08/21 Max Planck Institute for Mathematics, Bonn
Operad Pop-Up 2020/08/11 Online
Applied Category Theory 2020 2020/07/06 - 2020/07/10 Online
Higher Segal Spaces and their Applications to Algebraic K-Theory, Hall Algebras, and Combinatorics 2020/06/14 - 2020/06/19 Casa Matemática Oaxaca (Cancelled due to pandemic)
Special Session on Higher Structures in Topology, Geometry and Physics 2020/04/04 - 2019/04/05 AMS Spring Central Sectional Meeting, Purdue University (Cancelled due to pandemic)
(∞,n)-categories, factorization homology, and algebraic K-theory 2020/03/23 - 2020/03/27 MSRI
Tensor categories and topological quantum field theories 2020/03/16 - 2020/03/20 MSRI
Introductory Workshop: Higher Categories and Categorification 2020/02/10 - 2020/02/14 MSRI
Connections for Women: Higher Categories and Categorification 2020/02/06 - 2020/02/07 MSRI
Introductory Workshop: Quantum Symmetries 2020/01/27 - 2020/01/31 MSRI
Connections for Women: Quantum Symmetries 2020/01/23 - 2020/01/24 MSRI
Special Session on Applied Category Theory 2019/11/09 - 2019/11/10 AMS Fall Sectional Meeting, University of California, Riverside
Category Theory 2019 2019/07/07 - 2019/07/13 Edinburgh, Scotland
Workshop on Functor Calculus 2019/03/16 - 2019/03/17 Ohio State University
Special Session on Structured Homotopy Theory 2018/10/20 - 2018/10/21 AMS Central Sectional Meeting, University of Michigan
Topology in Australia and South Korea 2018/04/23 - 2018/04/27 IBS-CGP, Pohang, South Korea
Category Theory, Algebraic Topology, K-Theory at AustMS Meeting 2017/12/12 - 2017/12/15 Macquarie University, Sydney
Future Directions in Representation Theory 2017/12/04 - 2017/12/08 University of Sydney
Higher Structures Lisbon 2017/07/24 - 2017/07/27 Instituto Superior Técnico, Lisbon
Infinity-Operads and Applications 2017/07/12 - 2017/07/14 Osnabrück
Computational & Algorithmic Topology, Sydney 2017/06/27 - 2017/07/01 Sydney
Topology in Australia and South Korea 2017/05/01 - 2017/05/05 Melbourne
Higher geometric structures along the Lower Rhine VIII 2016/12/15 - 2016/12/16 MPIM Bonn
Hermitian K-theory and trace methods 2016/11/07 - 2016/11/11 Hausdorff Research Institute for Mathematics, Bonn
Configuration Spaces and Moduli Spaces in Homotopy Theory 2016/10/20 - 2016/10/21 Hausdorff Center for Mathematics, Bonn
Interactions between operads and motives 2016/09/14 - 2016/09/16 Hausdorff Research Institute for Mathematics, Bonn
Higher structures in geometry and physics 2016/06/06 - 2016/06/17 MATRIX Creswick, Victoria, Australia
Motives and derived algebraic geometry 2016/05/06 - 2016/05/08 Universität Duisburg-Essen
27th Nordic Congress of Mathematicians 2016/03/16 - 2016/03/20 Stockholm
Barcelona Topology Workshop 2015/11/27 - 2015/11/28 Barcelona
Nordic Topology Meeting 2015/08/27 - 2015/08/28 Stockholm
AWM Workshop on Homotopy Theory Joint Mathematics Meetings 2015/01/10 - 2015/01/13 San Antonio, TX
Nordic Topology Meeting 2014/11/27 - 2014/11/28 Norges teknisk-naturvitenskapelige universitet, Trondheim, Norway
Loop Spaces in Geometry and Topology 2014/09/01 - 2014/09/05 Centre de Mathématiques Henri Lebesgue, Nantes
ICM 2014 Satellite Conference on Algebraic Topology 2014/08/09 - 2014/08/12 Dalian Nationalities University, Dalian, China
Workshop on Algebraic Topology and Its Applications 2014/07/29 - 2014/08/08 Dalian University of Technology, Dalian, China
Homotopical Methods in Algebraic Geometry 2013/05/28 - 2013/06/01 University of Southern California
Special Session on Homotopy Theory and Commutative Algebra Joint Math Meetings 2013/01/10 - 2013/01/11 San Diego, CA
The legacy of Daniel Quillen: K-theory and homotopical algebra 2012/10/06 - 2012/10/08 MIT Cambridge, Massachusetts
Algebraic Topology: applications and new directions; Stanford Symposium 2012 2012/07/23 - 2012/07/27 Stanford University Palo Alto, CA
West Coast Algebraic Topology Summer School 2012/07/16 - 2012/07/16, Stanford
Virginia Conference on Algebraic Topology 2012/06/11 - 2012/06/15 Charlottesville, VA
CMS Summer Meeting 2012/06/02 - 2012/06/04 Regina, Saskatchewan
AMS Special Session on Homotopy Theory Joint Mathematics Meetings 2012/01/06 through 2012/01/07 Boston, MA
“Calculus of functors and its applications” AMS Special Session Joint Mathematics Meetings 2012/01/06 Boston, MA
West Coast Algebraic Topology Summer School 2011/08/26 - 2011/08/28 University of Washington, Seattle
NSF/CBMS Conference on Deformation Theory of Algebras and Modules 2011/05/16 - 2011/05/20 North Carolina State University
Special Session on Homotopy Theory and K-Theory 2010/10/09 - 2010/10/10 AMS Western Section Meeting, UCLA
West Coast Algebraic Topology Summer School: Homotopy theory of moduli spaces 2010/08/09 - 2010/08/14 University of Oregon
Midwest Topology Seminar 2010/04/24 Northwestern University
Graduate Student Topology and Geometry Conference 2010/04/10 - 2010/04/11 University of Michigan
Michigan Conference on Topology and Physics 2010/02/06 - 2010/02/07 University of Michigan
New Contexts in Homotopy Theory 2009/10/16 - 2009/10/18 University of Chicago
International Conference: Operads 2009/04/27 - 2009/04/30 CIRM Luminy, Marseille
Thematic School on Operads 2009/04/20 - 2009/04/25 CIRM Luminy, Marseille
Midwest Topology Seminar 2009/02/21 Purdue University
AMS Fall Central Section Meeting 2008/10/17 - 2008/10/19 Western Michigan University
Young Persons Workshop on String Topology and the Topology of Moduli Spaces 2008/03/24 - 2008/03/27 Mathematics Research Center, Stanford University
Midwest Topology Seminar 2008/02/23 University of Notre Dame
Midwest Topology Seminar 2007/10/13 University of Illinois at Urbana-Champaign
Midwest Topology Seminar 2007/04/28 - 2007/04/29 Wayne State University
Graduate Student Topology Conference 2007/04/21 - 2007/04/22 University of Chicago
Midwest Topology Seminar 2006/10/21 - 2006/10/22 Indiana University
Graduate Student Topology Conference 2006/04/01 - 2006/04/02 Indiana University
Midwest Geometry Conference 2005/04/29 - 2005/05/01 Ohio State University
AMS-MAA-SIAM Special Session on Research in Mathematics by Undergraduates Joint Mathematics Meetings 2004/01/08 - 2004/01/09 Phoenix, Arizona
Michigan Undergraduate Mathematics Conference 2003/10/25 Grand Valley State University
Big Sky Discrete Mathematics Conference 2003/09/11 - 2003/09/13 University of Montana-Missoula
Michigan Undergraduate Mathematics Conference 2003/02/15 University of Michigan-Dearborn