Research & academic service

Courses

• Spr 2026MATH 201Linear Algebra
• Spr 2026MATH 332Abstract Algebra
• Fall 2025MATH 113Discrete Structures
• Spr 2025MATH 112Intro to Analysis
• Spr 2025MATH 113Discrete Structures
• Fall 2024MATH 201Linear Algebra
• Fall 2024MATH 412Topics in Algebra: Galois Theory

• Spr 2024MATH 113Discrete Structures
• Spr 2023MATH 113Discrete Structures
• Spr 2023MATH 342Topology
• Fall 2022MATH 113Discrete Structures
• Spr 2022MATH 201Linear Algebra
• Spr 2022MATH 442Algebraic Topology
• Fall 2021MATH 201Linear Algebra
• Spr 2020MATH 201Linear Algebra
• Spr 2019MATH 201Linear Algebra
• Fall 2018MATH 113Discrete Structures
• Fall 2018MATH 341Topics in Geometry
• Spr 2018MATH 201Linear Algebra
• Spr 2018MATH 342Topology
• Fall 2017MATH 201Linear Algebra
• Fall 2017MATH 412Topics in Algebra: Representation Theory
• Spr 2016MATH 212Multivariable Calculus II
• Fall 2015MATH 211Multivariable Calculus I
• Fall 2015MATH 331Linear Algebra
• Spr 2015MATH 112Intro to Analysis
• Spr 2015MATH 342Topology
• Fall 2014MATH 111Calculus
• Fall 2014MATH 211Multivariable Calculus I
• Fall 2013MATH 111Calculus

Papers

Preprints

• A comparison of definitions of equivariant trees
  with Julia E. Bergner, Maxine E. Calle, David Chan, and Maru Sarazola
  PDF
• Characterizing model structures on finite posets
  with Kristen Mazur, Constanze Roitzheim, Rekha Santhanam, Danika Van Niel, and Valentina Zapata Castro
  PDF
• Realizing compatible pairs of transfer systems by combinatorial N_∞-operads
  with David Chan, Myungsin Cho, David Mehrle, Pablo S. Ocal, Ben Szczesny, and Paula Verdugo
  PDF
• Enumerating submonoids of finite commutative monoids
  with Caoilainn Kirkpatrick, Amelie el Mahmoud, Kyle Ormsby, Dale Schandelmeier-Lynch, Riley Shahar, Lixing Yi, Avery Young, and Saron Zhu
  PDF

Research publications

• Uniquely compatible transfer systems for cyclic groups of order p^rq^s
  with Kristen Mazur, Constanze Roitzheim, Rekha Santhanam, Danika Van Niel, and Valentina Zapata Castro
  Topology Appl. 376 (2025), Paper No. 109443, 21 pp.
  PDF
• Equivariant infinite loop space theory, I. The space level story
  with J. Peter May and Mona Merling
  Mem. Amer. Math. Soc. 305 (2025), no. 1540
  PDF
• The symmetric monoidal 2-category of permutative categories
  with Nick Gurski and Niles Johnson
  High. Struct. 8, no. 1, 244–320, 2024
  PDF
• Model structures on finite total orders
  with Scott Balchin, Kyle Ormsby, and Constanze Roitzheim
  Math. Z. 304, no. 3, Paper No. 40, 35 pp., 2023
  PDF
• Multiplicative equivariant K-theory and the Barratt–Priddy–Quillen theorem
  with Bert Guillou, J. Peter May, and Mona Merling
  Adv. Math. 414, Paper No. 108865, 111 pp., 2023
  PDF
• Saturated and linear isometric transfer systems for cyclic groups of order p^mqⁿ
  with Usman Hafeez, Peter Marcus, and Kyle Ormsby
  Topology Appl. 317, Paper No. 108162, 20 pp., 2022
  PDF
• Self-duality of the lattice of transfer systems via weak factorization systems
  with Evan Franchere, Kyle Ormsby, Weihang Qin, and Riley Waugh
  Homology Homotopy Appl. 24, no. 2, 115–134, 2022
  PDF
• 2-categorical opfibrations, Quillen's Theorem B, and S^-1S
  with Nick Gurski and Niles Johnson
  New York J. Math. 27, 1009–1059, 2021
  PDF
• Biased permutative equivariant categories
  with Kayleigh Bangs, Skye Binegar, Young Kim, Kyle Ormsby, David Tamas-Parris, and Livia Xu
  Homology Homotopy Appl. 23, no. 1, 77–100, 2021
  PDF
• Comparison of Waldhausen constructions
  with Julia E. Bergner, Viktoriya Ozornova, Martina Rovelli, and Claudia Scheimbauer
  Ann. K-Theory 6, no. 1, 97–136, 2021
  PDF
• A multiplicative comparison of Waldhausen and Segal K-theory
  with Anna Marie Bohmann
  Math. Z. 295, no. 3-4, 1205–1243, 2020
  PDF
• 2-Segal objects and the Waldhausen construction
  with Julia E. Bergner, Viktoriya Ozornova, Martina Rovelli, and Claudia Scheimbauer
  Algebr. Geom. Topol. 21, no. 3, 1267–1326, 2021
  PDF
• Symmetric monoidal G-categories and their strictification
  with Bert Guillou, J. Peter May, and Mona Merling
  Q. J. Math. 71, no. 1, 207–246, 2020
  PDF
• The edgewise subdivision criterion for 2-Segal objects
  with Julia E. Bergner, Viktoriya Ozornova, Martina Rovelli, and Claudia Scheimbauer
  Proc. Amer. Math. Soc. 148, no. 1, 71–82, 2020
  PDF
• The 2-dimensional stable homotopy hypothesis
  with Nick Gurski and Niles Johnson
  J. Pure Appl. Algebra 223(10):4348–4383, 2019
  PDF
• A symmetric monoidal and equivariant Segal infinite loop space machine
  with Bert Guillou, J. Peter May, and Mona Merling
  J. Pure Appl. Algebra 223(6):2425–2454, 2019
  PDF
• 2-Segal sets and the Waldhausen construction
  with Julia E. Bergner, Viktoriya Ozornova, Martina Rovelli, and Claudia Scheimbauer
  Topology Appl. 235, 445–484, 2018
  PDF
• Stable Postnikov data of Picard 2-categories
  with Nick Gurski, Niles Johnson, and Marc Stephan
  Algebr. Geom. Topol. no. 5, 2763–2806, 2017
  PDF
• Extending homotopy theories across adjunctions
  with Nick Gurski and Niles Johnson
  Homology Homotopy Appl. 19, no. 2, 89–110, 2017
  PDF
• K-theory for 2-categories
  with Nick Gurski and Niles Johnson
  Adv. Math. 322: 378–472, 2017
  PDF
• Constructing equivariant spectra via categorical Mackey functors
  with Anna Marie Bohmann
  Algebr. Geom. Topol. 15(1):537–563, 2015
  PDF
• A model structure on GCat
  with Anna Marie Bohmann, Kristen Mazur, Viktoriya Ozornova, Kate Ponto, and Carolyn Yarnall
  Women in Topology: Collaborations in Homotopy Theory, Contemp. Math. 641, 123–134, 2015
  PDF
• Infinite loop spaces, and coherence for symmetric monoidal bicategories
  with Nick Gurski
  Adv. Math. 246:1–32, 2013
  PDF
• Modeling stable one-types
  with Niles Johnson
  Theory Appl. Categ. 26:520–537, 2012
  PDF
• Spectra associated to symmetric monoidal bicategories
  Algebr. Geom. Topol. 12(1):307–342, 2012
  PDF
• Explicit formulas for 2-characters
  Topology Appl. 157(2):369–377, 2010
  PDF

Other publications

• Homotopical Combinatorics
  joint with Andrew Blumberg, Mike Hill, Kyle Ormsby, and Constanze Roitzheim
  Notices of the AMS, Vol 71, No 2, 2024
  PDF
• Topological Invariants of Higher Categories
  joint with Nick Gurski and Niles Johnson
  Notices of the AMS, Vol 66, No 8, 2019
  PDF
• Invitación a la teoría de homotopía: Grupo fundamental y espacios recubridores
  Introduction to basic concepts in homotopy theory — in Spanish
  Lect. Mat. 39(1):29–48, 2018
  PDF
• Espacios de lazos infinitos
  Survey paper about infinite loop spaces — in Spanish
  Bol. Mat. 18(2):163–182, 2011
  PDF

Recorded talks

• Equivariant operads, multiplicative structures, and transfer systems
  eCHT, April 2025
• Equivariant operads, multiplicative structures, and transfer systems
  Operads and Calculus, INI Satellite event, Belfast, April 2025
• 2-categorical constructions and the equivariant Barratt–Priddy–Quillen theorem
  Chromatic Homotopy, K-theory and Functors, CIRM, January 2023
• 2-categorical opfibrations, Quillen's Theorem B, and S^-1S
  Higher Homotopical Structures Opening Workshop, CRM, February 2021
• Transfer Systems and Weak Factorization Systems
  Online Algebraic Topology Seminar, October 2020
• Operads, ¿cómo parametrizar operaciones de manera coherente?
  Cibercoloquio de Matemáticas, October 2020
• Equivariant infinite loop space machines
  IHES Summer School, July 2020
• Constructing equivariant spectra via categorical Mackey functors
  Banff Research Station, February 2016
• Modeling stable 2-types
  MSRI, April 2014

Graduate students

• Diego Manco

Frequent collaborators

Conference organizing

• Co-organizing the 2° Encuentro Colombiano de Geometría y Topología, Universidad del Valle, August 2026.
• Co-organizing the International Category Theory Conference, Johns Hopkins University, July 2026.
• Co-organized a Mathematical Research Community (MRC) on Homotopical Combinatorics, July 2024.
• Co-organized the fourth edition of the Women in Topology Workshop, Hausdorff Institute, Bonn, August 2023.
• Co-organized the third edition of the Women in Topology Workshop, Hausdorff Institute, Bonn, August 2019.
• Co-organized the 62nd Cascade Topology Seminar at PSU, May 11–12, 2019.
• Administrator for the mailing list of the Cascade Topology Seminar. Email me to be added.
• Reed College hosted the Underrepresented Students in Topology and Algebra Research Symposium (USTARS) in April 2018.
• Co-organized Homotopy Theory in the Ecliptic: Chromatic, Equivariant, and Motivic Mathematics, on the occasion of Doug Ravenel's 70th birthday, Reed College, August 18–21, 2017.
• Chair of the scientific committee for the Topology Ecuador 2017 Conference, Galápagos Islands, Ecuador, August 14–18, 2017.
• Organized, with Kyle Ormsby, the conference on Equivariant and Motivic Homotopy Theory, Reed College, May 30–31, 2015.

CV & departments

• Reed College Mathematics & Statistics Department
• University of Chicago Math Department
• MIT Math Department