Research papers.
- Categorifying rationalization (with Saul Glasman, Marc Hoyois, Denis Nardin, and Jay Shah).
![[ PDF ]](img/PDFlogo-med.png)
- Publication information.
- Submitted for publication (11 pages).
- arXiv reference.
- arXiv:1610.07162
- Parametrized higher category theory and higher algebra (with Emanuele Dotto, Saul Glasman, Denis Nardin, and Jay Shah)
- Fibrations in ∞-category theory (with Jay Shah).
- Publication information.
- Expository note (18 pages).
- arXiv reference.
- arXiv:1607.04343
- On the fibrewise effective Burnside ∞-category (with Saul Glasman).
- Publication information.
- Étude (10 pages).
- arXiv reference.
- arXiv:1607.02786
- A note on stable recollements (with Saul Glasman).
- Publication information.
- Étude (4 pages).
- arXiv reference.
- arXiv:1607.02064
- Cyclonic spectra, cyclotomic spectra, and a conjecture of Kaledin (with Saul Glasman).
- Publication information.
- Submitted for publication (27 pages).
- arXiv reference.
- arXiv:1602.02163
- Spectral Mackey functors and equivariant algebraic K-theory (II) (with Saul Glasman and Jay Shah).
- Publication information.
- Submitted for publication (37 pages).
- arXiv reference.
- arXiv:1505.03098
- Dualizing cartesian and cocartesian fibrations (with Saul Glasman and Denis Nardin).
- Publication information.
- To appear in Theory and Applications of Categories (20 pages).
- arXiv reference.
- arXiv:1409.2165
- Spectral Mackey functors and equivariant algebraic K-theory (I).
- Publication information.
- Advances in mathematics, vol. 304 (2017), no. 2, pp. 646-727.
- arXiv reference.
- arXiv:1404.0108
- Regularity of structured ring spectra and localization in K-theory (with Tyler Lawson).
- Publication information.
- Submitted for publication (9 pages).
- arXiv reference.
- arXiv:1402.6038
- Multiplicative structures on algebraic K-theory.
- Publication information.
- Documenta Mathematica 20 (2015) 859-878.
- arXiv reference.
- arXiv:1304.4867
- From operator categories to topological operads.
- Publication information.
- Submitted for publication (49 pages).
- arXiv reference.
- arXiv:1302.5756
- On the Q construction for exact ∞-categories (with John Rognes).
- Publication information.
- Preprint (22 pages).
- arXiv reference.
- arXiv:1301.4725
- On exact ∞-categories and the Theorem of the Heart.
- Publication information.
- Compositio Mathematica, vol. 151, no. 11 (Nov. 2015), pp. 2160–2186. DOI: 10.1112/S0010437X15007447
- arXiv reference.
- arXiv:1212.5232
- Quillen theorems Bn for homotopy pullbacks of (∞, k)-categories (with Dan Kan).
- Publication information.
- To appear in Homology, Homotopy, and Applications (28 pages).
- arXiv references.
- arXiv:1101.4879
- arXiv:1208.1777
- On the algebraic K-theory of higher categories.
- Publication information.
- Journal of Topology, vol. 9 (2016), pp. 245--347. DOI: 10.1112/jtopol/jtv042
- arXiv reference.
- arXiv:1204.3607
- On the unicity of the homotopy theory of higher categories (with Chris Schommer-Pries).
- Publication information.
- Submitted for publication (41 pages).
- arXiv reference.
- arXiv:1112.0040
- From partial model categories to ∞-categories (with Dan Kan).
- Publication information.
- Submitted for publication (17 pages).
- arXiv references.
- arXiv:1102.2512
- arXiv:1101.4879
- n-relative categories: A model for the homotopy theory of n-fold homotopy theories (with Dan Kan).
- Publication information.
- Homotopy, Homology, and Applications, vol. 15 (2013), no. 2, pp. 281--300. (HHA244)
- arXiv reference.
- arXiv:1102.0186
- A characterization of simplicial localization functors and a discussion of DK equivalences (with Dan Kan).
- Publication information.
- Indagationes Mathematicae 23 (2012), pp. 69-79. DOI: 10.1016/j.indag.2011.10.001
- arXiv references.
- arXiv:1012.1540
- arXiv:1012.1541
- Relative categories: Another model for the homotopy theory of homotopy theories (with Dan Kan).
- Publication information.
- Indagationes Mathematicae 23 (2012), pp. 42-68. DOI: 10.1016/j.indag.2011.10.002
- arXiv references.
- arXiv:1101.0772
- arXiv:1011.1691
- On left and right model categories and left and right Bousfield localizations.
- Publication information.
- Homology, Homotopy and Applications, vol. 12 (2010), no. 2, pp. 245-320. (HHA152)
- arXiv references.
- arXiv:0708.2067
- arXiv:0708.2832
- arXiv:0708.3435
Teaching materials.
Spring 2016. 18.06. Linear algebra.
Spring 2015. 18.917. Hurewicz maps for algebraic K-theory.
Spring 2014. 18.904. Seminar in topology.
Spring 2014. 18.024. Calculus with theory II.
Autumn 2013. 18.014. Calculus with theory I.
Autumn 2012. 18.915. Seminar in topology.
Autumn 2012. 18.917. Algebraic K-theory of higher categories.
Spring 2012. 18.024. Calculus with theory II.
Autumn 2011. 18.014. Calculus with theory I.
Spring 2011. 18.100C. Analysis I.
Autumn 2010. 18.02. Multivariable calculus (recitations).
Advising notes.
Undergraduate course 18 majors.
Undergraduate research opportunity program (UROP) advisees.
Current and former UROP advisees.
Papers.
- Katerina Velcheva. "Generalized edgewise subdivisions." arXiv:1404.3416
Online resources.
Graduate student advisees.
Current and former thesis advisees.
Papers.
- Saul Glasman. "A note on commutative algebras and their modules in quasicategories." arXiv:1409.3506
- Clark Barwick, Saul Glasman, and Denis Nardin. "Dualizing cartesian and cocartesian fibrations." arXiv:1409.2165
- Saul Glasman. "A spectrum-level Hodge filtration on topological Hochschild homology." arXiv:1408.3065
- Saul Glasman. "Day convolution for ∞-categories." arXiv:1308.4940
Online resources.
Postdoctoral researchers.
Current and former postdoctoral advisees.
Schedule and appointments.
![[ PDF ]](img/PDFlogo.png)
A general introduction.