Department of Mathematics, University of Chicago, 5734 S.
University Ave., Chicago, IL 60637-1514
amathew (at) math (dot) uchicago (dot) edu
: 326 Eckhart Hall
I am a Clay Research Fellow
at the University of Chicago.
is primarily in algebraic topology and its interactions with algebraic geometry
and algebraic K-theory.
Here is my
With Benjamin Antieau, Elden Elmanto, and Maria Yakerson, I am a co-organizer of the electronic algebraic K-theory seminar.
The Geometric Langlands seminar at UChicago, November 2020 (lecture series by Bhargav Bhatt).
Papers and preprints
- K-theory and polynomial functors,
with Clark Barwick, Saul Glasman, and
- Some recent advances in topological Hochschild homology.
- Descent and vanishing in chromatic algebraic K-theory via group actions, with Dustin Clausen, Justin Noel, and Niko Naumann.
- Purity in chromatically localized K-theory, with Markus Land, Lennart Meier, and Georg Tamme.
- On K(1)-local TR.
To appear in Compositio Mathematica.
- On the Beilinson fiber square, with Benjamin Antieau, Matthew Morrow, and Thomas Nikolaus.
- Remarks on K(1)-local K-theory, with Bhargav Bhatt and Dustin Clausen. Selecta Mathematica. (N.S.) 26 (2020), no. 3, Paper No. 39, 16pp.
- Faithfully flat descent of almost perfect complexes in rigid geometry.
- Counterexamples to Hochschild-Kostant-Rosenberg in characteristic p, with Benjamin Antieau and Bhargav Bhatt. To appear in Forum of Mathematics, Sigma.
- Hyperdescent and étale K-theory, with Dustin Clausen. To appear in Inventiones Mathematicae.
- Deformation theory and partition Lie algebras, with Lukas Brantner.
- The arc-topology, with Bhargav Bhatt. To appear in Duke.
- Revisiting the de Rham-Witt complex, with Bhargav Bhatt and Jacob Lurie. To appear in Astérisque.
- K-theory and topological cyclic
homology of henselian pairs, with Dustin
Clausen and Matthew
J. Amer. Math. Soc. 34 (2021), 411--473.
- Kaledin's degeneration theorem and topological Hochschild homology. Geom. Topol. 24 (2020), no. 6, 2675--2708.
- On the Blumberg-Mandell Künneth theorem for TP, with Benjamin Antieau and Thomas Nikolaus. Selecta Mathematica N.S. 24 (2018), no. 5, 4555--4576.
- Monadicity of the Bousfield-Kuhn
functor, with Rosona Eldred, Gijs Heuts, and Lennart Meier.
Proc. Amer. Math. Soc. 147 (2019), no. 4, 1789--1796.
- Examples of descent up to nilpotence.
Geometric and topological aspects of the representation theory of finite groups, 269--311, Springer Proc. Math. Stat., 242, Springer, Cham, 2018.
A short proof of telescopic Tate vanishing, with Dustin Clausen. Proc. Amer. Math. Soc. 145 (2017), no. 12, 5413--5417.
Descent in algebraic K-theory and a conjecture of Ausoni-Rognes, with Dustin Clausen,
Niko Naumann and Justin Noel. J. Eur. Math. Soc. (JEMS) 22 (2020), no.4, 1149--1200.
Torus actions on stable module categories, Picard groups, and localizing subcategories (last updated Dec. 2015).
Picard groups of higher real K-theory
spectra at height p-1, with Drew
Heard and Vesna Stojanoska. Compos. Math. 153 (2017), no. 9, 1820--1854.
Derived induction and restriction theory, with Niko Naumann and Justin Noel.
Geom. Topol. 23 (2019), no. 2, 541--636.
Nilpotence and descent in equivariant stable homotopy theory, with Niko Naumann and Justin Noel.
Adv. Math. 305 (2017), 994--1084.
THH and base-change for Galois extensions of ring spectra.
Algebr. Geom. Topol. 17 (2017), no. 2, 693--704.
Residue fields for a class of
rational E_\infty-rings and applications.
J. Pure Appl. Algebra 221 (2017), no. 3., 707--748.
The Picard group of topological modular forms via descent theory, with Vesna Stojanoska. Geom. Topol. 20 (2016), no. 6, 3133--3217.
Torsion exponents in stable homotopy and the Hurewicz homomorphism.
Algebr. Geom. Topol. 16 (2016), no. 2, 1025--1041.
The homology of tmf. Homology Homotopy Appl. 18 (2016), no. 2., 1--29.
The Galois group of a stable homotopy
theory. Adv. Math. 291 (2016), 403-541.
Fibers of partial totalizations of a
pointed cosimplicial space, with Vesna Stojanoska.
Proc. Amer. Math. Soc. 144 (2016), no. 1, 445--458.
On a nilpotence conjecture of J.P. May, with Niko Naumann and Justin Noel. J. Topol. 8 (2015), no. 4, 917-932.
A thick subcategory theorem for modules over certain ring spectra. Geom. Topol. 19 (2015), no. 4., 2359-2392.
Affineness and chromatic homotopy theory, with Lennart Meier. J. Topol. 8 (2015), no. 2, 476-528.
Note: There is a small mistake in the published version in the results on Tmf with level structures. This is corrected in the arXiv version (last updated June 2016).
Categories parametrized by schemes and representation theory in complex
rank. J. Algebra 381 (2013), 140-163.