Postal address: Department of Mathematics, University of Chicago, 5734 S.
University Ave., Chicago, IL 60637-1514
Email address: amathew (at) math (dot) uchicago (dot) edu
Office: 326 Eckhart Hall
Teaching: This fall quarter, I am teaching a topics course on perfectoid spaces. Here is the course webpage.
I am a Clay Research Fellow
at the University of Chicago. For fall 2018 I am also a visiting assistant professor here, and in spring 2019 I will be based at MSRI.
is primarily in algebraic topology and its interactions with algebraic geometry
and algebraic K-theory.
I completed my PhD in mathematics in May 2017 at
Harvard University, where my advisor was Jacob Lurie.
From May-August 2015 and October-November 2016, I was a guest at the Hausdorff Institute of Mathematics in Bonn.
For the 2014-2015 academic year, I was a graduate student at the University of California at Berkeley.
Here is my
Papers and preprints
- The arc-topology, with Bhargav Bhatt (last updated August 2018).
- Revisiting the de Rham-Witt complex, with Bhargav Bhatt and Jacob Lurie (last updated September 2018).
- K-theory and topological cyclic
homology of henselian pairs, with Dustin
Clausen and Matthew
Morrow (last updated March 2018).
- Kaledin's degeneration theorem and topological Hochschild homology (last updated
- On the Blumberg-Mandell Künneth theorem for TP, with Benjamin Antieau and Thomas Nikolaus (last updated
July 2018). To appear in Selecta Mathematica New Series.
- Monadicity of the Bousfield-Kuhn
functor, with Rosona Eldred, Gijs Heuts, and Lennart Meier (last updated
July 2017). To appear in Proceedings of the AMS.
- Examples of descent up to nilpotence (last updated Dec. 2016). To appear in Geometric and Topological Aspects of the Representation Theory of Finite Groups, proceedings for a conference in honor of Dave Benson.
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 (last updated November 2017). To appear in Journal of the European Mathematical Society.
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
(last updated Sep. 2018). To appear in Geometry and Topology.
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.