Akhil Mathew
Associate Professor
Department of Mathematics,
University of Chicago
5734 S.
University Ave., Chicago, IL 606371514
Email: amathew (at) math (dot) uchicago (dot) edu
Office: 326 Eckhart Hall
Research interests: homotopy theory and arithmetic geometry
Curriculum Vitae
Editorial work: Compositio
Mathematica, International Mathematics
Research Notices, Journal of
Topology, Nagoya
Mathematical Journal.
IHES summer school
Recent Advances in
Algebraic Ktheory, July 2023.
Teaching
Papers and preprints
 The mod p RiemannHilbert correspondence and the perfect site.
To appear in Tunisian J. Math.
 The Ktheory of perfectoid rings, with Benjamin Antieau and Matthew Morrow.
To appear in Documenta Math.
 Syntomic complexes and padic
étale Tate twists, with Bhargav Bhatt.
Forum Math. Pi 11 (2023), E1.
 Ktheory and polynomial functors,
with Clark Barwick, Saul Glasman, and
Thomas Nikolaus.
 Some recent advances in topological Hochschild homology.
Bull. Lond. Math. Soc. 54 (2022), no. 1, 144.
 Descent and vanishing in chromatic algebraic Ktheory via group actions, with Dustin Clausen, Justin Noel, and Niko Naumann. To appear in Annales Sciéntifiques de l'École Normale Supérieure.
 Purity in chromatically localized Ktheory, with Markus Land, Lennart Meier, and Georg Tamme.
 On K(1)local TR.
Compos. Math. 157 (2021), no. 5, 10791119.
 On the Beilinson fiber square, with Benjamin Antieau, Matthew Morrow, and Thomas Nikolaus.
Duke Math J. 171 (2022), no. 18, 37073806.
 Remarks on K(1)local Ktheory, 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. J. Pure Appl. Algebra 226 (2022), no. 5, Paper No. 106938 .
 Counterexamples to HochschildKostantRosenberg in characteristic p, with Benjamin Antieau and Bhargav Bhatt. Forum Math. Sigma. 9 (2021), Paper No. e49, 26pp.
 Hyperdescent and étale Ktheory, with Dustin Clausen. Invent. Math. 225 (2021), no. 3, 9811076.
 Deformation theory and partition Lie algebras, with Lukas Brantner.
 The arctopology, with Bhargav Bhatt. Duke Math. J. 170 (2021), no. 9, 18991988.
 Revisiting the de RhamWitt complex, with Bhargav Bhatt and Jacob Lurie. Astérisque, No. 424, (2021).
 Ktheory and topological cyclic
homology of henselian pairs, with Dustin
Clausen and Matthew
Morrow.
J. Amer. Math. Soc. 34 (2021), 411473.
 Kaledin's degeneration theorem and topological Hochschild homology. Geom. Topol. 24 (2020), no. 6, 26752708.
 On the BlumbergMandell Künneth theorem for TP, with Benjamin Antieau and Thomas Nikolaus. Selecta Mathematica N.S. 24 (2018), no. 5, 45554576.
 Monadicity of the BousfieldKuhn
functor, with Rosona Eldred, Gijs Heuts, and Lennart Meier.
Proc. Amer. Math. Soc. 147 (2019), no. 4, 17891796.
 Examples of descent up to nilpotence.
Geometric and topological aspects of the representation theory of finite groups, 269311, 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, 54135417.

Descent in algebraic Ktheory and a conjecture of AusoniRognes, with Dustin Clausen,
Niko Naumann and Justin Noel. J. Eur. Math. Soc. (JEMS) 22 (2020), no.4, 11491200.

Torus actions on stable module categories, Picard groups, and localizing subcategories (last updated Dec. 2015).

Picard groups of higher real Ktheory
spectra at height p1, with Drew
Heard and Vesna Stojanoska. Compos. Math. 153 (2017), no. 9, 18201854.

Derived induction and restriction theory, with Niko Naumann and Justin Noel.
Geom. Topol. 23 (2019), no. 2, 541636.

Nilpotence and descent in equivariant stable homotopy theory, with Niko Naumann and Justin Noel.
Adv. Math. 305 (2017), 9941084.

THH and basechange for Galois extensions of ring spectra.
Algebr. Geom. Topol. 17 (2017), no. 2, 693704.

Residue fields for a class of
rational E_\inftyrings and applications.
J. Pure Appl. Algebra 221 (2017), no. 3., 707748.

The Picard group of topological modular forms via descent theory, with Vesna Stojanoska. Geom. Topol. 20 (2016), no. 6, 31333217.

Torsion exponents in stable homotopy and the Hurewicz homomorphism.
Algebr. Geom. Topol. 16 (2016), no. 2, 10251041.

The homology of tmf. Homology Homotopy Appl. 18 (2016), no. 2., 129.

The Galois group of a stable homotopy
theory. Adv. Math. 291(2016), 403541.

Fibers of partial totalizations of a
pointed cosimplicial space, with Vesna Stojanoska.
Proc. Amer. Math. Soc. 144 (2016), no. 1, 445458.

On a nilpotence conjecture of J.P. May, with Niko Naumann and Justin Noel. J. Topol. 8 (2015), no. 4, 917932.

A thick subcategory theorem for modules over certain ring spectra. Geom. Topol. 19 (2015), no. 4., 23592392.

Affineness and chromatic homotopy theory, with Lennart Meier. J. Topol. 8 (2015), no. 2, 476528.
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), 140163.
Talks
Other materials