About me
I am a mathematician, currently a Hakubi Fellow (Associate Professor) at Kyoto University.
My CV is available here.
Some of the talks I gave recently:
- at the Newton Institute on the monochromatic Hahn-Wilson conjecture,
- at the Abel Symposium on unstable synthetic deformations,
Notes
p-adic analytic groups - Harvard Math 291Y, Fall 2023
Finite height chromatic homotopy theory - Harvard Math 252Y, Spring 2021
Papers
14. Adams spectral sequences and Franke's algebraicity conjecture. Joint with Irakli Patchkoria.
(To appear in Memoirs of the American Mathematical Society)13. Quivers and the Adams spectral sequence. Joint with Robert Burklund.
(To appear in Advances in Mathematics)12. Perfect even modules and the even filtration.
(To appear in the Journal of European Mathematical Society)11. Dirac geometry II: Coherent cohomology. Joint with Lars Hesselholt.
(Forum of Mathematics, Sigma, vol. 12, Feb. 2024)10. The Intrinsic Normal Cone for Artin Stacks. Joint with Dhyan Aranha.
(Annales de l'Institut Fourier, Volume 74, 2024, no. 1)9. Morava K-theory and Filtrations by Powers. Joint with Tobias Barthel.
(Journal of the Institute of Mathematics of Jussieu, 2023, 1–77)8. Dirac Geometry I: Commutative Algebra. Joint with Lars Hesselholt.
(Peking Mathematical Journal, 2023, 1-76)7. Moduli of spaces with prescribed homotopy groups.
(Journal of Pure and Applied Algebra, Volume 227, Issue 10, 2023)6. Synthetic spectra and the cellular motivic category.
(Inventiones mathematicae, 232, 553–681, 2023)5. Chromatic Picard groups at large primes.
(Proceedings of the American Mathematical Society, 150, 2022, 4981-4988)4. Adams-type maps are not stable under composition. Joint with Robert Burklund and Ishan Levy.
(Proceedings of the American Mathematical Society, Ser. B Vol. 9, 2022, 373-376)3. On dualizable objects in monoidal bicategories.
(Theory and Applications of Categories, Vol. 38, No. 9, 2022)2. Abstract Goerss-Hopkins theory. Joint with Paul Vankoughnett.
(Advances in Mathematics, Volume 395, 2022, 108098, ISSN 0001-8708)1. Chromatic homotopy is algebraic when p > n2+n+1.
(Advances in Mathematics, Volume 391, 2021, 107958, ISSN 0001-8708)
Preprints
A note on weight filtrations at the characteristic (arXiv:2502.19626) - In this joint work with Toni Annala, we show that logarithmic variants of (p-adic) cohomology theories admit a canonical weight filtration on resolvable motives, for example on the motive associated to a projective relative strict normal crossing divisor pair. Importantly, the produced filtrations are invariants of the open part of the log scheme, thus providing new, computable invariants of smooth schemes admitting a good compactification.
The monochromatic Hahn-Wilson conjecture (arXiv:2410.08029) - In this joint work with David Lee, we prove the K(n)-local analogue of the Hahn-Wilson conjecture on fp-spectra, which states that the truncated Brown-Peterson spectra generate the category of fp-spectra as a thick subcategory. As a corollary, we deduce the original conjecture at height 1. Along the way, we prove the existence of K(n)-local finite complexes with particularly regular rings of homotopy groups.
Spectral weight filtrations (arXiv:2309.15072) - In this joint work with Peter Haine, we provide a description of Voevodsky's ∞-category of motivic spectra in terms of the subcategory of motives of smooth proper varieties. As applications, we construct weight filtrations on the Betti and étale cohomologies of algebraic varieties with coefficients in any complex oriented ring spectrum. We show that these filtrations satisfy ldh-descent, giving an effective way of calculating them in positive characteristic. In the complex motivic case, we further refine the weight filtration to one defined at the level of stable homotopy types.
On dualizable objects in monoidal bicategories, framed surfaces and the Cobordism Hypothesis (arXiv:1411.6691) - We prove coherence theorems related to dualizability in symmetric monoidal bicategories, classify two-dimensional framed topological field theories and give a new proof of the Cobordism Hypothesis in dimension two. The first part of the paper was already published, see above.
Non-mathematical interests
I love spending time with my dogs, though unfortunately, they live in Poland. Here's a picture of one of them, Ida.
© 2025 Piotr Pstrągowski