Mathematics

I am a doctor in mathematics since 27 February 2025.

My math-genealogy record.

My Academic CV (Nov 2024)

My PhD Thesis: Power Tower Theory:
Foliations and Galois Theory
in Positive Characteristic

My PhD thesis - with hyperlinks

My PhD thesis - with cover

I am a doctor in mathematics.

The PhD defence was on 27 February 2025 at 13:00
at Agnietenkapel in Amsterdam.

My Publications:

Foliations and Galois Theory in Positive Characteristic. (2023) (To be updated) Arxiv

My short lecture on YT: LINK.

(future) Abstract: The paper is about power towers. A power tower is an object analogous to a foliation, but in positive characteristic. They generalise fibrations. They include purely inseparable morphisms. We develop a Galois-type correspondence for power towers. This gives a useful framework for working with purely inseparable morphisms. In particular, we prove a formula for a pullback of a canonical divisor with respect to any such morphism.

Comment: The paper will contain the results from my PhD thesis.

Canonical Liftings of Calabi–Yau Hypersurfaces: Dwork Hypersurfaces. (2025) (Published) Arxiv

Abstract: We explicitly compute canonical liftings modulo p^2 in a sense of Achinger--Zdanowicz of Dwork hypersurfaces. The computation involves studying a compatibility between Hodge filtrations and a crystalline Frobenius. In particular, remarkably, we explicitly compute a partial data of the crystalline Frobenius modulo p^2.

Comment: This paper covers the results from my Master thesis. I defended it in September 2020.

Finite orthogonal groups and periodicity of links. (2020) (Published) Arxiv

Joint work with Maciej Borodzik, Adam Król, Maria Marchwicka.

Abstract: For a prime number q not equal 2 and r > 0

we study, whether there exists an isometry of order q^r

acting on a free Z^p^k-module equipped with a scalar product. We investigate, whether there exists such an isometry with no non-zero fixed points. Both questions are completely answered in this paper if p is not 2 and not q. As an application we refine Naik's criterion for periodicity of links in S^3. The periodicity criterion we obtain is effectively computable and gives concrete restrictions for periodicity of low-crossing knots.

Comment: My work that I did in Borodzik's grant (2017-2018) is a part of this paper.

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