Papers

• Wojciech Wawrów, On torsion of superelliptic Jacobians, Journal de Théorie des Nombres de Bordeaux, Tome 33 (2021) no. 1, pp. 223-235. Available online. arXiv version.

Dissertations

• Berkovich spaces, MSc dissertation, supervised by Dr Federico Bambozzi.

• Algebraic curves and Jacobian varieties, BSc dissertation, supervised by Prof. Wojciech Gajda.

Projects

• Syntomic cohomology and the Poznań spectral sequence, LSGNT miniproject, supervised by Sarah Zerbes.

• Fargues-Fontaine curve via symplectic geometry, LSGNT miniproject, joint with Wei Zhou, supervised by Yankı Lekili.

Notes

Those are various notes I have typeset. Many of them are likely to contain errors, all corrections will be appreciated.

• Condensed mathematics and analytic geometry, some notes based on Scholze's notes on condensed mathematics and analytic geometry. Originally meant as a write-up of a talk for a reading group on relative algebraic geometry, but since expanded to cover more topics.

• Shimura Varieties, notes prepared while reading J. Milne's notes on the topic. Cover basics of the general theory up to the definition of canonical models (but not their uniqueness or existence.) They might be expanded to cover other topics in the future.

• Higher ramification groups, an overview of some results regarding ramification groups of extensions of local fields. Based loosely on Anschütz's course.

• Sheafiness of adic spectra, a proof of sheafiness of adic spectra under usual conditions like stable uniformity. Based on proofs in Morel's and Wedhorn's notes.

• Class Field Theory, notes prepared while reading J. Milne's notes on the topic. Essentially a fully self-contained proof of global reciprocity, omitting sections from Milne's notes not necessary for this proof (I, IV, VI, most of VIII).

• Algebraic Geometry and Arithmetic Curves, notes prepared while reading Q. Liu's book with the same title. They miss some of the crucial definitions, but assuming familiarity with the definition of a scheme, they are reasonably complete up to chapter 6.

• The Class Field Tower Problem, notes prepared for a talk at the Oxford Junior Number Theory seminar,

• Quadratic Reciprocity via Algebraic Number Theory, notes for a talk I gave at 20th International Workshop for Young Mathematicians.

Notes from talks I gave to students or counsellors during PROMYS Europe or PROMYS Bridge programs.

• Perfectoid fields, counselor seminar, PROMYS Bridge 2020.

• Hilbert Class Field, counsellor talk, PROMYS Europe 2019.

• Impossibility of Geometric Constructions, student talk, PROMYS Europe 2019.

• Higher Reciprocity Laws, counsellor talk, PROMYS Europe 2018.

• Modular forms and their applications, counsellor talk, PROMYS Europe 2018.

• Computational complexity, student talk, PROMYS Europe 2018.

• Riemann Zeta Function, student talk, PROMYS Europe 2018.

• Distribution of Primes, counsellor talk during PROMYS Europe 2017.

• Ergodic approach to Szemeredi's theorem, counsellor seminar on additive combinatorics, PROMYS Europe 2017.

• Bertrand's postulate, student talk, PROMYS Europe 2017.

• Ultrafilters and Hindman's Theorem, student talk, PROMYS Europe 2016.

Notes from courses I took, some of them are incomplete due to missed lectures.

• Analytic number theory, taught by Prof. Jerzy Kaczorowski at AMU.

• C2.1 Lie Algebras, taught by Prof. Nikolay Nikolov at Oxford. Official course page

• C2.2 Homological Algebra, taught by Prof. Andre Henriques at Oxford. Official course page

• C2.4 Infinite Groups, taught by Prof. Cornelia Drutu at Oxford. Official course page

• C2.5 Non-Commutative Rings, taught by Prof. Nikolay Nikolov at Oxford. Official course page

• C2.6 Introduction to Schemes, taught by Prof. Alexander Ritter at Oxford. Official course page

• C3.2 Geometric Group Theory, taught by Prof. Cornelia Drutu at Oxford. Official course page

• C3.4 Algebraic Geometry, taught by Prof. Balazs Szendroi at Oxford. Official course page

Miscellaneous