PhD thesis

Synthetic modular forms | DOI | local PDF
Defended on 11 November 2025.

My thesis consists of (the first version of) my expository paper [5] on filtered and synthetic spectra, together with modified versions of the two papers [2, 3] joint with Carrick and Davies linked below.

Papers

Entries appear in reverse chronological order of first appearance.

[5] Introduction to filtered and synthetic spectra | arXiv | local PDF

Expository paper; based on first part of my PhD thesis.
26 September 2025. Preprint.

[4] Cellularity of chromatic synthetic spectra | arXiv | local PDF

Joint with Shaul Barkan.
2 May 2025. Preprint.

[3] The descent spectral sequence for topological modular forms | arXiv | local PDF

Joint with Christian Carrick and Jack Davies.
2 December 2024. Preprint, submitted.

Talk by me.

[2] Descent spectral sequences through synthetic spectra | DOI | arXiv | local PDF

Joint with Christian Carrick and Jack Davies.
International Mathematics Research Notices (IMRN), 15 (2025).
Published 24 July 2025.

[1] The K-theory cochains of H-spaces and height 1 chromatic homotopy theory | arXiv | local PDF

With a joint appendix with Max Blans.
Last updated 4 March 2025.
To appear in Algebraic & Geometric Topology (AGT).

[0] Topological phases and K-theory | local PDF

Bachelor’s thesis.
6 July 2019.