Papers and preprints

1. Global Koszul duality (with A. Lazarev)
   Submitted.
   pdf | ArXiv
   Oberwolfach abstract
2. The derived deformation theory of a point
   Math. Z. 300 (2022), no. 3, 3023--3082, available online
   pdf | ArXiv | DOI
3. Singularity categories via the derived quotient
   Adv. Math. 381 (2021), 107631
   pdf | ArXiv | DOI
   Errata
4. The derived contraction algebra
   pdf | ArXiv | ERA
   This is my PhD thesis, and subsumes the previous two preprints.
5. The derived contraction algebra
   pdf | ArXiv
6. Noncommutative deformation theory, the derived quotient, and DG singularity categories
   pdf | ArXiv

In Preparation

• Nonsmooth Calabi-Yau structures for algebras and coalgebras (with J. Chuang and A. Lazarev)
• Mac Lane cohomology and square-zero extensions of abelian categories (with D. Kaledin and W. Lowen)
• Topological Hochschild cohomology for schemes (with D. Kaledin and W. Lowen)
• Reflexive DG categories in algebra and topology (with I. Goodbody and S. Opper)
• How to invert well-pointed endofunctors
• Untitled project on particle systems and representation theory (with K. Calvert, D. Fretwell, J. Jay and B. Lees)

Other writing

• An informal set of notes from the infinity categories seminar I ran in Lancaster - presented as is with no guarantee of correctness.
• A similar set of notes from the Lancaster singularity categories seminar.
• A "poster" I presented at Będlewo.
• A poster I took around a few conferences in summer 2017.
• A quick cheatsheet for dg objects.
• I wrote Chapter 5 of the lecture notes from the TFT Seminar. It's a nicer version of the notes from my talk.
• Differential graded algebras and applications, a report on DGAs written in collaboration with three other PhD students. I wrote Chapter Four and parts of Chapter One.