# writing

These are some of the things I have written over the past few years, all preprints are on the arXiv.

## Papers

### Published

- The point variety of quantum polynomial rings, joint with Kevin De Laet and Lieven Le Bruyn (arXiv:1509.07312),

published in*Journal of Algebra, volume 463, 10–22* - Embeddings of algebras in derived categories of surfaces, joint with Theo Raedschelders (arXiv:1501.04197),

published in*Proceedings of the American Mathematical Society, volume 145, number 7, 2757–2770* - Relative tensor triangular Chow groups for coherent algebras, joint with Sebastian Klein (arXiv:1607.03423)

published in Journal of Algebra, volume 487, 386–428

### Accepted for publication

- Constructing noncommutative surfaces with exceptional collections of length 4, joint with Dennis Presotto (arXiv:1705.06943), accepted for publication in Journal of the London Mathematical Society

### Preprints

- Derived categories of noncommutative quadrics and Hilbert schemes, joint with Theo Raedschelders (arXiv:1605.02795)
- Hochschild cohomology of noncommutative planes and quadrics (arXiv:1705.06098)
- Examples violating Golyshev's canonical strip hypothesis, joint with Sergey Galkin and Swarnava Mukhopadhyay (available on request, will be on the arXiv soon, see also the related repositories 1 and 2)
- Derived categories of moduli spaces of higher rank vector bundles on curves, joint with Swarnava Mukhopadhyay (available on request, will be on the arXiv soon)

### In preparation

- Comparing two constructions of a noncommutative del Pezzo surface, joint with Dennis Presotto and Michel Van den Bergh
- Derived categories and deformations of Hilbert squares (preliminary title), joint with Lie Fu and Theo Raedschelders
- Artin–Schelter regular algebras versus smooth projective varieties (very preliminary version, maybe to be rewritten with stronger results)

## Reviews

I do reviews for## Notes

You might also be interested in the 'math' category of my blog.### 2017

- Hochschild–Kostant–Rosenberg decomposition for surfaces, dimensions of components in the Hochschild–Kostant–Rosenberg decomposition for surfaces relevant to deformation theory

### 2016

- Segre symbols, a short note defining Segre symbols as a method of classifying base loci of pencils of quadric hypersurfaces
- The restriction of a homotopy-injective complex to a Zariski open subset is not necessarily homotopy-injective, details for the construction of such a complex, based on an explanation by Leonid Positselski
- Cheat sheet for mutations, because remembering where left and right goes is difficult

### 2015

- Cheat sheet for the simplicial indexing category, in case you always forget the notation (like me)
- Cheat sheet for recollements, the definition of a recollement and how to remember it
- The torsor for a formally smooth morphism, rough notes related to my lecture on lifting along a smooth morphism for ANAGRAMS about Hodge-to-de Rham degeneration

### 2014

- Spectral sequences: examples in algebra and algebraic geometry, notes for my lecture for ANAGRAMS about spectral sequences
- Quivers of exceptional collections on smooth projective varieties, poster for the British Algebraic Geometry meeting
- Positselski's main lemma, a short note elaborating on a lemma of Positselski that recognises vector bundles in the derived category
- Stratification of triangulated categories, notes for the lecture series by Henning Krause at the summer school on derived categories in Nantes (with corrections by Henning Krause, thanks!)
- Depth, and measuring singularities, notes for my short lecture for ANAGRAMS in the series on dimension functions
- My lecture series on Grothendieck duality for ANAGRAMS, also available as a single set of notes:
- Riemann–Roch theorem and Serre duality, notes for the first lecture
- More on Riemann–Roch and Serre duality, with applications, notes for the second lecture
- Derived categories and Grothendieck duality, notes for the third lecture
- Sketches of some of the proofs, notes for the fourth lecture

### 2013

- The $(\infty,1)$-topos of derived stacks, notes for my lecture at the Winter school on derived algebraic geometry
- Understanding $\mathbf{D}^{\mathrm{b}}(kQ)$ using moduli spaces, slides for my lecture at Young researchers in representation theory
- The triangulated structure on the category of projectives, notes for my lecture at the Summer school on preprojective algebras
- The derived Torelli theorem, notes for my lectures at the summer seminar in algebraic geometry of Columbia University and my exam for
*Surfaces K3 et théorie des déformations* - Grothendieck topologies and étale cohomology, notes for my lecture for the course
*Fonctions zêta et L de variétés et de motifs* - The derived stack of perfect complexes, notes for my lecture in Autour de la Géométrie Algébrique Dérivée, subsumed in the notes of the seminar
- Differential graded categories, notes for my lecture in Autour de la Géométrie Algébrique Dérivée, subsumed in the notes of the seminar

## Non-mathematical writing

- The fugue and the guitar (in Dutch)