writing

These are the things I have written over the past years.

Papers

• accepted for publication
• published
• preprints
• other publications (appendices, conference proceedings, ...)
• for a broader audience

Accepted for publication

1. Derived categories of (nested) Hilbert schemes

   with Andreas Krug.

   accepted for publication in Michigan Mathematical Journal,

   arXiv1909.04321

2. Projectivity of the moduli space of vector bundles on a curve

   with Jarod Alper, Daniel Bragg, Jason Liang, Tuomas Tajakka.

   accepted for publication in SPEC: Stacks Project Expository Collection,

   arXiv2206.06195

3. Homological projective duality for the Segre cubic

   with Thorsten Beckmann.

   accepted for publication in Proceedings of Nottingham Algebraic Geometry Seminar,

   arXiv2202.08601

Published

1. Embeddings of algebras in derived categories of surfaces

   with Theo Raedschelders.

   Proceedings of the American Mathematical Society, volume 145, number 7, 2017, pages 2757–2770

   arXiv1501.04197 MR3637928 Zbl1378.16035 doi10.1090/proc/13497

2. The point variety of quantum polynomial rings

   with Kevin De Laet, Lieven Le Bruyn.

   Journal of Algebra, volume 463, 2016, pages 10–22

   arXiv1509.07312 MR3637928 Zbl1454.14043 doi10.1016/j.jalgebra.2016.06.013

3. Derived categories of noncommutative quadrics and Hilbert squares

   with Theo Raedschelders.

   IMRN, volume 2020, issue 19, pages 6042–6069

   arXiv1605.02795 MR4165471 doi10.1093/imrn/rny192

4. Relative tensor triangular Chow groups for coherent algebras

   with Sebastian Klein.

   Journal of Algebra, volume 487, 2017, pages 386–428

   arXiv1607.03423 MR3671198 Zbl1400.14049 doi10.1016/j.jalgebra.2017.05.024

5. Hochschild cohomology of noncommutative planes and quadrics

   Journal of Noncommutative Geometry, volume 13, 2019, pages 769–795

   arXiv1705.06098 MR3988086 Zbl1429.14002 doi10.4171/JNCG/338

6. Constructing noncommutative surfaces with exceptional collections of length 4

   with Dennis Presotto.

   Journal of the London Mathematical Society (2), volume 98, 2018, pages 85–103

   arXiv1705.06943 MR3847233 Zbl1441.14008 doi10.1112/jlms.12126

7. Examples violating Golyshev's canonical strip hypothesis

   with Sergey Galkin, Swarnava Mukhopadhyay.

   Experimental Mathematics, volume 31 (1), 2022, pages 233–237,

   arXiv1806.07644 doi10.1080/10586458.2019.1602571

   see also the related repositories

   • canonical-strip-moduli-of-vector-bundles
   • ehrhart-polynomials-toric-fanos

8. Admissible subcategories in derived categories of moduli of vector bundles on curves

   with Swarnava Mukhopadhyay.

   Advances in Mathematics, volume 351, 2019, pages 653–675

   arXiv1807.00216 MR3954042 Zbl1440.14079 doi10.1016/j.aim.2019.05.019

9. Hilbert squares: derived categories and deformations

   with Lie Fu, Theo Raedschelders.

   Selecta Mathematica, volume 25, 2019, paper 37

   arXiv1810.11873 MR3950704 Zbl1423.14115 doi10.1007/s00029-019-0482-y

10. Automorphisms of Hilbert schemes of points on surfaces

    with Georg Oberdieck, Jørgen Vold Rennemo.

    Transactions of the American Mathematical Society, volume 373 (9), 2020, pages 6139–6156

    arXiv1907.07064 MR4155174 Zbl1451.14008 doi10.1090/tran/8106

11. Derived categories of the Cayley plane and the coadjoint Grassmannian in type F

    with Alexander Kuznetsov, Maxim Smirnov.

    Transformation Groups, published online ahead of print

    arXiv2005.01989 doi10.1007/s00031-021-09657-w

Preprints

1. Comparison of two constructions of noncommutative surfaces with exceptional collections of length 4

   with Dennis Presotto, Michel Van den Bergh.

   arXiv1811.08810

   We will retitle this to "The Hirzebruch isomorphism for exotic noncommutative surfaces".

2. Hochschild cohomology of generalised Grassmannians

   with Maxim Smirnov.

   arXiv1911.09414

3. Moduli spaces of semiorthogonal decompositions in families

   with Shinnosuke Okawa, Andrea Ricolfi.

   arXiv2002.03303

4. Derived categories of standard flips and cubic hypersurfaces

   with Lie Fu, Theo Raedschelders.

   arXiv2002.04940

5. Indecomposability of derived categories in families

   with Francesco Bastianelli, Shinnosuke Okawa, Andrea Ricolfi.

   arXiv2007.00994

6. Decompositions of moduli spaces of vector bundles and graph potentials

   with Sergey Galkin, Swarnava Mukhopadhyay.

   arXiv2009.05568v3

7. Polyvector fields for Fano 3-folds

   with Enrico Fatighenti, Fabio Tanturri.

   arXiv2104.07626

8. Graph potentials and topological quantum field theories

   with Sergey Galkin, Swarnava Mukhopadhyay.

   arXiv2205.07244

9. Graph potentials and symplectic geometry of moduli spaces of vector bundles

   with Sergey Galkin, Swarnava Mukhopadhyay.

   arXiv2206.11584

Preprints nearing completion

1. A combinatorial non-abelian Torelli theorem

   with Sergey Galkin, Swarnava Mukhopadhyay.

   available on request

2. Effective bounds and ampleness of determinantal line bundles on moduli spaces of quiver representations

   with Chiara Damiolini, Hans Franzen, Vicky Hoskins, Svetlana Makarova, Tuomas Tajakka.

   working title

Other publications

1. Semiorthogonal decompositions for moduli of sheaves on curves

   Oberwolfach Reports 24/2018, Interactions between Algebraic Geometry and Noncommutative Algebra, pages 1473–1476

   pdflink

2. Comparing definitions of Hochschild cohomology for algebraic stacks

   Advances in Mathematics, volume 364, 2020

   arXiv1809.08715 MR4057490 Zbl1435.14005 doi10.1016/j.aim.2020.106978

   appendix to The Hochschild cohomology ring of a global quotient orbifold, by Cris Negron and Travis Schedler

3. How do semiorthogonal decompositions behave in families?

   Oberwolfach Reports 19/2020, Algebraic Geometry: Moduli Spaces, Birational Geometry and Derived Aspects, pages 985–989

   pdflink

4. Projectivity of good moduli spaces of semistable quiver representations and vector bundles

   Oberwolfach Reports ??/2022, Interactions between Algebraic Geometry and Noncommutative Algebra

   pdflink

5. Mirror symmetry for moduli of rank 2 bundles on a curve

   Oberwolfach Reports ??/2022, Algebraic Geometry: Moduli Spaces, Birational Geometry and Derived Aspects

   pdflink

For a broader audience

1. Het Stacks project

   with Aise Johan de Jong.

   Nieuw Archief voor Wiskunde (serie 5), volume 21 (3), 2020, pages 167–173

   pdflink

2. Curating Online Mathematical Resources

   Notices of the American Mathematical Society, volume 69 (9), 2021, pages 1524–1527

   pdflink

3. The periodic tables of algebraic geometry

   Snapshots of modern mathematics from Oberwolfach,

Lecture notes

• Stratification of triangulated categories

  pdflink

  notes for the lecture series by Henning Krause at the summer school on derived categories in Nantes (with corrections by Henning Krause, thanks!)

• Grothendieck duality

  pdflink

  notes for a lecture series on Grothendieck duality for a graduate student seminar

• Hochschild (co)homology, and the Hochschild–Kostant–Rosenberg decomposition

  pdflink

  lecture notes for Advanced Topics in Algebra, a course from 2018 at the University of Bonn (to be expanded in the future)

Not intended for publication

• Segre symbols

  pdflink

  short note defining Segre symbols as a method of classifying base loci of pencils of quadric hypersurfaces

• Artin–Schelter regular algebras versus smooth projective varieties

  pdflink

  short note, possibly to be extended at some point

Non-mathematical writing

• The fugue and the guitar

  pdflink

  final project for my composition course (in Dutch)

This gives the following list of coauthors: Jarod Alper, Francesco Bastianelli, Thorsten Beckmann, Daniel Bragg, Chiara Damiolini, Aise Johan de Jong, Kevin De Laet, Enrico Fatighenti, Hans Franzen, Lie Fu, Sergey Galkin, Vicky Hoskins, Sebastian Klein, Andreas Krug, Lieven Le Bruyn, Jason Liang, Svetlana Makarova, Swarnava Mukhopadhyay, Alexander Kuznetsov, Georg Oberdieck, Shinnosuke Okawa, Dennis Presotto, Theo Raedschelders, Andrea Ricolfi, Jørgen Vold Rennemo, Maxim Smirnov, Tuomas Tajakka, Fabio Tanturri, Michel Van den Bergh

Editorial work

Stacks Project Expository Collection, (soon to be) published by Cambridge University Press in the London Mathematical Society Lecture Note Series, number 480

Table of contents (with links to preprint versions of chapters whenever available)

1. Projectivity of the moduli of curves, by Raymond Cheng, Carl Lian and Takumi Murayama
2. The stack of admissible covers is algebraic, by Elsa Corniani, Neeraj Deshmukh, Brett Nasserden, Emanuel Reinecke, Nawaz Sultani and Rachel Webb
3. Projectivity of the moduli space of vector bundles on a curve, by Jarod Alper, Pieter Belmans, Daniel Bragg, Jason Liang and Tuomas Tajakka
4. Boundedness of semistable sheaves, by Haoyang Guo, Sanal Shivaprasad, Dylan Spence and Yueqiao Wu
5. Theorem of the Base, by Raymond Cheng, Lena Ji, Matt Larson and Noah Olander
6. Weil restriction for schemes and beyond, by Lena Ji, Shizhang Li, Patrick McFaddin, Drew Moore and Matthew Stevenson
7. Heights over finitely generated fields, by Stephen McKean and Soumya Sankar
8. An explicit self-duality, by Nikolas Kuhn, Devlin Mallory, Vaidehee Thatte and Kirsten Wickelgren
9. Tannakian reconstruction of coalgebroids, by Yifei Zhao

Reviews

I have written reviews for

•  Mathematical Reviews
•  zbMath

Some other notes

You might also be interested in my blog, where various things that could also have been pdf's are written in html. The notes that are listed in what follows are less polished or less important (which is a vague opinion anyway) than the ones listed above as lecture notes or not intended for publication, or they are purely of expository and standard nature.

2021

• On $\int\mathrm{td}_X^{1/2}$ of O'Grady's exceptional hyperkähler varieties (short note on a computation, see also the accompanying code)

2017

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

2016

• 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
• Depth, and measuring singularities, notes for my short lecture for ANAGRAMS in the series on dimension functions

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