writing

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

Papers

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

Preprints

1. Moduli spaces of semiorthogonal decompositions in families

   with Shinnosuke Okawa, Andrea Ricolfi.

   with an appendix jointly with Wendy Lowen

   arXiv2002.03303

2. Graph potentials and topological quantum field theories

   with Sergey Galkin, Swarnava Mukhopadhyay.

   arXiv2205.07244

3. Projectivity and effective global generation of determinantal line bundles on quiver moduli

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

   arXiv2210.00033

4. Hochschild cohomology of Hilbert schemes of points on surfaces

   with Lie Fu, Andreas Krug.

   arXiv2309.06244

5. Rigidity and Schofield's partial tilting conjecture for quiver moduli

   with Ana-Maria Brecan, Hans Franzen, Gianni Petrella, Markus Reineke.

   arXiv2311.17003

6. On decompositions for Fano schemes of intersections of two quadrics

   with Jishnu Bose, Sarah Frei, Ben Gould, James Hotchkiss, Alicia Lamarche, Jack Petok, Cristian Andres Rodriguez Avila, Saket Shah.

   arXiv2403.12517

7. Central curves on noncommutative surfaces

   with Thilo Baumann, Okke van Garderen.

   arXiv2410.07620

8. The Albanese morphism for hyperelliptic varieties

   with Andreas Demleitner, Pedro Núñez.

   arXiv2411.14814

Accepted for publication

1. Homological projective duality for the Segre cubic

   with Thorsten Beckmann.

   accepted for publication in Proceedings of Nottingham Algebraic Geometry Seminar,

   arXiv2202.08601

2. Vector fields and admissible embeddings for quiver moduli

   with Ana-Maria Brecan, Hans Franzen, Markus Reineke.

   accepted for publication in Moduli,

   arXiv2311.17004

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 MR3527537 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 Zbl1481.14034 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,

   see also the related repositories

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

   arXiv1806.07648 MR4399121 Zbl1485.14071 doi10.1080/10586458.2019.1602571

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 standard flips and cubic hypersurfaces

    with Lie Fu, Theo Raedschelders.

    Proceedings of the London Mathematical Society, volume 125 (6), 2022, pages 1452–1482

    arXiv2002.04940 MR4524222 Zbl1520.14029 doi10.1112/plms.12487

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

    with Alexander Kuznetsov, Maxim Smirnov.

    Transformation Groups, volume 28, 2023, pages 9–34

    arXiv2005.01989 MR4552169 Zbl1517.14031 doi10.1007/s00031-021-09657-w

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

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

    SPEC: Stacks Project Expository Collection, chapter 3, pages 90–125

    arXiv2206.06195 MR4480534 Zbl1506.14072 doi10.1017/9781009051897.005

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

    with Sergey Galkin, Swarnava Mukhopadhyay.

    Forum of Mathematics, Sigma, volume 11:e16, 2023, pages 1–28

    arXiv2009.05568v3 MR4557892 Zbl1525.14016 doi10.1017/fms.2023.14

15. Polyvector fields for Fano 3-folds

    with Enrico Fatighenti, Fabio Tanturri.

    Mathematische Zeitschrift, volume 304, 12 (2023)

    arXiv2104.07626 MR4578397 Zbl1516.14077 doi10.1007/s00209-023-03261-2

16. Hochschild cohomology of generalised Grassmannians

    with Maxim Smirnov.

    Documenta Mathematica, volume 28 (2023), number 1, pages 11–53

    arXiv1911.09414 MR4706032 Zbl1528.14062 doi10.4171/dm/912

17. Derived categories of (nested) Hilbert schemes

    with Andreas Krug.

    Michigan Mathematical Journal, volume 74, number 1, pages 167–187

    arXiv1909.04321 MR4718496 Zbl1540.14008 doi10.1307/mmj/20216092

18. On Chow rings of quiver moduli

    with Hans Franzen.

    IMRN, volume 2024, issue 13, pages 10255–10272

    arXiv2307.01711 MR4770368 doi10.1093/imrn/rnad306

Preprints needing revision

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

   with Dennis Presotto, Michel Van den Bergh.

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

   arXiv1811.08810

2. Indecomposability of derived categories in families

   with Francesco Bastianelli, Shinnosuke Okawa, Andrea Ricolfi.

   arXiv2007.00994

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

   with Sergey Galkin, Swarnava Mukhopadhyay.

   arXiv2206.11584

Preprints nearing completion

1. Can you hear the shape of a random walk?

   with Sergey Galkin, Swarnava Mukhopadhyay.

   available upon request, previously titled A combinatorial non-abelian Torelli theorem and random walks

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

   doi10.14760/OWR-2018-24 pdflink

2. Comparing definitions of Hochschild cohomology for algebraic stacks

   Advances in Mathematics, volume 364, 2020

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

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

3. How do semiorthogonal decompositions behave in families?

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

   doi10.14760/OWR-2020-19 pdflink

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

   Oberwolfach Reports 22/2022, Interactions between Algebraic Geometry and Noncommutative Algebra

   doi10.14760/OWR-2022-23 pdflink

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

   Oberwolfach Reports 32/2022, Algebraic Geometry: Moduli Spaces, Birational Geometry and Derived Aspects

   doi10.14760/OWR-2022-32 pdflink

6. Hochschild cohomology of Hilbert schemes of points

   Oberwolfach Reports 20/2024, Hochschild (co)homology and applications

   doi10.14760/OWR-2024-20 pdflink

7. Algebraic geometry & noncommutative projective varieties

   Oberwolfach Reports 44/2024, Algebraic geometry & noncommutative projective varieties

   doi10.4171/OWR/2024/44 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

   doi10.1090/noti2344 pdflink

3. The periodic tables of algebraic geometry

   Snapshots of modern mathematics from Oberwolfach, 2023, number 2

   doi10.14760/SNAP-2023-002-EN pdflink

Lecture notes

• 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!)

  pdflink

• Grothendieck duality

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

  pdflink

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

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

  pdflink

Not intended for publication

• Segre symbols

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

  pdflink

• Artin–Schelter regular algebras versus smooth projective varieties

  short note, possibly to be extended at some point

  pdflink

Non-mathematical writing

• The fugue and the guitar

  final project for my composition course (in Dutch)

  pdflink

This gives the following list of coauthors: Jarod Alper, Francesco Bastianelli, Thilo Baumann, Thorsten Beckmann, Jishnu Bose, Daniel Bragg, Ana-Maria Brecan, Chiara Damiolini, Aise Johan de Jong, Kevin De Laet, Andreas Demleitner, Enrico Fatighenti, Hans Franzen, Sarah Frei, Lie Fu, Sergey Galkin, Ben Gould, Vicky Hoskins, James Hotchkiss, Colin Ingalls, Sebastian Klein, Andreas Krug, Alexander Kuznetsov, Alicia Lamarche, Lieven Le Bruyn, Jason Liang, Wendy Lowen, Svetlana Makarova, Swarnava Mukhopadhyay, Pedro Núñez, Georg Oberdieck, Shinnosuke Okawa, Jack Petok, Gianni Petrella, Dennis Presotto, Theo Raedschelders, Markus Reineke, Andrea Ricolfi, Jørgen Vold Rennemo, Cristian Andres Rodriguez Avila, Saket Shah, Maxim Smirnov, Tuomas Tajakka, Fabio Tanturri, Michel Van den Bergh, Okke van Garderen

Editorial work

Stacks Project Expository Collection, 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