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

Papers

Published

  1. Embeddings of algebras in derived categories of surfaces, joint with Theo Raedschelders (arXiv:1501.04197),
    published as Proceedings of the American Mathematical Society, volume 145, number 7, 2017, pages 2757–2770
  2. The point variety of quantum polynomial rings, joint with Kevin De Laet and Lieven Le Bruyn (arXiv:1509.07312),
    published as Journal of Algebra, volume 463, 2016, pages 10–22
  3. Derived categories of noncommutative quadrics and Hilbert squares, joint with Theo Raedschelders (arXiv:1605.02795),
    published online ahead of print in International Mathematics Research Notices
  4. Relative tensor triangular Chow groups for coherent algebras, joint with Sebastian Klein (arXiv:1607.03423),
    published as Journal of Algebra, volume 487, 2017, pages 386–428
  5. Hochschild cohomology of noncommutative planes and quadrics (arXiv:1705.06098),
    published as Journal of Noncommutative Geometry, volume 13, 2019, pages 769–795
  6. Constructing noncommutative surfaces with exceptional collections of length 4, joint with Dennis Presotto (arXiv:1705.06943),
    published as Journal of the London Mathematical Society, volume 98, 2018, pages 85–103
  7. Examples violating Golyshev's canonical strip hypothesis, joint with Sergey Galkin and Swarnava Mukhopadhyay (arXiv:1806.07648, see also the related repositories canonical-strip-moduli-of-vector-bundles and ehrhart-polynomials-toric-fanos)
    published online ahead of print in Experimental Mathematics
  8. Admissible subcategories in derived categories of moduli of vector bundles on curves, joint with Swarnava Mukhopadhyay (arXiv:1807.00216)
    published as Advances in Mathematics, volume 351, 2019, pages 653–675
  9. Hilbert squares: derived categories and deformations, joint with Lie Fu and Theo Raedschelders (arXiv:1810.11873)
    published as Selecta Mathematica, volume 25, 2019, paper 37
  10. Automorphisms of Hilbert schemes of points on surfaces, joint with Georg Oberdieck and Jørgen Vold Rennemo (arXiv:1907.07064)
    published online ahead of print in Transactions of the American Mathematical Society

Preprints

  1. Comparison of two constructions of noncommutative surfaces with exceptional collections of length 4, joint with Dennis Presotto and Michel Van den Bergh (arXiv:1811.08810)

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

  2. Derived categories of (nested) Hilbert schemes, joint with Andreas Krug (arXiv:1909.04321)
  3. Hochschild cohomology of generalised Grassmannians, joint with Maxim Smirnov (arXiv:1911.09414)
  4. Moduli spaces of semiorthogonal decompositions in families, joint with Shinnosuke Okawa and Andrea Ricolfi (arXiv:2002.03303)
  5. Derived categories of standard flips and cubic hypersurfaces, joint with Lie Fu and Theo Raedschelders (arXiv:2002.04940)
  6. Indecomposability of derived categories in families, joint with Francesco Bastianelli, Shinnosuke Okawa and Andrea Ricolfi

Work in progress

  1. Spanning classes on curves, joint with Swarnava Mukhopadhyay

Other

  1. Semiorthogonal decompositions for moduli of sheaves on curves, Oberwolfach Reports 24/2018, Oberwolfach Workshop 1822, Interactions between Algebraic Geometry and Noncommutative Algebra, pages 1473–1476
  2. appendix "Comparing definitions of Hochschild cohomology for algebraic stacks" to The Hochschild cohomology ring of a global quotient orbifold, by Cris Negron and Travis Schedler (arXiv:1809.08715)
    published online ahead of print in Advances in Mathematics
  3. Artin–Schelter regular algebras versus smooth projective varieties (short note, to be extended at some point)

Reviews

I have written reviews for

Notes

You might also be interested in my blog.

2018

2017

2016

2015

2014

2013

Non-mathematical writing