Anand Deopurkar

If you are thinking of doing a PhD with me, please read this page for prospective PhD students.

Here is a more detailed list with abstracts and other comments.

• A sphere of spherical objects, with Asilata Bapat, Anthony Licata (pdf, arxiv)
  Pre-print.
• The Thurston compactification of the stability manifold of a generic analytic K3 surface (pdf, repository)
  Mathematical Research Letters (accepted).
• Compactifications of moduli spaces of K3 surfaces with a higher-order nonsymplectic automorphism, with Valery Alexeev, Changho Han (pdf, arxiv)
  Pre-print.
• Syzygies of canonical ribbons on higher genus curves, with Jayan Mukherjee (pdf, arxiv)
  Pre-print.
• Counting 3-uple Veronese surfaces, with Anand Patel (pdf, arxiv)
  Pre-print.
• Equivariant classes of orbits in GL(2)-representations (pdf, arxiv, repository)
  Selecta Mathematica (accepted).
• Orbits of linear series on the projective line, with Anand Patel (pdf, arxiv, journal)
  International Mathematics Research Notices.
• A universal formula for counting cubic surfaces, with Anand Patel, Dennis Tseng (pdf, arxiv)
  Algebraic Geometry (to appear).
• Spherical objects and stability conditions on 2-Calabi–Yau quiver categories, with Asilata Bapat, Anthony Licata (pdf, arxiv, journal)
  Mathematische Zeitschrift.
• Vector bundles and finite covers, with Anand Patel (pdf, arXiv, journal)
  Forum of Mathematics, Sigma.
• Stable log surfaces, admissible covers, and canonical curves of genus 4, with Changho Han (pdf, arxiv, journal)
  Transactions of the Americal Mathematical Society.
• A Thurston compactification of the space of stability conditions, with Asilata Bapat, Anthony Licata (pdf, arxiv)
  Pre-print.
• Ramification divisors of general projections, with Eduard Duryev, Anand Patel (pdf, arxiv, journal)
  Documenta Mathematica.
• Anticanonical tropical cubic del Pezzos contain exactly 27 lines, with María Angélica Cueto (pdf, arxiv)
  Pre-print.
• Covers of stacky curves and limits of plane quintics (pdf, arxiv, journal)
  Transactions of the Americal Mathematical Society.
• Syzygy divisors on Hurwitz spaces, with Anand Patel (pdf, arxiv, journal)
  Contemporary Mathematics.
• The canonical syzygy conjecture for ribbons (pdf, arxiv)
  Mathematische Zeitschrift.
• Toward GIT stability of syzygies of canonical curves, with Maksym Fedorchuk, David Swinarski (pdf, arxiv, journal)
  Algebraic Geometry.
• The Picard rank conjecture for the Hurwitz spaces of degree up to five, with Anand Patel (pdf, arxiv, journal)
  Algebra & Number Theory.
• Groebner techniques for ribbons, with Maksym Fedorchuk, David Swinarski (pdf, journal)
  Albanian Journal of Mathematics.
• Compactifications of Hurwitz spaces (pdf, arxiv, journal)
  International Mathematics Research Notices.
• Class of the Hodge eigenbundle using orbifold Riemann-Roch (pdf)
  Pre-print, appendix to Cyclic covering morphisms on \(\overline M_{0,n}\) by Maksym Fedorchuk.
• Sharp slope bounds for sweeping families of trigonal curves, with Anand Patel (pdf, arxiv, journal)
  Mathematical Research Letters.
• Modular compactifications of the space of marked trigonal curves (pdf, arxiv, journal)
  Advances in Mathematics.

Here are some from the list of my expository articles and talks.

• An introduction to intersection homology (pdf) Minor thesis (Harvard)
• The arithmetic and geometry of branched coverings: theorems of Belyi and Darmon–Granville (pdf) Pre-print
• How to count using (co)homology (talk, Tata Institute of Fundamental Research) (notes)
• The work of Caucher Birkar (talk, Australian National University) (notes)
• The work of Maryam Mirzakhani (talk, Australian National University) (notes)

Here are some from the list of courses I have taught.

• Games, graphs, and machines, 2025 (course page)
• Fields and Galois theory (Algebra 2), 2025 (course page)
• Differential forms in algebraic topology, 2024 (course page)
• Groups and rings (Algebra 1), 2022 (course page)
• Mathematical writing, 2022 (course page)
• Algebraic Geometry (Algebra 3), 2021 (course page)
• Foundations of Algebraic Geometry: Schemes, 2020 (course page)
• Algebraic curves, 2017 (course page)
• Young tableaux in algebra and geometry, 2015 (course page)
• Moduli of curves, 2014 (course page)

• A list of all my talks (research and expository).
• Notes from some past seminars
  • DbCoh: ANU, 2021
  • Mixed hodge modules: UGA, 2017
  • Stable rationality: Columbia, 2016
• Categorical braid group actions
  With Asilata Bapat, I wrote Sage code to make explicit computations in the homotopy category of projective modules over a ring. In particular, this code can compute braid actions on complexes of projective modules over the zig-zag algebra of a quiver.
• GIT for syzygies of genus 7 curves
  This is an ongoing project to determine GIT stability for syzygies of genus 7 canonical curves. This is the first genus where canonical syzygies define an interesting GIT quotient, so it would be nice to understand the complete picture. One day…
• MSI course graph
  This is an interactive dependency graph of ANU math department’s course catalogue.
• A mystery hunt style puzzle
• Some visualisations
  • The blow up of a planar triple point (sage code)
  • A conic fibration on a cubic surface (sage code)
• Does course engagement correlate with final scores? I did a bit of data science based on a course in 2024; see the results.
• I am an advocate of free software and a user of emacs. I occasionally contribute to the development of org mode.