Anand Deopurkar

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

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

• The arithmetic and geometry of branched coverings: theorems of Belyi and Darmon–Granville.
  Pre-print.
• An introduction to intersection homology.
  Minor thesis (Harvard).
• Normalization of algebraic varieties.
  MIT Undergruate Journal of Mathematics.

• Fields and Galois theory (Algebra 2) (2025, 2024, 2023, 2014)
• Games, graphs, and machines (2024)
• Differential forms in algebraic topology (2024)
• Groups and rings (Algebra 1) (2022, 2013)
• Mathematical writing (2022)
• Algebraic Geometry (Algebra 3) (2021, 2019)
• Foundations of Algebraic Geometry: Schemes (2020)
• Algebraic curves (2018, 2017)
• Analysis and optimization (2016)
• Young tableaux in algebra and geometry (2015)
• Calculus (2015, 2014, 2013)
• Moduli of curves (2014)

Notes or slides for many of my talks are linked in the section on papers/pre-prints. Here are some additional talks:

• The geometry and combinatorics of Harder–Narasimhan filtrations.
  Braids in representation theory and algebraic combinatorics, Institute for Computational and Experimental Research in Mathematics, Providence, Rhode Island.
• The geometry of Fermat-like equations (expository).
  Trimester program on triangle groups, Belyi uniformization, and modularity, Bhaskaracharya Pratishthana, Pune, India.
• Algebraic curves and Belyi’s theorem (expository).
  Trimester program on triangle groups, Belyi uniformization, and modularity, Bhaskaracharya Pratishthana, Pune, India.
• Error correcting codes (expository).
  ANU Mathematics Extension Program, Canberra, Australia.
• The work of Claire Voisin (expository).
  Women in mathematics day, Australian National University, Canberra, Australia.
• Geometry of Hurwitz spaces.
  Character varieties and topological quantum field theory, University of Auckland, Auckland, New Zealand.
• The work of Caucher Birkar (expository).
  Colloquium, Australian National University, Canberra, Australia.
• How to count using (co)homology (expository).
  Tata Institute of Fundamental Research, Mumbai, India.
• Quadrature and algebraic geometry.
  Workshop on algebraic geometry approximation, and optimization, MATRIX, Creswick, Victoria, Australia.

• 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…
• 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.
• 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)
• Notes from some past seminars
  • DbCoh: ANU, 2021
  • Mixed hodge modules: UGA, 2017
  • Stable rationality: Columbia, 2016

• 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 occassionally contribute to the development of org mode.