Anand Deopurkar

• Orbits of linear series on the projective line.
  Pre-print, arXiv:2211.16603, with Anand Patel (pdf, arxiv).
• Spherical objects and stability conditions on CY2 quiver categories.
  Mathematische Zeitschrift (accepted), with Asilata Bapat, Anthony Licata (arxiv).
• Vector bundles and finite covers.
  Forum of Mathematics, Sigma (accepted), with Anand Patel (pdf, arXiv).
  Talks: Adelaide (slides), Jeju Island (notes).
• A universal formula for counting cubic surfaces.
  Pre-print, arxiv:2109.12672, with Anand Patel, Dennis Tseng (arxiv).
  Talk: Cambridge (notes).
• Stable log surfaces, admissible covers, and canonical curves of genus 4.
  Transactions of the Americal Mathematical Society 374, No. 1, 589-641 (2021), with Changho Han (pdf, arxiv).
  Talk: Sydney (notes).
• A Thurston compactification of the space of stability conditions.
  Pre-print, arXiv:2011.07908, with Asilata Bapat, Anthony Licata (arxiv).
  Talks: Bonn (slides), Mumbai (slides), Amidale (slides), Sydney (notes).
• Ramification divisors of general projections.
  Documenta Mathematica 25, 1917–1952 (2020), with Eduard Duryev, Anand Patel (pdf, arxiv).
  Talks: Mexico (slides), San Diego (slides).
• Anticanonical tropical cubic del Pezzos contain exactly 27 lines.
  Pre-print, arXiv:1906.08196, with María Angélica Cueto (arxiv).
• Covers of stacky curves and limits of plane quintics.
  Transactions of the Americal Mathematical Society, 371, 549–588 (2019) (pdf, arxiv).
  Talks: Boston (notes), Salt Lake City (poster).
• Syzygy divisors on Hurwitz spaces.
  Contemporary Mathematics 703, 209–222 (2018), with Anand Patel (pdf, arxiv).
• The canonical syzygy conjecture for ribbons.
  Mathematische Zeitschrift 288, No. 3-4, 1157–1164 (2018) (pdf, arxiv).
  Talk: Melbourne (notes).
• Toward GIT stability of syzygies of canonical curves.
  Algebraic Geometry 3, No. 1, 1–22 (2016), with Maksym Fedorchuk, David Swinarski (arxiv, journal).
  Talks: Daejeon (slides), Pohang (notes).
• The Picard rank conjecture for the Hurwitz spaces of degree up to five.
  Algebra & Number Theory 9, No. 2, 459–492 (2015), with Anand Patel (pdf, arxiv, journal).
• Groebner techniques for ribbons.
  Albanian Journal of Mathematics 8, No. 2, 55–70 (2014), with Maksym Fedorchuk, David Swinarski (pdf, journal).
• Compactifications of Hurwitz spaces.
  International Mathematics Research Notices 2014, No. 14, 3863–3911 (2014) (pdf, arxiv, journal).
  Talks: Palo Alto (notes), Cambridge (notes).
• Class of the Hodge eigenbundle using orbifold Riemann-Roch.
  Pre-print, appendix to Cyclic covering morphisms on \(\overline M_{0,n}\) by Maksym Fedorchuk (pdf).
• Sharp slope bounds for sweeping families of trigonal curves.
  Mathematical Research Letters 20, No. 5, 869–884 (2013), with Anand Patel (pdf, arxiv, journal).
  Talk: Boston (poster).
• Modular compactifications of the space of marked trigonal curves.
  Advances in Mathematics 248, 96–154 (2013) (pdf, arxiv).
  Talk: Cambridge (poster).
• Alternate compactifications of Hurwitz spaces.
  Thesis, Harvard, 2012 (pdf).
  Talks: Palo Alto (notes), Cambridge (notes).

Notes and other materials from some of my courses:

• Algebra 1, Australian National University, 2022.
• The language of mathematics, Australian National University, 2022.
• Algebraic Geometry (Algebra 3), Australian National University, 2021.
• Foundations of Algebraic Geometry (Schemes), Australian National University, 2020.
• Algebraic Geometry (Algebra 3), Australian National University, 2019.
• Reading course on Algebaric curves and Riemann surfaces by Rick Miranda, Australian National University, 2018.
• Algebraic curves, University of Georgia, 2017.
• Analysis and optimization, Columbia University, 2016.
• Young tableaux in algebra and geometry, Columbia University, 2015.
• Moduli of curves, Columbia University, 2014.
• Modern algebra 2, Columbia University, 2014.
• Modern algebra 1, Columbia University, 2013.

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

• A sketch of the Thurston compactification of the stability manifold for a generic non-algebraic K3 surface This is an instance of the construction proposed in the paper with Bapat and Licata.
• 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