Anand Deopurkar

Anand Deopurkar

Mathematical Sciences Institute
The Australian National University
Canberra, ACT, 2601, Australia

anand.deopurkar at anu dot edu dot au (pgp)
4.56 Hanna Neumann Building
+61 2 6125 4628

CV: html pdf

I am an algebraic geometer with broad interests. Being an algebraic geometer means that I fundamentally study solution spaces of algebraic equations. I am interested in classical algebraic geometry, enumerative geometry, deformation theory, algebraic stacks, derived categories, among other things.

Papers/pre-prints

  • 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).
  • Spherical objects and stability conditions on CY2 quiver categories.
    Pre-print, arXiv:2108.09155, with Asilata Bapat, Anthony Licata (arxiv).
  • 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).

Teaching

Notes and other materials from some of my courses:

Talks

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.

Odds and ends

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