# 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

• 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
• Notes from some past seminars
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